Patent Publication Number: US-6988058-B1

Title: Quantum computation with quantum dots and terahertz cavity quantum electrodynamics

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is related to Provisional Patent Application Ser. No. 60/112,439, filed Dec. 16, 1998, entitled “QUANTUM COMPUTATION WITH QUANTUM DOTS AND TERAHERTZ CAVITY QUANTUM ELECTRODYNAMICS,” by Mark S. Sherwin et al., and also related to Provisional Patent Application Ser. No. 60/123,220, filed Mar. 8, 1999, entitled “QUANTUM COMPUTATION WITH QUANTUM DOTS AND TERAHERTZ CAVITY QUANTUM ELECTRODYNAMICS,” by Mark S. Sherwin et al, which applications are incorporated by reference herein. This application also claims priority under 35 U.S.C. § 119(e) to both Provisional Patent Application Ser. No. 60/112,439, filed Dec. 16, 1998, entitled “QUANTUM COMPUTATION WITH QUANTUM DOTS AND TERAHERTZ CAVITY QUANTUM ELECTRODYNAMICS,” by Mark S. Sherwin et al. and Provisional Patent Application Ser. No. 60/123,220, filed Mar. 8, 1999, entitled “QUANTUM COMPUTATION WITH QUANTUM DOTS AND TERAHERTZ CAVITY QUANTUM ELECTRODYNAMICS,” by Mark S. Sherwin et al. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
     This invention was made with Government support under Grant No. ARO DAAG55-98-1-0366, awarded by the Army. The Government has certain rights in this invention. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates in general to quantum computation, and in particular to quantum computation with quantum dots and terahertz cavity quantum electrodynamics. 
     2. Description of Related Art 
     A quantum computer processes quantum information which is stored in “quantum bits,” also called qubits. If a small set of fundamental operations, or universal quantum logic gates, can be performed on the qubits, then a quantum computer can be programmed to solve an arbitrary problem. Quantum computation has been shown to efficiently factorize large integers, and the quantum information can be stored indefinitely, which provides the interest in quantum computation and machines that can perform quantum computation. 
     Consider, for example, the publication by Barenco, et al., entitled “Conditional Quantum Dynamics In Logic Gates,” Physical Review Letters, 15 May 1995, USA, vol. 74, no. 20, pages 4083–4086. This publication notes that quantum logic gates provide fundamental examples of conditional quantum dynamics, and could form the building blocks of general quantum information processing systems, which have recently been shown to have many interesting non-classical properties. This publication describes a simple quantum logic gate, the quantum controlled-NOT (CNOT), and analyzes some of its applications. The publication also discusses two possible physical realizations of the gates, one based on Ramsey atomic interferometry, and the other on the selective driving of optical resonances of two subsystems undergoing a dipole—dipole interaction. 
     However, the implementation of a large-scale quantum computer has remained a technological challenge. The qubits must be well isolated from the influence of the environment, but must remain manipulatable in individual units to initialize the computer, perform quantum logic operations, and measure the result of the computation. 
     Implementations of such a quantum computer have been proposed using atomic beams, trapped atoms and/or ions, bulk nuclear magnetic resonance, nanostructured semiconductors, and Josephson junctions. However, each scheme proposed has limitations that make large-scale implementation difficult and very limiting in performance. 
     For example, proposals using trapped atoms or ions, qubits couple with collective excitations or cavity photons. This coupling enables two-bit gates involving an arbitrary pair of qubits which makes programming straightforward. However, these schemes require serial gating schemes, whereas error correction schemes require parallelism, thereby limiting the usefulness of data gathered using an atomic or ion trapping machine. 
     In the semiconductor and superconductor schemes, only nearest-neighbor qubits can be coupled, and significant overhead is required to couple distant qubits. However, these machines can perform some gate operations in parallel, which allows for some error correction. 
     It can be seen, then, that there is a need in the art for a quantum computer. It can also be seen, then, that there is a need in the art for a quantum computer that can perform parallel gate operations. It can also be seen, then, that there is a need in the art for a quantum computer that can perform parallel gate operations without significant qubit overhead. 
