Patent Publication Number: US-11651266-B2

Title: Quantum random access memory system

Description:
BACKGROUND 
     Due to the increased demand for quantum computing devices and applications, quantum random access memory (RAM) systems are becoming increasingly important. RAM systems are used for short term memory whereby any storage location in the RAM can be accessed. Various applications of quantum computing include quantum computers, quantum communications, quantum artificial intelligence, quantum teleportation, and other quantum technologies. Currently, there is no effective RAM systems can be used for quantum computers and the mentioned application. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is an example of the proposed quantum circuit for the proposed QRAM; 
         FIG.  2    is a diagram of quantum registers; 
         FIG.  3    is a diagram of an example quantum CNOT gate; 
         FIG.  4    is a diagram of example elementary gates for S Operator; 
         FIG.  5    is a diagram of an example device; and 
         FIG.  6    is a diagram of an example process. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     The following detailed description refers to the accompanying drawings. The same reference numbers in different drawings may identify the same or similar elements. 
     Systems, devices, and/or methods described herein may provide for a quantum circuit design used within a quantum random access memory (“QRAM”) device. In embodiments, the quantum circuit design described herein may use universal gates and is not restricted to a particular quantum system. In embodiments, universal gates may include CNOT, NOT, control swap, Toffoli gates, and Hadamard gates. In embodiments, the quantum circuit design is more accurate in transferring information across the quantum circuit design. In embodiments, the quantum circuit design requires only a O(1) call to access a particular location rather than O(N) calls. Accordingly, in embodiments, the quantum circuit design results in faster calculations due to requiring only a O(1) call. Thus, the systems, devices, and/or methods described herein provide for a quantum circuit design that is faster in reading or writing information, has lower levels of error when information is sent across the quantum circuit design, and capable of using universal gates that allows for use of the quantum circuit design in various different quantum systems. Thus, embodiments, the quantum circuit design, described herein, may be used in a quantum RAM system which is faster in reading and writing information with less errors. In embodiments, while the proposed QRAM may be used in a quantum computer, the QRAM can also be used for a classical computer. In embodiments, by using the circuit design in a classical computer, the capacity of RAM can be increased from m GB to 2 m  GB. 
       FIG.  1    describes an example structure of the proposed QRAM circuit  100 . In embodiments, circuit  100  includes Hadamard gates  101 , S gates  102 , Toffoli gate  103 , gates  104 A, gates  104 B, Toffoli gate  105 , and S gates  106 . In embodiments, circuit design  100  may be a main quantum circuit for a proposed QRAM. In embodiments, Hadamard gates  101  may include n (n greater or equal to 1) Hadamard gates which aretype of quantum—gate which can act on a single qubit (quantum bit) where for each address qubit in the register |A&gt; there is a Hadamard gate. In embodiments, Hadamard gates  101  may be a one-qubit version of a quantum Fourier transform. In embodiments, S gates  102  and  106  may be a quantum circuit auxiliary operator that is composed of one or more CNOT gates and a quantum X-gate. In embodiments, S gates  102  and  106  may include a set of n CNOT gates and n quantum-NOT gates. In embodiments, one or more CNOT gates in S gates  102  and  106  may act as a two qubit gate. 
     In embodiments, Toffoli gates  103  and  105  are reversible quantum gates. As shown in  FIG.  2   , gate  104 A contains controlled SWAP gates and gate  104 B contains Toffoli gates. In embodiments, controlled-SWAP gates perform controlled two-qubit swap, this gate swaps the states of the qubits which has indices n+1, . . . , n+m of the register |qy&gt; with the states of register |D&gt; if the state of the control-qubit |r&gt;=|0&gt; and the state of the control-qubit |dq&gt;=1. In embodiments, S gates  106  can be used to undo the effect of S gates  102 . 
       FIG.  2    shows an example information table that describes various features of circuit  100 . As shown in  FIG.  2   , item  202  describes different registers that are shown in column  110  of  FIG.  1   . In embodiments, Register |A&gt; is an address register which is used to address the locations of register |D&gt;. Thus, register |A&gt; represents the addresses of the locations of the variables in a quantum RAM (QRAM). In embodiments, |A&gt; with the size of “n” qubits and is used to address 2 n  locations in the |D&gt; register. In embodiments, |D&gt; is with m qubits (where n≤m, or m≤n) and is used to store data. In embodiments, |dq&gt; has only one qubit and is used to mark a designated location/address. In embodiments, |dq&gt; may be initialized by state 10&gt;. In embodiments, |qy&gt; may have a qubit size of n+m and is used to carry the designated location/address and value needed to read from/write into QRAM. In embodiments, the first n qubits of register |qy&gt; are used to carry the address of variable location(s) provided by a quantum computer (or quantum circuit/device) while the other m qubits are used to carry the value in the variable to transfer it to a specific location in the quantum RAM (“QRAM”) or used to read the data from the QRAM. In embodiments, |r&gt; composed by only one qubit and it is used to decide if the running operation (|r&gt;=11&gt;) is a reading operation being conducted in the QRAM or a writing operation (|r&gt;=10&gt;) is being conducted in the QRAM (e.g., across circuit design  100 ). 
       FIG.  3    shows an example CNOT gate. In embodiments, |x&gt; qubit is a control qubit and |y&gt; is a target qubit. In embodiments, CNOT gate negates the state of the target qubit if the state of the control qubit is |1&gt;. 
     In embodiments, using the proposed circuit, of the proposed QRAM,  100 , an algorithm is applied by Hadamard gates  101 , wherein each of the Hadamard gates  101  is applied to a single qubit of register |A&gt; to address 2 n  locations in the QRAM. Next, when an address is loaded in the first n-qubit of register |qy&gt;, S gates  102  searches about this address in the QRAM. Thus, circuit  100  uses S gates  102  to find the address location, among 2 n  addresses of register |A&gt; which is then assigned by a quantum processor by first n qubits of the register |qy&gt;. In embodiments, S gates  102  is composed by C-NOT gates followed by Quantum X-gates. For example, S 102  is composed of a set of n CNOT gates and n quantum NOT gates (X gates). In embodiments, CNOT gates act as two qubit gates. 
     An example S gates  400  is shown in  FIG.  4   . In embodiments, S gates  400  are similar to S gates  102 , and/or S gates  106 . In embodiments,  FIG.  4    shows the structure of an Operator S. In  FIG.  4   , |ψ&gt; represents the first n qubits of the register |qy&gt; in  FIG.  1    and |φ&gt; represents the n qubits of the registers |A&gt;. As shown in  FIG.  4   , operation  402  may show a qubit that negates ( 402 B) if the state of the control qubit ( 402 A) is | 1 &gt;. In embodiments, X-gate  404  then negates the states of the qubit. As shown in  FIG.  4   , operation  406  may show a second qubit that negates ( 406 B) if the state of the control qubit ( 406 A) is | 1 &gt;. In embodiments, X-gate  408  then negates the second qubit. Furthermore, as shown in  FIG.  4   , operation  410  may show a third qubit that negates ( 410 B) if the state of the control qubit ( 410 A) is | 1 &gt;. In embodiments, X-gate  412  then negates the third qubit and any additional qubits. 
     After S gates  102 , Toffli gate  103  is used to mark the address which matches the input address in register |qy&gt; by entangling |dq&gt; with this address to mark this address in the superposition. In embodiments, Toffli gate  103  is defined as
 
