Quantum Computing Concept and Realization Quantum Computing by variablepitch343


									 Quantum Computing:
Concept and Realization

K. W. Kim, A. A. Kiselev, V. M. Lashkin,
      W. C. Holton, and V. Misra

    North Carolina State University

               NC STATE UNIVERSITY

- Classical vs. Quantum
- Performance vs. number of elements
- Gedanken quantum computer
- Implementations and comparison
- Our current proposal
     - Physics
     - Design
     - Future projections
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Classical Bit
vs. Quantum Qubit
         V1                            Quantum Bit
1=               |1〉 =               is any two-level
                                    quantum system,
0=       V0      |0〉 =                 for example,
                                      Electron Spin
    =?                     = C1|1〉 + C0|0〉
It’s an error!         It’s a superposition!
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Two spins:
          Four states in superposition: 22
          = C00|00〉 + C01|01〉 +
          Entanglement of spins 1 and 2
N spins:
               2N states in superposition
    ...      0...00 + 0…01 + … + 1…11
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Problem Solving:
              tractable vs. intractable

                      NP complete


- A classical computer solves problems of type P
- An N-bit quantum computer solves exponential problems
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                                               Moore’s Law
                                                         as a potential                         limitation
Number of chip components ~ performance

                                                           Classical Age                    Quantum Age



                                          106                                                Quantum Device
                                                101          100               10-1            10-2           10-3
                                                                   Feature Size (microns)
Another side --- cryptography
Security enabled
  by the Uncertainty Principle
  and by the No-Cloning Theorem

Basic ideas of QC
                                      |1〉 =        |0〉 =
- Information stored
  in spin 1/2 quantum systems (qubits)
- Quantum computation scheme
Initialization     Processing                 Measurement

  ψ i → U M KU 2U1 ψ i → ψ
         ˆ    ˆ ˆ
                                 f             0       1
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Fundamental gates:
  only two required for all operations
 1.       2 single   bit rotation
                         input                        output

 2. Controlled NOT
                A                                 A
                        B                         A XOR B
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Quantum computer
* Hamiltonian (coupled)
     Hˆ = 1 ω 1σˆ 1 + 1 ω 2σˆ 2 + 1 J σˆ 1 • σˆ 2
          2           2           4
           ω2                      ω2 + J         ω1 + J
                                            2              2
                           01                      ω1 − J
           ω2                        ω2 − J
                           00                 2

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Information processing
            via coherent pulses
- use superpositions
                                (ω                )
               00   →
                          1 2
                             ( 00 + 01
- use entangled states
                            (                 )
                             ( 00 + 11
                        π ω1 + J 2
               00    →                             )

Parallel computation and speed up!
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QC Requirements

• Possibility to address qubits
• Initialize qubits
• Perform one- and two-qubit operations
• Read-out final result
• Small decoherence rate compared to
  ops rate
• Scalability (the more qubits - the better)

- Not solid state QC
  * Trapped ions
  * NMR on molecules
  * Electrons trapped on liquid He
- Solid state QC
- Orbital degree of freedom
- Spin degree of freedom
- Macroscopic wavefunction in superconductor
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      Asymmetric III-V Quantum Dot Quantum Computer
      Asymmetric III-V Quantum Dot Quantum Computer

                                                          Top Contact

 Electrode                           Asymmetric                n
Surrounding                          AlGaAs/GaAs
   Pillar                            Quantum Dots              p

                                                               n+         Oxide
       Source               Source                                       Silicon


                GaAs Substrate                                                                                           0

                                                       Silicon pillar                                  5              x=
                                                                                                 0.4              ,

                                                                                           x   =             As
   Electric dipole qubit transitions with                                              ,              a 1-            Qubits unique by
                                                                                    As              G
                                                                                                 Al x
   dipole-dipole coupling                                                  G a 1-                                     fabrication
                                                                        Al x
                                        Sanders, Kim and Holton
                                       Phys. Rev. A 60 #5 4146 Nov 99
   Electrons trapped in quantum dots coupled to
   Electrons trapped in quantum dots coupled to
               terahertz cavity photons
              terahertz cavity photons

III-V Quantum dots distinguishable
electrically with each quantum dot
containing one electron. Dot array in
micro-cavity. Coupling via terahertz cavity
modes.                                            Electric dipole qubit transitions.