     SUMMARY OF THE INVENTION 
     To overcome the limitations in the prior art described above, and to overcome other limitations that will become apparent upon reading and understanding the present specification, the present invention discloses an apparatus and method for quantum computing. The apparatus comprises a control bit structure, a target bit structure, and gate electrodes, coupled to the control bit structure and the target bit structure, for applying a voltage across the control bit structure and the target bit structure, wherein the control bit structure and the target bit structure obtain quantum levels of excitation from the applied voltages based on an initial excitation level of the control bit structure and an initial excitation level of the target bit structure. 
     The method of the present invention comprises applying a first voltage across a control bit structure, applying a second voltage across a target bit structure, and obtaining quantum levels of excitation within the control bit structure and the target bit structure based on the applied first and second voltages, an initial excitation level of the control bit structure and an initial excitation level of the target bit structure. 
     An object of the present invention is to provide a quantum computer. Another object of the present invention is to provide a quantum computer that can perform parallel gate operations. A further object of the present invention is to provide a quantum computer that can perform parallel gate operations without significant qubit overhead. 
     These and various other advantages and features of novelty which characterize the invention are pointed out with particularity in the claims annexed hereto and form a part hereof. However, for a better understanding of the invention, its advantages, and the objects obtained by its use, reference should be made to the drawings which form a further part hereof, and to the accompanying detailed description, in which there are illustrated and described specific examples of a method and apparatus in accordance with the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Referring now to the drawings in which like reference numbers represent corresponding parts throughout: 
         FIG. 1  illustrates the computer of the present invention; 
         FIG. 2  illustrates the potential and four lowest electronic energy levels for a particular realization of a quantum dot within the computer of the present invention; 
         FIG. 3A  illustrates the energy levels of the transitions in a quantum dot computer of the present invention; 
         FIG. 3B  illustrates a sequence of voltage pulses that effect a two-qubit gate that is equivalent to a CNOT operation in a quantum dot computer of the present invention; 
         FIG. 4  illustrates a schematic diagram of a quantum computer of the present invention using quantum dot spins coupled to a cavity which is near resonance with an intraband transition in the quantum dots; 
         FIG. 5  illustrates the energy level structure, couplings, and detunings within a quantum bit of the computer of  FIG. 4 ; 
         FIG. 6  illustrates an illustration of a readout of a quantum bit in the spin-state computer of the present invention; and 
         FIG. 7  is a flow chart illustrating the steps used to practice the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     In the following description of the preferred embodiment, reference is made to the accompanying drawings which form a part hereof, and in which is shown by way of illustration a specific embodiment in which the invention may be practiced. It is to be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention. 
     Overview 
     A quantum computer of the present invention stores information in the two lowest quantum electronic states of doped quantum dots. Multiple quantum dots are located in a microcavity, and a pair of gates controls the energy levels in each quantum dot. A controlled NOT (CNOT) operations involving any pair of quantum dots can be effected by a sequence of gate voltage pulses which tune the quantum dot energy levels into resonance with frequencies of the cavity or a laser. The duration of a CNOT operation is estimated to be much shorter than the time for an electron to decohere by emitting an acoustic phonon. 
     Quantum Bits and Fundamental Quantum Logic Operations 
       FIG. 1  illustrates the computer of the present invention. The computer comprises two or more structures  100  embedded in a microcavity  126 . Each structure  100  is comprised of a control nanostructure  102  and a target nanostructure  104 . The control nanostructure  102  controls the control bit  102  of the computer, and the target nanostructure  104  controls the target bit  104  of the computer. Although described separately, control nanostructure  102  and target nanostructure  104  are substantially similar and interchangable within the computer. 