 T   A     1     A     2 . . .      A     n     d     q     n   =|A   1   A   2 . . .    A   n   d   q ,( A   1   A   2 . . .    A   n   +d   q )mod 2&gt;
 
     After Toffoli gate  103 , either controlled-SWAP gates  104 A or Toffoli gates  104 B are applied. The algorithm does the reading process from the given location provided by the quantum processor/microcontroller/quantum circuit through the first nth qubits of register |qy&gt;. If the qubit |r&gt; is loaded with state |1&gt; by the quantum processor/microcontroller/quantum circuit then the Toffli gates  104 B are running to make a decoupled copy of the value of the variable to the last m qubits of register |qy&gt;. Meanwhile, the controlled-SWAP gates are not working, and the reading process is done. On the other hand, if the quantum processor (e.g., microcontroller, quantum-circuit, etc.) loads the state |0&gt; to the qubit |r&gt;, consequently, the Controlled-SWAP gates  104 A are running to write the value stored in the last m qubits of the register |qy&gt; into QRAM location specified by the first n qubits. Meanwhile, Toffoli gates  104 B are not working as the writing process is being conducted. 
     After SWAP gates  104 A and Toffoli gates  104 B, Toffli gate  105  removes the marking entangled over qubit |dq&gt; by applying Toffoli gate  105  to make it disentangled. After Toffli gate  105 , S gates  106  undoes the effect of S gates  102  by applying S gates  106  once again to make the QRAM ready to next read/write process, where S gates  106  is applied. 
     In a first non-limiting example, the proposed QRAM, circuit  100  may be used to write a value [101] in a location/address |001&gt; and then reads the value from this location/address. In this non-limiting example, address initialization is conducted by applying three Hadamard gates to three qubits of register |A&gt; to create a complete superposition of states of the address register |A&gt; to address 2 3 =8 locations described by register |D&gt;, in the QRAM (e.g., circuit  100 ). This is also shown by: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                                            
                                           
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     In this first non-limiting example, once the address initialization is conducted, QRAM (e.g., circuit  100 ) can conduct a writing operation. In this non-limiting example, the value |101&gt; is to be stored in location/address |001&gt;. Thus, the first three qubits of register |qy&gt; are loaded with the target location in the QRAM (e.g., circuit  100 ) while loading the last three qubits with the value needed to store. 
     Thus, the state of the register |qy&gt; is |qy&gt;=|001, 101&gt; and set the control qubit |r&gt; to state | 0 &gt; for the QRAM to perform writing operations. In this first non-limiting example, an S operator (e.g., S gate  102 ) is applied between the first three qubits of register |qy&gt; and register |A&gt; to search for the designated location/address. Thus, the S operation transfers the designated location/address to state |111&gt; as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
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     In this first non-limiting example, T A     1     A     2     A     3     dq   3  gate is applied (e.g., Toffoli gate  103 ) and negates the state of the qubit |dq&gt; only if the state of the address register |A&gt; is in the state |A&gt;=|111&gt; as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
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               ) 
             
             . 
           
