Abstract:
A tunable superconducting circuit includes a first charge island, a second charge island, a third charge island, a fourth charge island, a first junction loop electrically coupled to the first and third charge islands, a second junction loop coupled to the second and third charge islands and a third junction loop coupled to the third and fourth charge islands, wherein the first, second and third junction loops are tuned in frequency to operate together as a qubit.

Description:
FEDERAL RESEARCH STATEMENT 
       [0001]    This invention was made with Government support under Contract No.: W911NF-10-1-0324 awarded by the U.S. Army. The Government has certain rights in this invention. 
     
    
     BACKGROUND 
       [0002]    The present invention relates to superconducting circuits, and more specifically, to multi-tunable superconducting circuit system. 
         [0003]    Superconducting circuits have experienced notable advances over the last few decades, finding numerous applications in nanotechnology. From extremely sensitive magnetometers to microwave amplifiers, photon detectors or qubits for quantum information processing, these devices offer an enormous versatility. For quantum computation, in particular, superconducting qubits in the circuit Quantum Electrodynamics (QED) architecture have proven very successful. In this architecture, one or more qubits are coupled to one or more resonators, which can act both as mediators of the coupling between the qubits and as readout elements. For systems with only a few qubits and resonators, the interaction between them does not need much tunability. As the size of the system grows, however, the ability to independently tune the coupling strength between different parts of the device becomes critical for the implementation of quantum algorithms. 
         [0004]    Several coupling schemes between two superconducting qubits and between one superconducting qubit and one resonator have been implemented over the years. However, no solution has been given to the problem of coupling one qubit to two resonators with independent tunability of the coupling to each of the resonators. Most tunable coupling schemes in superconducting circuits realized to date have been designed to tune the coupling between qubits. In these implementations, the coupling between the qubits has mainly been achieved by non-linear inductances and most of the designs give the ability to control both the magnitude and the sign of the coupling. 
         [0005]    Several solutions exist to couple qubits and resonators. One example is an RF SQUID in the non-hysteretic regime to couple a lumped element resonator to a phase qubit. Another example is a modified transmon with an extra degree of freedom in order to tune the dielectric dipole coupling between the qubit and the resonator. The absence of additional coupling elements significantly simplifies the circuitry. No solution has been given so far to the problem of achieving independent and tunable coupling between a quantum system and two resonators. 
       SUMMARY 
       [0006]    Exemplary embodiments include a tunable superconducting circuit, including a first charge island, a second charge island, a third charge island, a fourth charge island, a first junction loop electrically coupled to the first and third charge islands, a second junction loop coupled to the second and third charge islands and a third junction loop coupled to the third and fourth charge islands, wherein the first, second and third junction loops are tuned in frequencies to operate together as a qubit. 
         [0007]    Additional exemplary embodiments include a tunable superconducting circuit system, including a first resonator, a second resonator and a tunable superconducting circuit coupled between the first and second resonators, wherein the tunable superconducting circuit includes a non-linear quantum degree of freedom, which independently couples the first and second resonators with coupling strengths that are actively tunable by the tunable superconducting circuit. 
         [0008]    Further exemplary embodiments include a tunable superconducting circuit system, including a first resonator, a second resonator, a tunable superconducting circuit coupled between the first and second resonators, and including a first charge island, a second charge island, a third charge island, a fourth charge island, a first junction loop electrically coupled to the first and third charge islands, a second junction loop coupled to the second and third charge islands and a third junction loop coupled to the third and fourth charge islands. 
         [0009]    Additional features and advantages are realized through the techniques of the present invention. Other embodiments and aspects of the invention are described in detail herein and are considered a part of the claimed invention. For a better understanding of the invention with the advantages and the features, refer to the description and to the drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0010]    The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The forgoing and other features, and advantages of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which: 
           [0011]      FIG. 1  illustrates an exemplary tunable superconducting circuit system; 
           [0012]      FIG. 2  illustrates an exemplary superconducting circuit and exemplary resonators; 
           [0013]      FIG. 3  illustrates a flowchart for a method for characterizing a multi-tunable circuit in accordance with exemplary embodiments; 
           [0014]      FIG. 4  illustrates a flowchart for a method for operating a multi-tunable circuit in accordance with exemplary embodiments; 
           [0015]      FIG. 5  illustrates two plots of energy ratios that illustrate a quantity proportional to a coupling energy in arbitrary units as calculated from numerical simulations; and 
           [0016]      FIG. 6  illustrates a schematic layout of an embodiment of a multi-tunable circuit. 