     Each nanostructure  102  and  104  comprises outer semiconductor layers  106  and  108  and disks  110 – 114 . Although three disks  110 – 114  are shown, a larger or smaller number of disks  110 – 114  can be used without departing from the scope of the present invention. The disks  110 – 114  are typically smaller in bandgap than the outer semiconductor layers  106 – 108 , e.g., if the disks  110 – 114  are GaAs, then the outer semiconductor layers are of a larger band gap material than GaAs, e.g., AlGaAs. The central disk  112  is typically larger or taller than the outer disks  110  and  114 . The barrier  116  between disks  110  and  112  and the barrier  118  between disks  112  and  114  are sufficiently thin to allow an electron to rapidly tunnel through the barriers  116  and  118 . A structure consisting of a set of three disks  110 – 114  and the two intervening barriers  116 – 118  is hereafter called a quantum dot (QD), referred to herein as control bit  102  and target bit  104 . Each QD  102  and  104  that participates in the quantum computation must have one and only one electron within the QD  102  or  104 . 
     Below and above each QD  102  and  104  is an electrical gate  120  and  122 , shown in QDs  102  and  104 . These gates are used to apply electrical voltages substantially simultaneously to QD  102  and  104  across the length  124  of a QD  102  or  104 . The QDs  102  and  104  are located in a three-dimensional cavity  126 . The cavity  126  can contain many QDs  102  and  104 . 
       FIG. 2  illustrates the potential and four lowest electronic energy levels for a particular realization of a QD within the computer of the present invention. The lowest two energy levels  200  and  202 , also referred to as energy levels |1&gt; and |1&gt;, form the qubits which store quantum information. The third energy level  204 , also referred to as energy level |2&gt;, serves as an auxiliary state to perform conditional rotations of the state vector of the qubit. Voltages applied to the gates  120  and  122  are used to control the spacing between and absolute values of the energy levels of the QDs  102  and  104  via the Stark effect. As shown in  FIG. 2 , the energy levels  200 ,  202 ,  204  and  206  are all below the barrier heights of barriers  116  and  118 , and are allowed energy states in each of the disks  110 – 114 . A large number of individually-gated QDs  102  and  104  are contained in a 3-D microcavity  126  whose fundamental resonance has a wavelength λ C  much longer than the length of a QD  124 . A continuous-wave laser with a fixed wavelength different than λ C  is introduced through one side of the cavity  126 . 
       FIG. 3A  illustrates the energy levels of the transitions in a quantum dot computer of the present invention, and  FIG. 3B  illustrates a sequence of voltage pulses that effect a two-qubit gate that is equivalent to a CNOT operation in a quantum dot computer of the present invention. 
     With reference to  FIG. 3A , energies E 10    300  and E 20    302  show the state 0 to state 1 and state 0 to state 2 energy levels, respectively. The energies of a cavity  126  mode photon hω C ,  304 , a laser photon hω L    306 , and the sum of hω C +hω L    308 , are also shown. The state of an electron in a QD  102  or  104  can be coherently manipulated by tuning E 10    300  and E 20    302  into and out of resonance with  ω C ,  304 , hω L    306 , and the sum of hω C + ω L    308 . 
     A general Hamiltonian describing a QD  102  or  104  interacting with cavity  126  photons and the laser field is given by
 
 Ĥ=     ω   C   â   C   +E   10 ( e )σ 11   +E   20 ( e )σ 22 
 
 +     g   01 ( e ){ â   C +σ 01 +σ 10   +â   C }+ Ω 1,01 ( e ){σ 01  exp( iω   1   t )+σ 10  exp( iω   1   t )}
 
+   12 ( e ){ â   C +σ 12 +σ 12   â   C }+ Ω 1,12 ( e ){ â   C σ 12  exp( iω   1   t )+σ 21   â   C  exp( ωt )}
         where â C  denotes the cavity  126  mode annihilation operator, and   σ IJ =|i×j| is the projection operator from QD state |j&gt; to state |i&gt;.       

     The vacuum Rabi frequencies are g IJ ≈qz IJ e VAC ,
         where 
         e   VAC     =         ℏω   C       2   ⁢     ɛ   0     ⁢   ɛ   ⁢           ⁢   V             
    is the amplitude of the vacuum electric field in the cavity  126 ,   ε=the dielectric constant of the cavity  126 ,   V=the volume of the cavity  126 ,   q=the electronic charge, and   z IJ  is the dipole matrix of the |i&gt; to |j&gt; transition.       