         
       
     
     In this first non-limiting example, T rdqqy     n+i     D     i     3  gate will not be applied (e.g., gate  104 B) because the state of the qubit |r&gt; is |0&gt;. However, the gate C 0 −C−SW AP rdqqy     n+i     D     i    (i=1, 2, 3) (e.g. gate  104 A) will apply as it is controlled by state |r&gt;=|0&gt;. Thus, the writing operation is executed since the Controlled-SWAP gate is applied to write the value stored in the last m qubits of the register |qy&gt; into a QRAM location specified by the first n qubits. Thus: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             ❘ 
                                                             
                                                             ψ 
                                                             3 
                                                             
                                                             
                                                             〉 
                                                             
                                                             = 
                                                             
                                                             
                                                             1 
                                                             
                                                             8 
                                                             
                                                             
                                                             ⁢ 
                                                             
                                                             ( 
                                                             
                                                             
                                                             ❘ 
                                                             110 
                                                             
                                                             , 
                                                             000 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             101 
                                                             
                                                             , 
                                                             0 
                                                             
                                                             
                                                             
                                                             
                                                             〉 
                                                             
                                                             + 
                                                             
                                                             ❘ 
                                                             111 
                                                             
                                                             , 
                                                             101 
                                                             , 
                                                             1 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             0 
                                                             
                                                             〉 
                                                           
                                                           + 
                                                         
                                                         ⁢ 
                                                           
                                                         
                                                           
                                                             ❘ 
                                                             100 
                                                           
                                                           , 
                                                           000 
                                                           , 
                                                           0 
                                                           , 
                                                           
                                                             001 
                                                             ⁢ 
                                                                 
                                                             101 
                                                           
                                                           , 
                                                           0 
                                                         
                                                       
                                                       〉 
                                                     
                                                     + 
                                                   
                                                   ❘ 
                                                   101 
                                                 
                                                 , 
                                                 
                                                   00 
                                                   ⁢ 
                                                   
                                                     0 
                                                     . 
                                                   
                                                 
                                                 , 
                                                 0 
                                                 , 
                                                 
                                                   001 
                                                   ⁢ 
                                                       
                                                   101 
                                                 
                                                 , 
                                                 0 
                                               
                                               〉 
                                             
                                             ❘ 
                                             010 
                                           
                                           , 
                                           000 
                                           , 
                                           0 
                                           , 
                                           
                                             001 
                                             ⁢ 
                                                 
                                             101 
                                           
                                           , 
                                           0 
                                         
                                         〉 
                                       
                                       + 
                                     
                                     ❘ 
                                     011 
                                   
                                   , 
                                   000 
                                   , 
                                   0 
                                   , 
                                   
                                     001 
                                     ⁢ 
                                         
                                     101 
                                   
                                   , 
                                   0 
                                 
                                 〉 
                               
                               + 
                             
                               
                             ❘ 
                             000 
                           
                           , 
                           000 
                           , 
                           0 
                           , 
                           
                             001 
                             ⁢ 
                                 
                             101 
                           
                           , 
                           0 
                         
                         〉 
                       
                       + 
                     
                     ❘ 
                     001 
                   
                   , 
                   000 
                   , 
                   0 
                   , 
                   
                     001 
                     ⁢ 
                         
                     101 
                   
                   , 
                   0 
                 
                 〉 
               
               ) 
             
             . 
           
         
       
     
     In this first non-limiting example, QRAM (e.g., circuit  100 ) may undo the effect of a previous gate (e.g., gate  104 A) after the writing process is done by applying T A     1     A     2     A     3     dq   3  (e.g., Toffoli Gate  105 ) gate as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             ❘ 
                                                             
                                                             ψ 
                                                             3 
                                                             
                                                             
                                                             〉 
                                                             
                                                             = 
                                                             
                                                             
                                                             1 
                                                             
                                                             8 
                                                             
                                                             
                                                             ⁢ 
                                                             
                                                             ( 
                                                             
                                                             
                                                             ❘ 
                                                             110 
                                                             
                                                             , 
                                                             000 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             101 
                                                             
                                                             , 
                                                             0 
                                                             
                                                             
                                                             
                                                             
                                                             〉 
                                                             
                                                             + 
                                                             
                                                             ❘ 
                                                             111 
                                                             
                                                             , 
                                                             101 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             0 
                                                             
                                                             〉 
                                                             
                                                             + 
                                                           
                                                           ⁢ 
                                                             
                                                           
                                                             
                                                             ❘ 
                                                             100 
                                                             
                                                             , 
                                                             000 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             101 
                                                             
                                                             , 
                                                             0 
                                                           
                                                         
                                                         〉 
                                                       
                                                       + 
                                                     
                                                     ❘ 
                                                     101 
                                                   
                                                   , 
                                                   
                                                     00 
                                                     ⁢ 
                                                     
                                                       0 
                                                       . 
                                                     
                                                   
                                                   , 
                                                   0 
                                                   , 
                                                   
                                                     001 
                                                     ⁢ 
                                                         
                                                     101 
                                                   
                                                   , 
                                                   0 
                                                 
                                                 〉 
                                               
                                               + 
                                             
                                               
                                             ❘ 
                                             010 
                                           
                                           , 
                                           000 
                                           , 
                                           0 
                                           , 
                                           
                                             001 
                                             ⁢ 
                                                 
                                             101 
                                           
                                           , 
                                           0 
                                         
                                         〉 
                                       
                                       + 
                                     
                                     ❘ 
                                     011 
                                   
                                   , 
                                   000 
                                   , 
                                   0 
                                   , 
                                   
                                     001 
                                     ⁢ 
                                         
                                     101 
                                   
                                   , 
                                   0 
                                 
                                 〉 
                               
                               + 
                             
                               
                             ❘ 
                             000 
                           
                           , 
                           000 
                           , 
                           0 
                           , 
                           
                             001 
                             ⁢ 
                                 
                             101 
                           
                           , 
                           0 
                         
                         〉 
                       
                       + 
                     
                     ❘ 
                     001 
                   
                   , 
                   000 
                   , 
                   0 
                   , 
                   
                     001 
                     ⁢ 
                         
                     101 
                   
                   , 
                   0 
                 
                 〉 
               
               ) 
             
             . 
           