       
    
    
     DETAILED DESCRIPTION 
       [0017]      FIG. 1  illustrates an exemplary tunable superconducting circuit system  100 . The system includes multiple (superconducting) circuits  105  interconnected by multiple (superconducting) resonators  110 , which allows multi-tunable circuits within the system as further described herein. In exemplary embodiments, the system  100  can be implemented in a robust, scalable quantum computer. The system  100  includes a non-linear quantum degree of freedom, which independently couples to two separate resonators  110  via an intervening circuit  105 , with coupling strengths that are actively tunable. Many conventional superconducting architectures for quantum computing are based on a quantum bus mediating long-range interactions between the quantum bits. In exemplary embodiments, the system  100  allows a tunable interaction between the resonators  110  (e.g., as buses). The tunable interaction allows for large-scale quantum information processing, as unwanted long-range interactions are detrimental to making a fault-tolerant quantum computer. Other tunable couplers have been built but they lack independent coupling to more than one bus. 
         [0018]    In exemplary embodiments, there are multiple functionalities of each of the underlying circuits  105 . For example, each of the circuits  105  can be implemented as a qubit, which can be part of a larger network of qubits coupled to the resonators  110 , as shown in  FIG. 1 . As a qubit, each of the circuits  105  can be actively coupled to either of two resonators  110 , both, or neither. In addition, the coupling strengths are fully independently tunable, and the circuits  105  can be used directly as a tunable coupling element between two resonators  110 . In exemplary embodiments, the qubit state can either be protected or re-initialized by turning on the coupling to a high or low quality factor resonator, respectively. Furthermore, each of the circuits  105  can be used to couple separate qubits, which are each independently coupled to resonators  110  that are otherwise decoupled from one another. The system  100  can be implemented in numerous larger-scale superconducting quantum computing implementations, especially as a functional element for connecting modularized components comprising a few circuits  105  (qubits) and resonators  110 . 
         [0019]      FIG. 2  illustrates an exemplary superconducting circuit  200  (e.g., circuits  105  of  FIG. 1 ) and two adjacent resonators  205 ,  210  (e.g., resonators  110  of  FIG. 1 ), which are configured as harmonic oscillators. As described herein, the system  100  of  FIG. 1  enables multi-tunable circuits within the system  100 . In the example of  FIG. 2 , the circuit  200  is a double tunable circuit as now described. In exemplary embodiments, the circuit  200  includes three Josephson junction loops  201 ,  202 ,  203 , respectively shunted by capacitors C J1 , C J2 , C J3 , connected in parallel to the three Josephson junction loops  201 ,  202 ,  203 . Each of the Josephson junction loops  201 ,  202 ,  203  is respectively coupled to a flux bias line F B1 , F B2 , F B3  configured to provide a magnetic flux for tuning the circuit  200 . In exemplary embodiments, the three capacitively shunted Josephson junction loops  201 ,  202 ,  203  define four charge islands (as defined by the legend in  FIG. 2 ). Each of the four charge islands is capacitively coupled to the other three islands. As such, charge island #1 is coupled to charge island #2 via capacitor C C . Charge island #1 is coupled to charge island #3 via capacitor C J1 . Charge island #1 is coupled to charge island #4 via capacitor C I1 . Charge island #2 is coupled to charge island #3 via capacitor C J2 . Charge island #2 is coupled to charge island #4 via capacitor C I2 . Charge island #3 is coupled to charge island #4 via capacitor C J3 . In addition, Charge island #4 is coupled to ground via capacitor C G . In exemplary embodiments, the four charge islands are configured to operate as a superconducting qubit. Furthermore, charge island #1 is capacitively coupled to the resonator  205  via capacitor Cg1, and charge island #2 is capacitively coupled to the resonator  210  via capacitor Cg2. In the example of  FIG. 2 , the resonator  205  includes an inductor L R1  coupled in parallel with a capacitor C R1 , and the resonator  210  includes an inductor L R2  coupled in parallel with a capacitor C R2 . 