     One step in the CNOT operation is a Rabi oscillation between states |0&gt; and |2&gt; involving both cavity  126  and laser photons at e=e L+C . 
     Operation of the Quantum Computer 
     During the operation of the quantum computer of the present invention, a qubit that stores quantum information is in state |0&gt; or state |1&gt;, and the electric field across the qubit is held at a value where the energy levels of the qubit are not resonant with  ω C ,  ω L , or  ω C + ω L . The value of this electric field is typically zero, but can be other values. The typical value of the electric field is called the fiducial value of the electric field. For e≈e C , and either the cavity  126  contains one photon or the qubit state vector is in state |1&gt;, then the qubit will execute vacuum Rabi oscillations with frequency g 014 , in which the probability of finding one photon in the excited state oscillates ninety degrees out of phase with the probability of finding one photon in the cavity  126 . For e≈e L , the state vector of the qubit rotates between states |0&gt; and |1&gt; with laser Rabi frequency Ω 1,01 . For e≈e L+C , and the cavity  126  contains one photon and the qubit state vector begins in state |0&gt;, then the qubit rotates between states |0&gt; and the auxiliary state |2&gt; with frequency Ω(e L+C ). If either the qubit is in state |1&gt; or the cavity  126  does not contain a photon, then the qubit state vector is not rotated for e≈e L+C . 
     The Controlled NOT Operation 
     A Controlled NOT (CNOT) operation is effected by a series of voltage pulses applied across the gates of a pair of qubits. The pulses begin and end with the qubit at the fiducial electric field (e=0), and rise to a target value of e C , e L , or e L+C . 
     With reference to  FIG. 3B , the cavity  126  always begins without any photons. First, a “π” pulse  310  with height e C    312  and duration π/2g 01 ,  314  is applied to the control bit  102 , e.g., across contacts  120  and  122  of QD  102 . If the control bit  102  is in state |0&gt;, the control bit  102  is unaffected. If the control bit  102  is in state |1&gt;, the control bit  102  rotates into state |0&gt; and acquires a phase i, and the cavity  126  acquires a single photon. 
     A 2π pulse  316  with height e L+C    318  and duration π/Ω(e L+C )  320  is then applied to the target bit  104 . If the target bit  104  is in state |1&gt;, the target bit  104  is unaffected. If the target bit  104  is in state |0&gt;, and the cavity  126  contains one photon, the target bit  104  acquires a phase of −1. 
     A pulse  322  with height e C , substantially identical to the π pulse  310 , is again applied to the control bit  102 . If there is a photon in the cavity  126  it is absorbed by the control bit  102 , returning the control bit  102  to state |1&gt; while the control bit  102  acquires another phase i. The end result is a gate in which the state vector of the two-qubit system, e.g., the two qubits being the control bit  102  and the target bit  104 , acquires a phase −1 if and only if both control and target bits  102  and  104  are initially 1. 
     The sequence of state-vector rotations which is effected by the series of electric field pulses is identical to the sequence effected by a series of laser pulses applied to cold trapped ions. In order to effect a CNOT operation, i.e., inversion of the target bit  104  if and only if the control bit  102  is 1, it is necessary to apply to the target bit  104  “π/2” and “3π/2” pulses with height e L  and durations π/(4Ωe L+C ) and 3π/(4Ω L,01 ), respectively, before and after the sequence shown in  FIG. 3B . 
     In essence, the electric field pulses applying a first voltage across a control bit structure and a second voltage across a target bit structure. The quantum levels of excitation within the control bit structure and the target bit structure are obtained based on the applied first and second voltages, an initial excitation level of the control bit structure, and an initial excitation level of the target bit structure. As described above, the target bit structures and the control bit structure are interchangeable within the present invention, e.g., for a first computation, a first structure can be the control bit structure and a second structure can be the target bit structure. For a second computation, the first structure can be the target bit structure and the second structure can be the control bit structure. 