         
       
     
     In this first non-limiting example, the circuit undoes the effect of S gates  102  after the writing process is done by applying the S operator again (e.g., S gates  106 ). Thus: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             ❘ 
                                                             
                                                             ψ 
                                                             5 
                                                             
                                                             
                                                             〉 
                                                             
                                                             = 
                                                             
                                                             
                                                             1 
                                                             
                                                             8 
                                                             
                                                             
                                                             ⁢ 
                                                             
                                                             ( 
                                                             
                                                             
                                                             ❘ 
                                                             000 
                                                             
                                                             , 
                                                             000 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             101 
                                                             
                                                             , 
                                                             0 
                                                             
                                                             
                                                             
                                                             
                                                             〉 
                                                             
                                                             + 
                                                             
                                                             ❘ 
                                                             
                                                             
                                                             00 
                                                             
                                                             ⁢ 
                                                             1 
                                                             
                                                             
                                                             , 
                                                             101 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             0 
                                                             
                                                             〉 
                                                             
                                                             + 
                                                           
                                                           ⁢ 
                                                             
                                                           
                                                             
                                                             ❘ 
                                                             
                                                             
                                                             0 
                                                             
                                                             ⁢ 
                                                             10 
                                                             
                                                             
                                                             , 
                                                             000 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             101 
                                                             
                                                             , 
                                                             0 
                                                           
                                                         
                                                         〉 
                                                       
                                                       + 
                                                     
                                                     ❘ 
                                                     011 
                                                   
                                                   , 
                                                   
                                                     00 
                                                     ⁢ 
                                                     
                                                       0 
                                                       . 
                                                     
                                                   
                                                   , 
                                                   0 
                                                   , 
                                                   
                                                     001 
                                                     ⁢ 
                                                         
                                                     101 
                                                   
                                                   , 
                                                   0 
                                                 
                                                 〉 
                                               
                                               + 
                                             
                                               
                                             ❘ 
                                             100 
                                           
                                           , 
                                           000 
                                           , 
                                           0 
                                           , 
                                           
                                             001 
                                             ⁢ 
                                                 
                                             101 
                                           
                                           , 
                                           0 
                                         
                                         〉 
                                       
                                       + 
                                     
                                     ❘ 
                                     101 
                                   
                                   , 
                                   000 
                                   , 
                                   0 
                                   , 
                                   
                                     001 
                                     ⁢ 
                                         
                                     101 
                                   
                                   , 
                                   0 
                                 
                                 〉 
                               
                               + 
                             
                               
                             ❘ 
                             110 
                           
                           , 
                           000 
                           , 
                           0 
                           , 
                           
                             001 
                             ⁢ 
                                 
                             101 
                           
                           , 
                           0 
                         
                         〉 
                       
                       + 
                     
                     ❘ 
                     111 
                   
                   , 
                   000 
                   , 
                   0 
                   , 
                   
                     001 
                     ⁢ 
                         
                     101 
                   
                   , 
                   0 
                 
                 〉 
               
               ) 
             
             . 
           
         
       
     
     In this first non-limiting example, the state of registers |A, D&gt; is as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             ❘ 
                                                             A 
                                                             
                                                             , 
                                                             D 
                                                             
                                                             〉 
                                                             
                                                             = 
                                                             
                                                             
                                                             1 
                                                             
                                                             8 
                                                             
                                                             
                                                             ⁢ 
                                                             
                                                             ( 
                                                             
                                                             
                                                             ❘ 
                                                             000 
                                                             
                                                             , 
                                                             000 
                                                             
                                                             
                                                             
                                                             
                                                             〉 
                                                             
                                                             + 
                                                             
                                                             ❘ 
                                                             001 
                                                             
                                                             , 
                                                             101 
                                                             
                                                             〉 
                                                             
                                                             + 
                                                           
                                                           ❘ 
                                                           010 
                                                         
                                                         , 
                                                         000 
                                                       
                                                       〉 
                                                     
                                                     + 
                                                   
                                                   ❘ 
                                                   011 
                                                 
                                                 , 
                                                 000 
                                               
                                               〉 
                                             
                                             + 
                                           
                                           ⁢ 
                                             
                                           
                                             
                                               ❘ 
                                               100 
                                             
                                             , 
                                             000 
                                           
                                         
                                         〉 
                                       
                                       + 
                                     
                                     ❘ 
                                     101 
                                   
                                   , 
                                   000 
                                 
                                 〉 
                               
                               + 
                             
                             ❘ 
                             110 
                           
                           , 
                           000 
                         
                         〉 
                       
                       + 
                     
                     ❘ 
                     111 
                   
                   , 
                   000 
                 
                 〉 
               
               ) 
             
             . 
           
         
       
     
     Thus, in this first non-limiting example, the value |101&gt; is stored in the location |001&gt;. 
     In a second non-limiting example, once address initialization is conducted (similar to that described in the first non-limiting example), a value |101&gt; is read from location/address |001&gt;. In this second non-limiting example, the first n qubits of register |qy&gt; are loaded with the target location in the QRAM (e.g., circuit  100 ). Thus, the state of the register qubit |r&gt; to state |1&gt; to perform a reading operation. Thus, the state of the QRAM is: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             ❘ 
                                                             
                                                             ψ 
                                                             0 
                                                             
                                                             
                                                             〉 
                                                             
                                                             = 
                                                             
                                                             
                                                             1 
                                                             
                                                             8 
                                                             
                                                             
                                                             ⁢ 
                                                             
                                                             ( 
                                                             
                                                             
                                                             ❘ 
                                                             000 
                                                             
                                                             , 
                                                             000 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             1 
                                                             
                                                             
                                                             