         [0020]    In exemplary embodiments, the example of  FIG. 2  provides six Josephson junctions arranged in three two junction loops among the four charge islands. As described herein, charge island #1 is capacitively coupled to the resonator  205 , and charge island #2 is capacitively coupled to the resonator  210 . In exemplary embodiments, tuning the magnetic flux through each of the three loops  201 ,  202 ,  203  respectively through the flux bias lines F B1 , F B2 , F B3  allows for control of the coupling energy between each resonator  205 ,  210  and the superconducting circuit  200  independently. The circuit  200  can be tuned to maintain a constant resonant frequency while varying the coupling to the resonators  205 ,  210 , thereby coupling nearby circuits in the system  100 . 
         [0021]    In exemplary embodiments, coupling among the four-island qubit and each resonator  205 ,  210  can be tuned by changing the energies of the islands relative to each other. Therefore, the operation of the circuit  200  includes independently tuning the energy of each island. In exemplary embodiments, tuning can be implemented by driving a direct current (DC) current through the flux bias lines F B1 , F B2 , F B . The DC current originates a magnetic flux that biases the junction energy according to the formula: 
         [0000]        E   J   =I   0 *φ 0 /2π*cos(2πφ/φ 0 )  EQ. 1
 
         [0022]    where I 0  is the total critical current of the junction loop, φ is the magnetic flux threading the loop and T o  is the flux quantum. The other relevant energy in play is the electron charging energy E C =4e 2 /2C, where e is the electron charge and C is the renormalized capacitance of the junction loop. These energies define the resonance frequency of each of the Josephson junction loops  201 ,  202 ,  203 . A ground and first excited states of each junction loop are spaced by an energy approximately equal to E q =(8E J E C ) 1/2    
         [0023]    Operation of the circuit is now described.  FIG. 3  illustrates a flowchart for a method  300  for characterizing a multi-tunable circuit in accordance with exemplary embodiments. At block  310 , the user selects an operating DC flux value for one of the charge islands. For illustrative purposes, the user selected an operating F B3  DC flux value. It will be appreciated that the other flux bias lines F B1 , F B2  can be selected as well. The operating F B3  DC flux value corresponds to an energy for the Josephson junction loop  3 ,  203  which determines the “qubit” working frequency f Q . The operating F B3  DC flux value is referred to as F B3 0. 
         [0024]    At block  320 , the user tunes the operating DC flux values for two other charge islands. In the example, the user tunes flux bias lines F B1 , F B2  over a flux quantum with the other flux bias line (F B2  or F B1 ) fixed at an arbitrary value and flux bias line F B3  at F B3 0. 
         [0025]    At block  330 , the user measures coupling energies between the circuit  200  and each of the resonators  205 ,  210 . For each flux bias lines F B1 , F B2  line value, the user measures the coupling energies g 1 , g 2 , respectively between the circuit  200  (i.e., the qubit) and resonators  205 ,  210 , as described further herein. The respective values for the value for the flux bias line F B1 , F B2  for which the coupling energies g 1 , g 2  are at their relative maximum values are F B1   M , F B2   M , and the respective values for the value for the flux bias line F B1 , F B2  for which the coupling energies g 1 , g 2  are at their relative minimum values are F B1   m , F B2   m . 
         [0026]    At block  340 , the qubit frequencies are measured. Several different measurements are made. First, the flux bias line F B1  is held at F B1   m , while the flux bias line F B2  is held at an arbitrary value and F B3  is held at F B3   0 . The user measures the “qubit” frequency, which is given by the energy of junction loop  203 , and calls this frequency f Q1 . The flux bias line F B3  is tuned until f Q1 =f Q . The value of F B3  for which f Q1 =f Q  is called F B3   1 . Then, the flux bias line F B2  is held at F B2   m , while the flux bias line F B1  is held at an arbitrary value and F B3  is held at F B3   0 . The user measures the “qubit” frequency, which is given by the energy of junction loop  203 , and calls this frequency f Q2 . The flux bias line F B3  is tuned until f Q2 =f Q . The value of F B3  for which f Q2 =f Q  is called F B3   2 . Finally, the flux bias line F B1  is held at F B1   m , while the flux bias line F B2  is held at F B2   m  and F B3  is held at F B3 °. The user measures the “qubit” frequency, which is given by the energy of junction loop  203 , and calls this frequency f Q12 . The flux bias line F B3  is tuned until f Q12 =f Q . The value of F B3  for which f Q12 =f Q  is called F B3   12 . 