     To ensure the fidelity of CNOT operations, the rise and fall times of the pulses  310 ,  316 , and  322  must be short compared to the period of the Rabi oscillation at the target bit  104  electron. At the same time, in order to minimize the probability of a transition between the |0&gt; and |1&gt; states induced by the ramping electric field, the changes to the Hamiltonian must be adiabatic, e.g., δt&gt;&gt; /E 10 . Further, the timing between the successive pulses  310 ,  316 , and  322  in the CNOT operation must be adjusted to compensate for the quantum-mechanical phases accumulated by inactive qubits in their excited states. It also may be required to adjust the heights and durations of the pulses  310 ,  316 , and  322  to account for alternating current Stark shifts in the energy levels of the QDs  102 – 104  which are induced by the laser field. 
     Other Actions Performed on the Quantum Computer 
     Other actions that are performed or required by a quantum computer include initialization of the computer, inputting data, reading out the data stored in the computer, correcting errors in the computer, and decoherence of the electronic state of the QD  102  and  104 . 
     Initialization of the quantum computer requires that each qubit  102 – 104  be in a well-defined state prior to any quantum computation. The present invention performs initialization by applying the proper fiducial voltage to the gates  120 – 122  of the qubits  102 – 104 , and a proper temperature to each qubit  102 – 104  for the requisite amount of time, until each qubit  102 – 104  relaxes to a ground state. Typically, a voltage of 0 volts, a temperature of T&lt;120 Kelvin, and a wait of less than one second ensures that all qubits  102 – 104  are in state |0&gt;. 
     To input initial data, arbitrary rotations of the state vectors of the qubits  102 – 104  are required to load data into the qubit  102 – 104  registers. Arbitrary one-bit rotations of the qubits  102 – 104  are effected in the present invention by using Rabi oscillations induced by the laser field, by applying pulses with height e L  and duration between 0 and 2π/(Ω L,01 ). To read the data back from the qubit  102 – 104  registers after a quantum computation is completed, the state of each qubit  102 – 104  is measured. A narrow-band detector with high quantum efficiency is used to detect single terahertz (THz) photons at the frequency of the cavity  126  mode ω C . The qubits  102 – 104  can then be read out sequentially by tuning each qubit  102 – 104  to ω C . If the qubit  102 – 104  is in state |1&gt;, it will emit a photon which will be detected by the narrow-band detector. If the qubit  102 – 104  is in state |0&gt;, no photon will be emitted. The emissions and non-emissions from each qubit  102 – 104  can then be read by the detector and reported. 
     For error correction, the qubits  102 – 104  must be executed in parallel. To perform parallel execution, the cavity  126  is enlarged to create several cavity  126  modes in the frequency range over which the QD  102 – 104  energy level spacings are tunable. A separate but equivalent approach is to couple nearest-neighbor QDs  102 – 104 , and perform an enlarged cavity  126  schema as in the present invention. 
     Decoherence 
     Decoherence of the electronic state of the QD  102 – 104  as well as decoherence of the cavity  126  photons are problematic areas for quantum computers  100 . Deductions on the energy relaxation times result in times of q/I=10 −7  seconds for transitions with energies near 50 microelectron volts (μeV). However, the geometry of the present invention is quite different, and, as such, results in different relaxation times. The lifetime of a cavity  126  photon must be sufficiently long to enable many NOT operations with high fidelity. As such, the cavities must be low-loss, few-mode THz cavities. 
     Decoherence and CNOT Performance Times 
     Consider now a specific GaAs/AlGa is QD and lossless dielectric cavity  126  designed to minimize the time required for a CNOT operation, while at the same time avoiding the emission of longitudinal optical (LO) phonons ( ω LO ≈36 meV in GaAs) and also minimizing the rate of acoustic phonon emission. Cavity  126  and laser photon energies are chosen to be 11.5 and 15 meV. These energies are sufficiently large to enable an adequate vacuum electric field e VAC  while their sum is still comfortably smaller than  ω LO . Assuming perfect cylindrical symmetry of the disks  110 – 114 , the states  200 – 206  are labeled with quantum numbers |1,m,n&gt;, associated with the radial, azimuthal and axial degrees of freedom, respectively. 