                                                             
                                                             〉 
                                                             
                                                             + 
                                                             
                                                             ❘ 
                                                             
                                                             
                                                             00 
                                                             
                                                             ⁢ 
                                                             1 
                                                             
                                                             
                                                             , 
                                                             101 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             1 
                                                             
                                                             〉 
                                                             
                                                             + 
                                                           
                                                           ⁢ 
                                                             
                                                           
                                                             
                                                             ❘ 
                                                             
                                                             
                                                             0 
                                                             
                                                             ⁢ 
                                                             10 
                                                             
                                                             
                                                             , 
                                                             000 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             1 
                                                           
                                                         
                                                         〉 
                                                       
                                                       + 
                                                     
                                                     ❘ 
                                                     011 
                                                   
                                                   , 
                                                   000 
                                                   , 
                                                   0 
                                                   , 
                                                   
                                                     001 
                                                     ⁢ 
                                                         
                                                     000 
                                                   
                                                   , 
                                                   1 
                                                 
                                                 〉 
                                               
                                               + 
                                             
                                             ❘ 
                                             100 
                                           
                                           , 
                                           000 
                                           , 
                                           0 
                                           , 
                                           
                                             001 
                                             ⁢ 
                                                 
                                             000 
                                           
                                           , 
                                           1 
                                         
                                         〉 
                                       
                                       + 
                                     
                                     ❘ 
                                     101 
                                   
                                   , 
                                   000 
                                   , 
                                   0 
                                   , 
                                   
                                     001 
                                     ⁢ 
                                         
                                     000 
                                   
                                   , 
                                   1 
                                 
                                 〉 
                               
                               + 
                             
                             ❘ 
                             110 
                           
                           , 
                           000 
                           , 
                           0 
                           , 
                           
                             001 
                             ⁢ 
                                 
                             000 
                           
                           , 
                           1 
                         
                         〉 
                       
                       + 
                     
                     ❘ 
                     111 
                   
                   , 
                   000 
                   , 
                   0 
                   , 
                   
                     001 
                     ⁢ 
                         
                     000 
                   
                   , 
                   1 
                 
                 〉 
               
               ) 
             
             . 
           
         
       
     
     In this second non-limiting example, an S operator (e.g., S gate  102 ) is applied between the first three qubits of register |qy&gt; and register |A&gt; to search for a designated location/address. Thus, the S operator transfer the designated location/address to state |111&gt; as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             ❘ 
                                                             
                                                             ψ 
                                                             1 
                                                             
                                                             
                                                             〉 
                                                             
                                                             = 
                                                             
                                                             
                                                             1 
                                                             
                                                             8 
                                                             
                                                             
                                                             ⁢ 
                                                             
                                                             ( 
                                                             
                                                             
                                                             ❘ 
                                                             110. 
                                                             
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             1 
                                                             
                                                             
                                                             
                                                             
                                                             〉 
                                                             
                                                             + 
                                                             
                                                             ❘ 
                                                             
                                                             
                                                             11 
                                                             
                                                             ⁢ 
                                                             1 
                                                             
                                                             
                                                             , 
                                                             101 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             1 
                                                             
                                                             〉 
                                                             
                                                             + 
                                                           
                                                           ⁢ 
                                                             
                                                           
                                                             
                                                             ❘ 
                                                             
                                                             
                                                             
                                                             100. 
                                                             
                                                             000 
                                                             
                                                             .0 
                                                             
                                                             
                                                             , 
                                                             
                                                             001 
                                                                 
                                                             0.1 
                                                             
                                                           
                                                         
                                                         〉 
                                                       
                                                       + 
                                                     
                                                     ❘ 
                                                     101 
                                                   
                                                   , 
                                                   
                                                     00 
                                                     ⁢ 
                                                     
                                                       0 
                                                       . 
                                                     
                                                   
                                                   , 
                                                   0 
                                                   , 
                                                   
                                                     001 
                                                     ⁢ 
                                                         
                                                     000 
                                                   
                                                   , 
                                                   1 
                                                 
                                                 〉 
                                               
                                               + 
                                             
                                               
                                             ❘ 
                                             010 
                                           
                                           , 
                                           000 
                                           , 
                                           0 
                                           , 
                                           
                                             001 
                                             ⁢ 
                                                 
                                             000 
                                           
                                           , 
                                           1 
                                         
                                         〉 
                                       
                                       + 
                                     
                                     ❘ 
                                     011 
                                   
                                   , 
                                   000 
                                   , 
                                   0 
                                   , 
                                   
                                     001 
                                     ⁢ 
                                         
                                     000 
                                   
                                   , 
                                   1 
                                 
                                 〉 
                               
                               + 
                             
                               
                             ❘ 
                             000 
                           
                           , 
                           000 
                           , 
                           0 
                           , 
                           
                             001 
                             ⁢ 
                                 
                             000 
                           
                           , 
                           1 
                         
                         〉 
                       
                       + 
                     
                     ❘ 
                     001 
                   
                   , 
                   000 
                   , 
                   0 
                   , 
                   
                     001 
                     ⁢ 
                         
                     000 
                   
                   , 
                   1 
                 
                 〉 
               
               ) 
             
             . 
           