                       Sherwin, Imamoglu, and Montroy
                           Phys. Rev. A 60 #5 3508 Nov 99
            Quantum dot spins and cavity QED
            Quantum dot spins and cavity QED

III-V quantum dot electron spins coupled          Qubit coupling mediated by
       through microcavity mode                   microcavity mode

   Qubits individually addressed by
   tapered fiber tips

             Imamoglu, Awschalom, Burkard, DiVincenzo et al
                           PRL 83 #20 4204 15 Nov 99
Coupled Nuclear Spins Arrayed in Silicon
Coupled Nuclear Spins Arrayed in Silicon
         Quantum Computer
         Quantum Computer

   P – impurities with spin = ½ interact through trapped
             electron to form coupled system

                      SET used to measure spin-state of final

                Nature 393 133 14 May 1999
 Electron Spin Transistor (Transpinor) for Quantum
 Electron Spin Transistor (Transpinor) for Quantum

Qubits distinguishable by addressing. Coupling by exchange interaction.
 in Silicon-Germanium
    Heterostructures                              in Silicon Quantum Dots

                                           Potential pad
                                               Si Oxide
                                              Doped Si

        Wang et al                                         Kim and Holton
Quant-ph/9905096 11 June 1999
                  Solid State Quantum Computers
                  Solid State Quantum Computers
                            Parameter Comparison
                                   Parameter Comparison
                                  OrbitalDegree of Freedom
                                  Orbital Degree of Freedom

                            Sanders, Kim and        Sherwin, Imamoglu &        Platzman & Dykman
                                  Holton                   Montroy
                         Electrons trapped in III- Electrons trapped in III-   Electrons on liquid He
                             V quantum dots        V quantum dots in cavity           Surface
                           Electronic states of      Electronic states of       Electronic states of
Storage Mechanism
                            trapped electrons         trapped electrons          trapped electrons
                            Controlled size of                                   Externally applied
Qubit Distinguishability                                 Voltage pulse
                               quantum dots                                           voltage
Single bit Ops Rate               1013 Hz                   109 Hz                    109 Hz
Two bit Compute Rate              1010 Hz                   108 Hz                    107 Hz
Decoherence Time                   10-6 s                   10-4 s                    10-4 s
Ops to Decoherence                104 ops                  104 ops                   103 ops
Initialization Process       77K Temperature           Low Temperature          0.1K Temperature
                           Optical emisson from     TACIT photon detector      Electron extraction via
Readout Process                 ensemble                within cavity                 tunneling
Scalability                      50 qubits               > 100 qubits                109 qubits
                      Solid State Quantum Computers
                      Solid State Quantum Computers
                                Parameter Comparison
                                      Parameter Comparison
                                      JJ               Spin Degree of Freedom
                                                      Spin Degree of Freedom

                            Makhlin, Schon &        Buckard, Loss &      Imamoglu, Awschalom,
                               Shnirman               DiVincenzo            Divincenzo et al
                             Cooper pair with     Electrons trapped in Electrons trapped in III-V
                           superconducting box     III-V quantum dots       Quantum Dots

                                                   Magnetic states of      Magnetic states of
Storage Mechanism          Josephson junctions
                                                   trapped electrons       trapped electrons
                            Physical location        Magnetic field
Qubit Distinguishability                                                    Physical location
                                     10                     10                       11
Single bit Ops Rate             10        Hz           10 Hz                    10        Hz
Two bit Compute Rate                 11                     10                       10
                                10        Hz           10        Hz             10        Hz
Decoherence Time                 10-7 s                 10-9 s                   10-4 s
Ops to Decoherence              104 ops                10 ops                  106 ops
Initialization Process      Low Temperature        77K Temperature           Not described
                           Coupling to normal                           Interaction w. laser field
Readout Process                                    Photon Scattering
                            state transistor                               & photon emission
Scalability                     20 qubits            Not discussed            > 100 qubits
                  Solid State Quantum Computers
                  Solid State Quantum Computers
                            Parameter Comparison
                               Parameter Comparison
                                Spin Degree of Freedom
                               Spin Degree of Freedom

                                                  Vrijin, Yablonovitch, Sanders, Kim and
Author                            Kane
                                                       Wang et al.            Holton
                                                  Electrons trapped at Electrons trapped in
Structure                   P-impurities in Si
                                                  P-impurities in Si/Ge quantum dots in Si
                            Nuclear magnetic       Magnetic states of   Magnetic states of
Storage Mechanism          states of P impurity    trapped electrons    trapped electrons
                            Voltage applied          Voltage applied       Variable local
Qubit Distinguishability
                            locally to P-gate       locally to P-gate     magnetic field

Single bit Ops Rate              104 Hz                1010 Hz               1010 Hz

Two bit Compute Rate             104 Hz                 108 Hz               108 Hz
Decoherence Time                 106 s                  10-3 s                10-3 s
Ops to Decoherence             1010 ops                105 ops              105 ops
Initialization Process     0.8K Temperature        Low Temperature      Low Temperature
                           Charge transfer to      Charge transfer to   Charge transfer to
Readout Process
                             singlet/triplet         singlet/triplet      singlet/triplet
Scalability                      6                      6                     6
                              10 qubits              10 qubits             10 qubits
   Electron Spins Trapped Beneath
       Coupled Quantum Dots