     The potential along the cylindrical axis of the QD (z-direction)  102  and the numerically-computed four lowest energy levels  200 – 206  are depicted in  FIG. 2 . FIG.  3 A shows the transitions E 10  and E 20  vs. electric field e. Assuming infinite walls in the radial direction, the radial wavefunctions are given by Bessel functions. The difference between the energy of the ground state  200  and first radial excited state  202  is ΔE R =30 meV for radius of the disks  110 – 114  of a=13 nm, assuming m*=m C /15. This is higher than the highest energy reached by an electron during a CNOT operation (26.5 mEv= ω 1 + ω C ), eliminating dccoherence arising from coupling between axial and radial excited states of the QD  102 – 104 . 
     The time required to execute a CNOT operation for the QD structure of  FIG. 1  is estimated at 150 microseconds. Unconditional 1-bit rotations which occur at e=e L  take only a few picoseconds for a laser electric field of 30 kV/m. Although the laser might need attenuation for such rotations to have a transition time for the electrical pulse shorter than the period of the Rabi oscillation at the target electric field, the decoherence times and transition times allow the computer to perform several thousand CNOT operations before decoherence occurs. 
     Additional Embodiment of the Quantum Computer 
     The present invention can also be embodied as a quantum dot doped with a single electron. The spin-states of this conduction-band electron can serve as a qubit with long coherence times. 
       FIG. 4  illustrates a schematic diagram of a quantum computer of the present invention using quantum dot spins coupled to a cavity which is near resonance with an intraband transition in the quantum dots. 
     Disk  400  is a whispering gallery mode resonator for terahertz radiation, typically fabricated from an undoped semiconductor material, such as silicon or gallium arsenide. Quantum dots  402 – 426  are embedded in disk  400 . Each quantum dot  402 – 426  contains a single electron. Each quantum dot  400 – 426  has an intraband transition which is close to the resonant frequency of the same single mode of the whispering gallery mode resonator disk  400 . For an alternative implementation, a magnetic field  428  can be used. Laser beams  430 – 436  are focused on quantum dots  402 – 426 , such that a set of laser beams  430 – 432  are focused on each quantum dot  402 – 426 . For ease of illustration, only laser beams  430 – 436  are shown, but each quantum dot  402 – 426  has a set of laser beams, e.g., L n   a , L n   b , L n   c , . . . for quantum dot “n”  402 – 426 . Each laser beam  430 – 436  has a frequency and intensity which can be adjusted independently of the other laser beams  430 – 436 . The laser beams  430 – 436  are used to effect one- and two-bit quantum logic gates from the quantum dots  402 – 426 . Alternatively, the cavity of disk  400  can be embodied as a defect in a photonic bandgap structure instead of a whispering gallery mode resonator, or in a superconductor. The cavity structure shown in  FIG. 4  illustrates a spin-terahertz cavity quantum electron dot structure  438 . Although shown in a substantially horizontal orientation, quantum dots  402 – 426  can be coupled in any direction, e.g., horizontal, vertical, or any combination of horizontal and vertical orientations. Each quantum dot  402 – 426  can also have internal structures similar to that described in  FIG. 1 , thereby making each quantum dot  402 – 426  a quantum bit in a quantum computer. 
     This structure  438  allows for a spin-splitting of the ground-state quantum dot  402 – 426  conduction band electron, using either a non-zero magnetic field  428  across disk  400 , or a pseudo-magnetic field generated using an off-resonant circularly polarized laser beam  430 – 436 . When using laser beams  430 – 436 , large effective magnetic fields are used to introduce large effective magnetic fields yielding a spin-splitting that can be as large as 5 meV. 