         
       
     
     In this second non-limiting example, another gate (e.g., gate  104 B) is applied. Thus, this particular gate negates the state of the qubit |dq&gt; only if the state of the address register |A&gt; is in the state |A&gt;=|111&gt; as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             ❘ 
                                                             
                                                             ψ 
                                                             1 
                                                             
                                                             
                                                             〉 
                                                             
                                                             = 
                                                             
                                                             
                                                             1 
                                                             
                                                             8 
                                                             
                                                             
                                                             ⁢ 
                                                             
                                                             ( 
                                                             
                                                             ❘ 
                                                             
                                                             110. 
                                                             .0 
                                                             .001 
                                                                 
                                                             0.1 
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             〉 
                                                             
                                                             + 
                                                             
                                                             ❘ 
                                                             
                                                             
                                                             
                                                             11 
                                                             
                                                             1.101 
                                                             
                                                             .1 
                                                             .001 
                                                                 
                                                             0.1 
                                                             
                                                             
                                                             〉 
                                                             
                                                             + 
                                                           
                                                           ⁢ 
                                                             
                                                           
                                                             ❘ 
                                                             
                                                             
                                                             
                                                             100. 
                                                             
                                                             000 
                                                             
                                                             .0 
                                                             .001 
                                                                 
                                                             0.1 
                                                             
                                                           
                                                         
                                                         〉 
                                                       
                                                       + 
                                                     
                                                     ❘ 
                                                     101. 
                                                   
                                                   , 
                                                   0 
                                                   , 
                                                   
                                                     001 
                                                         
                                                     0.1 
                                                   
                                                 
                                                 〉 
                                               
                                               + 
                                             
                                               
                                             ❘ 
                                             010 
                                           
                                           , 
                                           000 
                                           , 
                                           0 
                                           , 
                                           
                                             001 
                                             ⁢ 
                                                 
                                             000 
                                           
                                           , 
                                           1 
                                         
                                         〉 
                                       
                                       + 
                                     
                                     ❘ 
                                     011 
                                   
                                   , 
                                   0. 
                                   , 
                                   
                                     001 
                                     ⁢ 
                                         
                                     000 
                                   
                                   , 
                                   1 
                                 
                                 〉 
                               
                               + 
                             
                               
                             ❘ 
                             000 
                           
                           , 
                           000 
                           , 
                           0 
                           , 
                           
                             001 
                             ⁢ 
                                 
                             000 
                           
                           , 
                           1 
                         
                         〉 
                       
                       + 
                     
                     ❘ 
                     001 
                   
                   , 
                   000 
                   , 
                   0 
                   , 
                   
                     001 
                     ⁢ 
                         
                     000 
                   
                   , 
                   1 
                 
                 〉 
               
               ) 
             
             . 
           
         
       
     
     In this second non-limiting example, gates C 0 −C−SW AP rdqqy     n+i     D     i    (i=1, 2, 3) (e.g., gate  104 A) does not work because the state of qubit |r&gt; is |1&gt;. Meanwhile, the gates T rdqqy     n+i     D     i     3  (C-C-NOT gate) work because they are controlled by state |r&gt; is |1&gt;. Thus, the reading operation occurs as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             ❘ 
                                                             
                                                             ψ 
                                                             2 
                                                             
                                                             
                                                             〉 
                                                             
                                                             = 
                                                             
                                                             
                                                             1 
                                                             
                                                             8 
                                                             
                                                             
                                                             ⁢ 
                                                             
                                                             ( 
                                                             
                                                             
                                                             ❘ 
                                                             110 
                                                             
                                                             , 
                                                             000 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             1 
                                                             
                                                             
                                                             
                                                             
                                                             〉 
                                                             
                                                             + 
                                                             
                                                             ❘ 
                                                             
                                                             
                                                             11 
                                                             
                                                             ⁢ 
                                                             1 
                                                             
                                                             
                                                             , 
                                                             101 
                                                             , 
                                                             1 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             101 
                                                             
                                                             , 
                                                             1 
                                                             
                                                             〉 
                                                             
                                                             + 
                                                           
                                                           ⁢ 
                                                             
                                                           
                                                             
                                                             
                                                             ❘ 
                                                             100 
                                                             
                                                             
                                                             , 
                                                             000 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             1 
                                                           
                                                         
                                                         〉 
                                                       
                                                       + 
                                                     
                                                     ❘ 
                                                     101 
                                                   
                                                   , 
                                                   
                                                     00 
                                                     ⁢ 
                                                     
                                                       0 
                                                       . 
                                                     
                                                   
                                                   , 
                                                   0 
                                                   , 
                                                   
                                                     001 
                                                     ⁢ 
                                                         
                                                     000 
                                                   
                                                   , 
                                                   1 
                                                 
                                                 〉 
                                               
                                               + 
                                             
                                               
                                             ❘ 
                                             010 
                                           
                                           , 
                                           000 
                                           , 
                                           0 
                                           , 
                                           
                                             001 
                                             ⁢ 
                                                 
                                             000 
                                           
                                           , 
                                           1 
                                         
                                         〉 
                                       
                                       + 
                                     
                                     ❘ 
                                     011 
                                   
                                   , 
                                   000 
                                   , 
                                   0 
                                   , 
                                   
                                     001 
                                     ⁢ 
                                         
                                     000 
                                   
                                   , 
                                   1 
                                 
                                 〉 
                               
                               + 
                             
                               
                             ❘ 
                             000 
                           
                           , 
                           000 
                           , 
                           0 
                           , 
                           
                             001 
                             ⁢ 
                                 
                             000 
                           
                           , 
                           1 
                         
                         〉 
                       
                       + 
                     
                     ❘ 
                     001 
                   
                   , 
                   000 
                   , 
                   0 
                   , 
                   
                     001 
                     ⁢ 
                         
                     000 
                   
                   , 
                   1 
                 
                 〉 
               
               ) 
             
             . 
           
