# Quantum Computing Concept and Realization Quantum Computing by variablepitch343

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```									 Quantum Computing:
Concept and Realization

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

North Carolina State University

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Outline

- 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〉 +
C10|10〉+C11|11〉
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
Universal
Exponential

NP complete
NP

P

- 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

1018
Classical Age                    Quantum Age

1014
2010

10
2000
10
1990

106                                                Quantum Device
1970
CMOS
102
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

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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
π
1.       2 single   bit rotation
input                        output
R

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
11
ω2                      ω2 + J         ω1 + J
2              2
10
ω1
01                      ω1 − J
2
ω2                        ω2 − J
00                 2

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

Parallel computation and speed up!
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QC Requirements

individually
• Initialize qubits
• Perform one- and two-qubit operations
• Small decoherence rate compared to
ops rate
• Scalability (the more qubits - the better)

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Implementations
Implementations
- 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

Drain
Gate
Insulator
Top Contact

p+
Electrode                           Asymmetric                n
Surrounding                          AlGaAs/GaAs
Pillar                            Quantum Dots              p

n+         Oxide
Source               Source                                       Silicon

.2

s
GaAs Substrate                                                                                           0

aA
Silicon pillar                                  5              x=
0.4              ,

G
x   =             As
x
Electric dipole qubit transitions with                                              ,              a 1-            Qubits unique by
As              G
Al x
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

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
state

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

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

Si Oxide
Doped Si
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
Author
Holton                   Montroy
Electrons trapped in III- Electrons trapped in III-   Electrons on liquid He
Structure
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
JJ               Spin Degree of Freedom
Spin Degree of Freedom

Makhlin, Schon &        Buckard, Loss &      Imamoglu, Awschalom,
Author
Shnirman               DiVincenzo            Divincenzo et al
Cooper pair with     Electrons trapped in Electrons trapped in III-V
Structure
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
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
singlet/triplet         singlet/triplet      singlet/triplet
Scalability                      6                      6                     6
10 qubits              10 qubits             10 qubits
Electron Spins Trapped Beneath
Coupled Quantum Dots

B

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
V

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Typical Design Parameters

30nm

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

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

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Single electron occupancy

• Single electron
occupancy in the
quantum dot holds over a
finite range of the gate
voltage:
• 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

Magnetic
Field

Unique current addressing. Controllable coupling. Uniform µ-
wave field. Transpinor output.
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
Electrode

Pulsed Magnetic field out
of paper from blue & red
currents

qubit

Interconnect array
X-axis
!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
Resonator

Permanent Magnet              Static Magnetic Field *
From Permanent Magnet

Quantum Dot Quantum
Strong microwave H fields                              Computer Silicon Chip

Critical
coupling
Microwave
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
Q-Dot
Q-Computer
Q-Computer
" 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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# Scalable using mainstream silicon technology.
# 1,000,000 qubits.
# Hi-speed single bit ops rate and compute rate.