     Further, one bit rotations of a single quantum dot  402 – 426  electron spin can simply be achieved by spin-flip near-resonant Raman transitions via intermediate valence-band states. The large spin-orbit coupling in the valence band enables coherent flipping of the electron spin in short time scales using two laser beams, e.g.,  430 – 432  for quantum dot  402 , with orthogonal linear polarizations that can realize π/r pulses, where r is any real number. If the spin splitting is generated by the ac-stark effect of laser beams  430 – 436  rather than a magnetic field  428 , then the spin-flipping can be accomplished by irradiating the entire sample with an oscillating magnetic field, and using the ac stark effect to tune the spin-splitting of selected quantum dots into resonance with the oscillating magnetic field for a duration long enough to effect π/r pulses. 
     Structure  438  allows for a cavity mode that has an energy that corresponds to an intra-band energy spacing. The advantage of structure  438  and structure  100  over other embodiments using this terahertz cavity-quantum electron dot regime is that the wavelength of the cavity mode, which in turn determines the length scale of the quantum dot  402 – 426  array, could exceed 100 microns, which allows for a large number of quantum dots  402 – 426  to be coupled through the same cavity mode. 
       FIG. 5  illustrates the energy level structure, couplings, and detunings within a quantum bit of the computer of  FIG. 4 . 
     To effect non-trivial two-qubit interactions, structure  438  uses selective introduction of a transverse spin-spin coupling between two distant quantum dots. However, structure  438  allows for a coherent drive that couples the ground state  500  and excited state  502  with opposite spin in a single quantum dot  402 – 426 . Further, the cavity mode couples ground state  500  and excited state  502  with the same spin. The coherent drive at a particular quantum dot n  402  and the cavity mode are detuned by an energy  504 , shown as δ c-c   n . Together, the coherent drive and the cavity coupling provide a Raman coupling between spin up and spin down in the quantum dot  502 , separated by an energy  506  δ spin   n . The detuning of the Raman transition in a particular dot from the spin-flip transition is Δ n =δ c-c   n −δ spin   n . Distant quantum dots with the same detuning Δ experience an effective 2 qubit interaction which leads to controlled entanglement in general and CNOT operations in particular. CNOT operations between pairs of quantum dots  402  and  404  with different shared detunings can thus proceed in parallel with the present invention. For example, if quantum dots  402  and  404  share detuning Δ a , and quantum dots  406  and  408  share a detuning Δ b  not equal to Δ a , the CNOT operations involving quantum dots  402  and  404  can proceed in parallel with the CNOT operations involving dots  406  and  408 . 
     The coherent drive can be implemented in a variety of ways. For example, two of the laser beans  430  and  432 , with frequencies differing by ω coherent drive , shown as difference  508  in  FIG. 5 , can be applied to each individual quantum dot  402 – 426 . In this case, the coherent coupling is enhanced if the shape of the quantum dot  402 – 406  is asymmetric. An alternative embodiment of implementing coherent coupling is via a coherent terahertz field and a magnetic field  428  that is perpendicular to the effective magnetic field induced by a circularly polarized laser beam  430 . 
     The method described with respect to the present invention is useful in implementing a two-qubit operation, like a CNOT operation, between distant spins embedded in a cavity which is resonant with an intraband transition. 
     One method is to set the real magnetic field  428  B=0. Two laser beams  430  and  432  are used, e.g., L m   a  and L m   b  and are incident on quantum dot  402 , while a second pair of laser beams  434  and  436  are incident on quantum dot  404 . One of these laser fields, e.g., L m   a , is circularly polarized, and determines the spin splitting of the ground state of quantum dot  402 , via the ac Stark effect. The second laser field focused on quantum dot  402 , L m   b , is detuned from the frequency of L m   a  by ω coherent drive , providing an effective coherent drive. When the two-photon detunings Δ are chosen, they are determined by the energy difference between spin splitting and the energy difference of the cavity mode and the coherent drive and are identical for the control and target qubits. Transverse spin-spin coupling can thus be established. Such coupling can implement a CNOT gate. One advantage of this particular implementation is that the energies of the spin states in a quantum dot  402 – 426  are different only while the lasers  430 – 436  are turned on. While the lasers  432 – 436  are off, no quantum-mechanical phase difference between ground state  500  and excited state  502  will accumulate. 