         
       
     
     In this second non-limiting example, the QRAM undoes the effect of step  3  after the reading process is completed by applying the T A     1     A     2     A     3     dq   3  (e.g., Toffoli Gate  105 ), as follows: 
     In this second non-limiting example, the circuit undoes the effect of S gates  102  after the writing process is done by applying the S operator again (e.g., QHD  106 ). Thus: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             ❘ 
                                                             
                                                             ψ 
                                                             4 
                                                             
                                                             
                                                             〉 
                                                             
                                                             = 
                                                             
                                                             
                                                             1 
                                                             
                                                             8 
                                                             
                                                             
                                                             ⁢ 
                                                             
                                                             ( 
                                                             
                                                             
                                                             ❘ 
                                                             000 
                                                             
                                                             , 
                                                             000 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             1 
                                                             
                                                             
                                                             
                                                             
                                                             〉 
                                                             
                                                             + 
                                                             
                                                             ❘ 
                                                             
                                                             
                                                             00 
                                                             
                                                             ⁢ 
                                                             1 
                                                             
                                                             
                                                             , 
                                                             101 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             101 
                                                             
                                                             , 
                                                             1 
                                                             
                                                             〉 
                                                             
                                                             + 
                                                           
                                                           ⁢ 
                                                             
                                                           
                                                             
                                                             
                                                             ❘ 
                                                             010 
                                                             
                                                             
                                                             , 
                                                             000 
                                                             , 
                                                             0 
                                                             , 
                                                             
                                                             001 
                                                             ⁢ 
                                                                 
                                                             000 
                                                             
                                                             , 
                                                             1 
                                                           
                                                         
                                                         〉 
                                                       
                                                       + 
                                                     
                                                     ❘ 
                                                     011 
                                                   
                                                   , 
                                                   000 
                                                   , 
                                                   0 
                                                   , 
                                                   
                                                     001 
                                                     ⁢ 
                                                         
                                                     000 
                                                   
                                                   , 
                                                   1 
                                                 
                                                 〉 
                                               
                                               + 
                                             
                                               
                                             ❘ 
                                             100 
                                           
                                           , 
                                           000 
                                           , 
                                           0 
                                           , 
                                           
                                             001 
                                             ⁢ 
                                                 
                                             000 
                                           
                                           , 
                                           1 
                                         
                                         〉 
                                       
                                       + 
                                     
                                     ❘ 
                                     101 
                                   
                                   , 
                                   000 
                                   , 
                                   0 
                                   , 
                                   
                                     001 
                                     ⁢ 
                                         
                                     000 
                                   
                                   , 
                                   1 
                                 
                                 〉 
                               
                               + 
                             
                               
                             ❘ 
                             110 
                           
                           , 
                           000 
                           , 
                           0 
                           , 
                           
                             001 
                             ⁢ 
                                 
                             000 
                           
                           , 
                           1 
                         
                         〉 
                       
                       + 
                     
                     ❘ 
                     111 
                   
                   , 
                   000 
                   , 
                   0 
                   , 
                   
                     001 
                     ⁢ 
                         
                     000 
                   
                   , 
                   1 
                 
                 〉 
               
               ) 
             
             . 
           
         
       
     
     In embodiments, |ψ&gt; represents the first n qubits of the register |qy&gt; in  FIG.  1    and |φ&gt; represents the n qubits of the registers |A. Thus, in this second non-limiting example, the state of register |qy&gt; has the following state: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               ❘ 
                               qy 
                             
                             〉 
                           
                           = 
                           
                             
                               
                                 7 
                                 8 
                               
                             
                             ❘ 
                             001 
                           
                         
                         , 
                         000 
                       
                       〉 
                     
                     + 
                     
                       1 
                       
                         8 
                       
                     
                   
                   ❘ 
                   001 
                 
                 , 
                 101 
               
               〉 
             
             . 
           
         
       