                      ψ1             ψ2
! Hamiltonian for a single quantum dot pair.
          H = µ B gB 1 S 1 + µ B gB 2 S 2 + JS 1 • S 2
! Exchange coupling between adjacent quantum dots.
                r r          r * r           r * r
     2 J = ∫ u (r1 − r2 ) 1 (r1 ) 1 (r2 ) 2 (r2 ) 2 (r1 )dV
                        ψ       ψ       ψ       ψ

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         Typical Design Parameters


• Pillar radius ~50 nm                        Gate
• Gate radius~15 nm
• Pillar height~100 nm
                                             Undoped    65nm
• SiO2 region~15 nm                             Si
• Doping region~20 nm
• Donor concentration ~3.e18                 Doped Si   20nm
• Temperature~1.6 K

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      Confining in the radial direction

• Strong electrostatic
  confinement in the radial
  and z-directions along
  with the SiO2/Si interface
  potential barrier serves
  to confine a single
  electron in the quantum

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       Single electron occupancy

• Single electron
  occupancy in the
  quantum dot holds over a
  finite range of the gate
• 0.23<V<0.31 (Volts)

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           Exchange energy control

• A single electron trapped
  beneath each dot gate
  provides the magnetic spin
  utilized in the quantum
  computer. A gate
  intermediate to the gate that
  performs the electron
  trapping can serve to vary
  the coupling between a
  given pair of electrons.

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Reconfigurable Quantum Computer Showing
Reconfigurable Quantum Computer Showing
        Transpinor Output Sensors
        Transpinor Output Sensors

       Current conductors to generate time dependent magnetic field bias, enabling single qubit addressing

        Potential pads enabling single electron trapping
                                                                                             Transpinor output
      Wave function distortion pads                                                          detectors on periphery

   Charge transfer pad


 Unique current addressing. Controllable coupling. Uniform µ-
                wave field. Transpinor output.
                                   Address Array
                               provides unique magnetic field at addressed qubit

         Interconnect array                                                        Pulsed current to generate
         Y-axis                                                                    local magnetic field

    Pulsed Magnetic field
    into paper from blue &
    red currents

     Quantum Dot

   Pulsed Magnetic field out
   of paper from blue & red


Interconnect array
              Qubit Addressing
!For an external magnetic field = 3.0 Tesla
!The resonant microwave frequency = ω = 94 GHz
!And with a line width ~ 0.3 gauss or 1 MHz
!And requiring a magnetic field address on 30x line width
 = 9 gauss
!A current in the addressing wire = 1.12 10-4 amp
!And with a wire dimension of 100x100 angstrom
!The current density = 5 107 amp/cm2

!This is just at the threshold for electro migration for dc
 current at RT, but is OK for our application of pulses at
 low temperature.
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    Pulsed Microwave Field Generated Using a Microstrip

                            Permanent Magnet              Static Magnetic Field *
                                                          From Permanent Magnet

                                                       Quantum Dot Quantum
Strong microwave H fields                              Computer Silicon Chip

           Pin diode                               Pin diode                      Input

        Ceramic Substrate
                                                                  Pin diode bias for rapidly turning
                                                                  on and off the H field

                                                               * Interconnect wires on chip to generate
                                                               pulsed magnetic field at each qubit
                                                                and chip pin-out not shown in this figure.

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        Fabrication of Silicon Q-Dot Array
" Manufacturable using Integrated Circuit technology specified for the 70-
  nm technology node. (International Technology Roadmap for
  Semiconductors, 1999 edition).
" Layout and addressing for dynamic Quantum Computer control
  analogous to DRAM design and manufacture. (number of metal/dielectric
  layers considerably less than for 1Mbit DRAM).
" Resulting Quantum Computer chip coupled to microwave radiation field
  at ~ 94 GHz by placement in stripline cavity.
   " External magnetic field ~ 3.0 Tesla provided by permanent magnet
     outside the microwave cavity.
" Readout achieved by charge transfer via SETs on periphery (not shown)
  dependent on spin orientation (similar to readout for other proposed
  Quantum Computer designs based on spin).

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      Distinct Advantage of Design

# Scalable using mainstream silicon technology.
  # 1,000,000 qubits.
# Hi-speed single bit ops rate and compute rate.
  #Both readily tunable.
# Randomly and individually addressable qubits.
# Large number of ops before loss of coherence.
  # 100,000 ops to coherence loss.
# Dynamically Reconfigurable.

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