         [0027]      FIG. 4  illustrates a flowchart for a method  400  for operating a multi-tunable circuit in accordance with exemplary embodiments. At block  410 , the charge island(s) for coupling to one or more of the resonators are selected. There are several possibilities for selecting the charge islands. The circuit  200  can be coupled to both resonators  205 ,  210 . The circuit  200  can be coupled to only resonator  205 . The circuit  200  can be coupled to only resonator  210 . The circuit  500  can be operated uncoupled from both the resonators  205 ,  210 . At block  420 , the operating DC flux values are selected. There are several possibilities for selecting the operating DC flux values. When the circuit  200  is coupled to both resonators  205 ,  210 , the user sets F B1 =F B1   M , F B2 =F B2   M , and F B3 =F B3   0 . When the circuit  200  is coupled to only resonator  205 , the user sets F B1 =F B1   M , F B2 =F B2   m  and F B3 =F B3   2 . When the circuit  200  is coupled to only resonator  210 , the user sets F B1 =F B1   m , F B2 =F B2   m  and F B3 =F B3   1 . When the circuit  500  can be operated uncoupled from both the resonators  205 ,  210 , the user sets F B1 =F B1   m , F B2 =F B2   m  and F B3 =F B3   12 . 
         [0028]    At block  430 , with the values of energies E J3 , E C3  held at a constant value, say E J3 /E C3 =75, the values of energies E J1 , E J2  are independently swept by driving DC currents through flux bias lines F B1 , F B2 , respectively. For each value of the energies E J1 , E J2 , the coupling of the circuit  200  to each resonator  205 ,  210  can be measured by applying a microwave frequency pulse on the flux bias line F B3  at the frequency associated with an energy E q3 , of the circuit  200 , with the right power and duration so that the Josephson Junction loop  203  ends in the first excited state and then measuring the resonance frequency shift of each resonator  205 ,  210 . The measured resonance frequency shift is proportional to the square of the coupling energy g to the circuit  200 . 
         [0029]      FIG. 5  illustrates plots  505 ,  510  showing a magnitude (in arbitrary units) of the coupling of the exemplary superconducting circuit  200  and the adjacent resonators  205 ,  210  as a function of the energies in two Josephson junction loops  201 ,  202  while the energy in another Josephson junction loop  203  is kept constant. The minimum coupling energies are much lower than any other energy relevant to the system  100 . As such, at the relative minimum coupling energies described herein, the circuit  200  can be considered completely decoupled from either resonator. 
         [0030]    In exemplary embodiments, the energy at which the circuit operates as a qubit, at energy Eq3, changes slightly near the regions of minimum coupling to each resonator  205 ,  210  due to interactions with the other two Josephson junction loops  201 ,  202 . Therefore, in order to operate the device as a qubit, a correcting DC flux needs to be applied through flux bias line F B3  to keep the energy Eq3 constant. 
         [0031]      FIG. 6  illustrates a schematic layout of an embodiment of a multi-tunable circuit  200  as shown herein. In the example, the three Josephson junction loops  201 ,  202 ,  203  and respective capacitors are arranged within a pocket of dimensions 400×300 microns. The Josephson junction loops  201 ,  202 ,  203  have an area of 15×15 micron squared. The flux bias lines F B1 , F B2 , F B3  are shorted in order to drive a DC current through them. The resonators  205 ,  210 , flux bias lines F B1 , F B2 , F B3 , capacitors and junctions are made of a superconducting material. In the example, the resonators  205 ,  210 , the ground plane  605  and the bias lines F B1 , F B2 , F B3  are made out of niobium, whereas the capacitors and the Josephson junctions are made out of aluminum. The superconducting material is deposited on top of a chip that can be Silicon, sapphire or other suitable dielectric. 
         [0032]    The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one more other features, integers, steps, operations, element components, and/or groups thereof. 
         [0033]    The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the invention. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated 
         [0034]    The flow diagrams depicted herein are just one example. There may be many variations to this diagram or the steps (or operations) described therein without departing from the spirit of the invention. For instance, the steps may be performed in a differing order or steps may be added, deleted or modified. All of these variations are considered a part of the claimed invention. 
         [0035]    While the preferred embodiment to the invention had been described, it will be understood that those skilled in the art, both now and in the future, may make various improvements and enhancements which fall within the scope of the claims which follow. These claims should be construed to maintain the proper protection for the invention first described.