     
     In embodiments, the first non-limiting example and the second non-limiting example shows how a proposed QRAM writes the value |101&gt; in the location/address |001&gt;, then how it reads this value from this location/address. 
       FIG.  5    is a diagram of example components of a device  500 . Device  500  may correspond to a computing device, such as devices that may use circuit  100  (the proposed QRAM). As shown in  FIG.  5   , device  500  may include a quantum bus  510 , a processor  520 , a memory (QRAM)  530 , quantum input component  540 , quantum output component  550 , and a communications interface  560 . In other implementations, device  500  may contain fewer components, additional components, different components, or differently arranged components than depicted in  FIG.  5   . Additionally, or alternatively, one or more components of device  500  may perform one or more tasks described as being performed by one or more other components of device  500 . 
     Bus  510  may include a path that permits communications among the components of device  500 . Processor  520  may include one or more processors, microprocessors, and/or processing logic (e.g., a field programmable gate array (FPGA), quantum teleportation devices, quantum communication devices, quantum computing circuits, quantum encryption applications and/or an application specific integrated circuit (ASIC)) that interprets and executes instructions. Memory  530  may include the proposed QRAM circuit for use by processor  520 . Input component  540  may include a mechanism that permits a user to convert classical information to quantum input information to device  500 , such as a quantum circuit, a quantum-based application, a keyboard, a keypad, a button, a switch, voice command, etc. Output component  550  may include a mechanism that outputs information and transforms quantum information to classical information to be provided to the user, such as a display, a speaker, one or more light emitting diodes (LEDs), etc. 
     Communications interface  560  may include any transceiver-like mechanism that enables device  500  to communicate with other devices and/or systems. For example, communications interface  560  may include an Ethernet interface, an optical interface, a coaxial interface, a wireless interface, or the like and quantum-to-classical and vice versa unit. 
     In another implementation, communications interface  560  may include, for example, a transmitter that may convert baseband signals from processor  520  to radio frequency (RF) signals and/or a receiver that may convert RF signals to baseband signals. Alternatively, communications interface  560  may include a transceiver to perform functions of both a transmitter and a receiver of wireless communications (e.g., radio frequency, infrared, visual optics, quantum wireless, quantum channels, quantum fiber optics, quantum teleportation, quantum communication devices/networks, quantum encryption devices, etc.), wired communications (e.g., conductive wire, twisted pair cable, coaxial cable, transmission line, fiber optic cable, waveguide, single-photon channels, multi-photon channels, etc.), or a combination of wireless and wired communications. 
     Communications interface  560  may connect to an antenna assembly (not shown in  FIG.  5   ) for transmission and/or reception of the RF signals, and/or quantum channels. The antenna assembly may include one or more antennas to transmit, quantum channels and/or receive RF signals over the air. The antenna assembly may, for example, receive RF signals and/or quantum information from communications interface  560  and transmit the RF signals over the air, and receive RF signals over the air and provide the RF signals to communications interface  560 . In one implementation, for example, communications interface  560  may communicate with a network (e.g., a wireless network, quantum network, quantum channel, wired network, Internet, quantum internet, etc.). In embodiments, an antenna may be implemented by quantum teleportation protocols, quantum communication protocols and/or quantum encryption protocols. 
     As will be described in detail below, device  500  may perform certain operations. Device  500  may perform these operations in response to processor  520  executing software instructions (e.g., computer program(s), quantum computing circuit, quantum teleportation, etc.) contained in a computer-readable medium/quantum-based computing, such as memory  530 , a secondary storage device (e.g., hard disk, CD-ROM, etc.), or other forms of RAM or ROM. In embodiments, a part of memory  530  may include circuit  100  as described in  FIG.  1   . A computer-readable medium may be defined as a non-transitory memory device. A memory device may include space within a single physical memory device or spread across multiple physical memory devices. The software instructions may be read into memory  530  from another computer-readable medium or from another device. The software instructions contained in memory  530  may cause processor  520  to perform processes described herein. Alternatively, hardwired circuitry may be used in place of or in combination with software instructions to implement processes described herein. Thus, implementations described herein are not limited to any specific combination of hardware circuitry and software. 
       FIG.  6    is an example diagram.  FIG.  6    describes device  600 , input  602 , and output  604 . In embodiments, device  600  may a computing device with features/structures similar to that described in  FIG.  6   . In embodiments, device  600  may be a computing device that is part of a laptop, desktop, tablet, smartphone, quantum computer, quantum computing device, quantum communication device, quantum teleportation device, quantum encryption device, quantum internet device, and/or any other device. In embodiments, device  600  may include a QRAM (e.g., circuit  100 ) similar to that described the above figures. 
     In embodiments, device  600  may receive communication  602 , analyze communication  602 , and generate output  604 . In embodiments, based on the QRAM in device  600 , output  604  which gives a writing fidelity of 99.9971% and a reading fidelity of 99.983% which mean that the QRAM may have a 99.980% accuracy in the information in output  604 . 
     Even though particular combinations of features are recited in the claims and/or disclosed in the specification, these combinations are not intended to limit the disclosure of the possible implementations. In fact, many of these features may be combined in ways not specifically recited in the claims and/or disclosed in the specification. Although each dependent claim listed below may directly depend on only one other claim, the disclosure of the possible implementations includes each dependent claim in combination with every other claim in the claim set. 
     While various actions are described as selecting, displaying, transferring, sending, receiving, generating, notifying, and storing, it will be understood that these example actions are occurring within an electronic computing, electronic networking, quantum computing and/or quantum networking environment and may require one or more computing devices, as described in  FIG.  5    to complete such actions. Furthermore, it will be understood that these various actions can be performed by using a touch screen on a computing device (e.g., touching an icon, swiping a bar or icon), using a keyboard, a mouse, or any other process for electronically selecting an option displayed on a display screen to electronically communicate with other computing devices, quantum computer, cloud quantum circuit/computer, quantum communication devices, quantum teleportation devices, quantum encryption circuit/devices, and/or quantum networks. Also it will be understood that any of the various actions can result in any type of electronic information and/or quantum information to be displayed in real-time and/or simultaneously on multiple user devices. For  FIGS.  3  to  6   , any electronic graphs and/or quantum information may be generated by a computing device, such as device  500 , and displayed via a graphical user device (GUI) or cloud environment. 
     No element, act, or instruction used in the present application should be construed as critical or essential unless explicitly described as such. Also, as used herein, the article “a” is intended to include one or more items and may be used interchangeably with “one or more.” Where only one item is intended, the term “one” or similar language is used. Further, the phrase “based on” is intended to mean “based, at least in part, on” unless explicitly stated otherwise. Also, the phrase “converted text,” or “converted information” may indicate information that has been converted from handwritten or non-handwritten information to printed information. The phrase “information” may indicate letters, words, numbers, and/or symbols. The phrase “text” may indicate letters, numbers, and/or symbols. The phrases “information” and “text” may indicate the same thing, i.e., letters, numbers, and/or symbols. Also, while the above examples are associated with prescriptions, pharmacists, and doctors, the above example actions may also be used for other scenarios and analysis of other types of handwritten text, such as with purchase orders, shipping orders, etc. 
     In the preceding specification, various preferred embodiments have been described with reference to the accompanying drawings. It will, however, be evident that various modifications and changes may be made thereto, and additional embodiments may be implemented, without departing from the broader scope of the invention as set forth in the claims that follow. The specification and drawings are accordingly to be regarded in an illustrative rather than restrictive sense.