     Another method to implement the two-qubit operation is to set an external magnetic field  428  B=B x  where field  428  is substantially perpendicular to the effective magnetic field induced by the circularly polarized laser beam  430 . For example, in disk-shaped quantum dots  402 – 426  with strong confinement in the z-direction, a circularly polarized laser field  430  is applied that generates an effective magnetic field in the z-direction. A coherent terahertz field is applied that is polarized parallel to the cavity mode. In such a configuration, parallel linearly polarized coherent terahertz and cavity modes with energy difference near the ground-state spin-splitting can be used to achieve the necessary coupling between the two spin states. 
       FIG. 6  illustrates an illustration of a readout of a quantum bit in the spin-state computer of the present invention. The states of the quantum bits  402  and  404  can be read by using resonant fluorescence of the quantum bits  402  and  404 . A magnetic field  428  is applied to disk  400 , which splits the spin states of the electron and the hole in each quantum dot  402 – 426 . A circularly polarized laser beam  430  is tuned to a transition between the valence band and one of the spin states  600 – 606  in the quantum dot  402 – 426 . If the spin state is empty, e.g., states  600  and  602  in quantum dot  404 , the laser  430  field alternatively populates and stimulates emission from the empty state  602 , which results in a resonance fluorescence signal. The resonance fluorescence signal lasts for as long as the state  602  remain empty. If the state  602  is occupied by an electron, e.g., as shown in quantum dot  402 , the absorption of the laser  420  field is Pauli blocked, and no light is emitted from the quantum dot  402 . The emission/lack of emission provides a readout of the state of quantum dots  402 – 426 . 
     Process Chart 
       FIG. 7  is a flow chart illustrating the steps used to make the quantum dots of the present invention. 
     Block  700  illustrates performing the step of growing a first quantum dot layer on an edge layer. 
     Block  702  illustrates performing the step of growing a first barrier layer on the first quantum dot layer. 
     Block  704  illustrates performing the step of growing a second quantum dot layer on the first barrier layer. 
     Block  706  illustrates performing the step of growing a second barrier layer on the second quantum dot layer. 
     Block  708  illustrates performing the step of growing a third quantum dot layer on the second barrier layer. 
     Block  710  illustrates performing the step of growing a second edge layer on the third quantum dot layer wherein the edge layer, first quantum dot layer, first barrier layer, second quantum dot layer, second barrier layer, third quantum dot layer, and second edge layer comprise at least one bit in the quantum computer. 
     To grow the quantum dots of the present invention as shown in  FIG. 1 , stacked self-assembled quantum dots can be used. Another method is to make QDs made by growing GaAs/AlGaAs quantum wells with the conduction band profile tailored to give the desired potential in the z-direction, depositing small islands on top of the quantum well to serve as an etch mask, etching through the quantum well layers which are not protected by the islands, and then regrowing AlGaAs. The growth methods used to grow the QDs  102  and  104  comprise those used in the art, such as Metal Organic Chemical Vapor Deposition (MOCVD), Metal Organic Molecular Beam Epitaxy (MOMBE), wet or dry etching of the materials, or other growth methods. 
     CONCLUSION 
     In summary, the present invention discloses an apparatus and method for quantum computing. The apparatus comprises a control bit structure, a target bit structure, and gate electrodes, coupled to the control bit structure and the target bit structure, for applying a voltage across the control bit structure and the target bit structure, wherein the control bit structure and the target bit structure obtain quantum levels of excitation from the applied voltages based on an initial excitation level of the control bit structure and an initial excitation level of the target bit structure. 
     The method of the present invention comprises applying a first voltage across a control bit structure, applying a second voltage across a target bit structure, and obtaining quantum levels of excitation within the control bit structure and the target bit structure based on the applied first and second voltages, an initial excitation level of the control bit structure and an initial excitation level of the target bit structure. 
     The foregoing description of the preferred embodiment of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto.