Group Presentation

1
Quantum Computation Physical Implementation in
Silicon
Cheuk Chi Lo

• Group Presentation
• March 9, 2005

2
Presentation Overview

• Introduction Why Quantum Computers?
• Fundamentals of QC
• Considerations for Realizing QC
• Silicon based QC
• Summary and Conclusions

3
(I) Introduction Why Quantum Computers?
4
Future of Computation

• Nano-computers?
• DNA Computation
• Molecular Electronics
• Quantum Computation

Popular Science (June 2002)
5
Why Quantum Computation?

• Information is physical ? Manipulation of
  information is determined by the physics available

• More tools are available to manipulate
  information in the quantum world
• Can design better algorithms to solve computation
  problems

6
Why Quantum Computation?

• Information is physical ? Manipulation of
  information is determined by the physics available

• More tools are available to manipulate
  information in the quantum world
• Can design better algorithms to solve computation
  problems

7
Why Quantum Computation?

• Information is physical ? Manipulation of
  information is determined by the physics available

• More tools are available to manipulate
  information in the quantum world
• Can design better algorithms to solve computation
  problems

8
The Quantum Advantage

• Topology of Quantum Information

MA Nielsen, Scientific American, (Nov 2002)

• Exponential speed-up can be accomplished for
  certain tasks
• For instance, factoring a 300 digit number
  (RSA)
• Classical ? 150,000 yrs at tetrahertz speed
• Quantum ? lt1sec at tetrahertz speed

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(II) Fundamentals of QC
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New tools from a quantum world

• The two most useful resources that we get from a
  QC (that are not available from a Classical
  Computer) are
• Superposition of quantum states
• Entanglement of different quantum particles
  (interaction)
• E.g. Bell States/EPR pairs

Y? a1? b0?
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The Bit and the Qubit

• Computational Basis
• Classical Bit
• Information contained is either 1 or 0
• Quantum Qubit
• superposition of 1 and 0 possible
• Bloch sphere representation
• Analog bit? Not quite ? qubit collapses to one
  of the eigenstates upon measurement

Y? a0? b1?
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Qubit Operations

• All operations (gates) must be represented by
  unitary operators (i.e. U-1UI). (This is also
  the only constraint on quantum gates)
• Unitary gates preserve total probability adds up
  to 1 after operation
• Also implies that operations are always time
  reversible (can determine input from output)

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Single Qubit Gates
NOT
Z-Gate
Hadamard (H)
. .
Infinite number of single-qubit unitary gates!
General 2x2 unitary operation
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Multiple Qubit Gates
Universal Gates
NAND
Cant be used since irreversible!
C-NOT
(used in combination with single qubit operations
for universality)
B-Gate
J. Zhang et al, PRL, 93(2) 020502-1 (2004)
Any arbitrary quantum gate can be implemented by
using two qubit operations (such as C-NOT) along
with single qubit operations.
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Simulating a Classical Computer

• To simulate a classical computer using a QC
• Can make use of Toffoli gates (which is
  reversible)
• Implementing the Classical NAND gate
• Implementing the Classical FANOUT
• We can do anything Classical computers can do
  using QC!

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Quantum Parallelism

• Quantum Parallelism
• Evaluate the output for a given function, f(x),
  for many different values of x simultaneously
• For example, suppose f(x) is a function with
  one-bit domain and range f(x) 0,1 ? 0,1
• We can design a quantum circuit Uf that computes
  for any input state x, ygt x, ygt ? x, y?f(x)gt
• Obtain the results simultaneously for both f(0)
  and f(1)!
• BUT, any measurement of the output state will
  collapse the superposition and give us only f(0)
  or f(1)
• need clever tricks to extract more values of f(x)
  at the end
• Deutschs algorithm
• By using 3 H-gates with Uf in the above example,
  can measure the value of f(0)?f(1) directly
  (global property measurement)
• A Classical computer would require 3 different
  computation steps to accomplish the same task!

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Quantum Algorithms

• Quantum Fourier Transform
• H-gate is an example of Discrete Fourier
  Transform
• Deutschs algorithm, Deutsch-Jozsa, Shors fast
  factoring (Nlog(N) vs log2(N)), discrete
  logarithmetc
• Quantum Search Algorithms
• Grovers algorithm search through a random stack
  (N vs vN)
• Quantum Simulations
• Quantum state with n distinct components require
  cn bits of memory, but only kn qubits (c and k
  are both constants).
• Quantum corollary to Moores Law only need to
  add one qubit every 18 months!
• Other neat tricks Quantum Communication
• Quantum teleportation
• Quantum Cryptography
• Superdense coding

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Quantum Error Correction
M.A. Nielsen, Scientific American (Nov 2002)
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(III) Considerations for Realizing QC
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Example Infinite Potential Well

• How do we translate the transformation matrices
  to real systems?
• Consider an infinite potential well
• Hamiltonian Hp2/2m V
• Use 2 Lowest eigenstates as basis for qubit
• What happens if we perturb the well with
• And calculate the matrix elements ltY1dVY1gt,
  ltY1dVY2gt etc by calculating the inner products
  explicitly, will find that
• Thus, weve implement the quantum NOT gate on
  this single qubit simply by varying the well
  voltage! Key is to tune Hamiltonian carefully.

Y1? v(2/L)sin(?x/L) Y2? v(2/L)sin(2?x/L)
dV(x)-Vo(t)9p2/(16L)(x/L-1/2)
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Requirements for QC Implementation

• DiVincenzo criteria
• For Quantum Computation
• Well characterized qubits scalability (gt103-106
  qubits)
• State initialization
• Long decoherence time of qubits (and short gate
  operation time)
• Universal set of quantum gates
• Qubit-specific measurement capacity
• In addition, for Quantum Communication
• Ability to interconvert stationary and flying
  qubits
• Faithfully transmit flying qubits between
  specific locations (Quantum Cryptography)
• Physical systems being pursued
• Nuclear spin, electron spin, ion trap, quantum
  dot, optical cavity, microwave cavity, Josephson
  junctions (phase, charge, flux qubits), electrons
  on Helium

DP DiVincenzo, Scalable Quantum Computers (Ed
Braunstein Lo), Wilet-vch (2000)
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NMR based Quantum Computer

• The NMR QC
• Nuclear spin of organic molecules as qubit
• Pulsed magnetic field for unitary evolution
• Chemical bonds within molecule provide qubit
  interaction
• 7-qubit NMR QC demonstrated by I. Chuang et al.
  in 2002 ? still the most powerful QC to date!
• Was able to factor the number 15
• Drawbacks of the NMR
• Cannot create pure states (initialization)
• Relies on bulk/ensemble measurements with large
  number of molecules computing in parallel
• Not scalable (10 qubits max.)

Alanine a 3-qubit quantum computer
MA Nielsen and I Chuang, Quantum Information and
Quantum Computation, Cambridge Press (2002)
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(IV) Silicon Based Quantum Computers
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Why Silicon QC?

• Various solid-state QC schemes have been
  proposed, and one of the most attractive ones is
  based on shallow donors in silicon
• Donor nuclear spins are well isolated from
  environment ? low error rates and long
  decoherence time (103s), ideal for storing
  quantum information
• We know how to handle silicon! Benefit from
  expertise from processing of conventional
  microelectronics
• Easier integration with conventional electronics
  when linking the quantum states to the outside
  world

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Silicon QC Schemes On Paper

• Several silicon based QC schemes have been
  proposed
• Kane I (1998)
• Kane II (2003)
• Das Sarma (2004)
• Si QC and the DiVincenzo criteria
• Qubits Donor/donor electron spins are used to
  store quantum information. Low T required to
  localize donor electrons to donor sites and
  reduce thermal fluctuations.
• State Initialization Strong B field (gt5T) and
  Low T (lt0.3K) (Zeeman split)
• Decoherence time T2 ? 104Tgate (scheme specific)
• Universal set of quantum gates Pulsed E or B
  field. Qubit-qubit interaction by exchange
  coupling, magnetic dipole coupling or hyperfine
  interaction.
• Spin-state read-out Single electron transistors,
  Spin-dependent transport (SDT) MOS etc.

26
Silicon QC Schemes Kane (1998)

• Kane I (1998)
• Qubit nuclear spin of P donors in Si
• Unitary Evolution Use of A and J gates to
  influence couplings to neighbor spin and an AC
  B-field (via gate influence on donor electrons)
• Initial state preparation apply strong B-field
  and thus Zeeman split
• Qubit interaction (entanglement) direct exchange
  coupling of adjacent donor electrons
• Read-out Spin transfer from nucleus to electron,
  and then electron spin measurement
• Exchange coupling requires donor spacing of
  10nm, and is restricted to nearest neighbor
• However, J-oscillations would make such a scheme
  extremely difficult to achieve ? need donor
  positioning with accuracy of 1nm

JL OBrien et al, Smart Mater. Struct., 11 741
(2002)
AS Martins et al, PR B, 69 085320 (2004) B
Koiller and X Hu, IEEE Trans. On Nanotech., 4 (1)
1536 (2005)
BE Kane, Nature, 393 133 (1998)
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Silicon QC Schemes Kane (2003)

• Kane II (2003)
• Qubit Encoded in P nuclear and electron spins
  (hydrogenic spin qubit)
• Unitary Evolution Single qubit logic implemented
  by pulses to alternate control between by
• Electrode-switched on and off hyperfine
  interaction 0?1??0?-1?
• Electron-nuclear spin pairs controlled by a DC
  B-field 0??1?
• Initial state preparation electron-spin pair
  transfer to electron-donor spin
• Qubit interaction electron shuttling between
  donors for multi-qubit interaction
• Read-out Spin transfer from nucleus to electron,
  and then electron spin measurement
• Electron shuttling requires donor spacing
  electron spin decoherence length (gt100?m)

0? (?e ?n? -?e ?n?)/v2
1? (?e ?n? ?e ?n?)/v2
AJ Skinner et al, PRL, 90(8) 087901-1 (2003)
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Silicon QC Schemes Das Sarma (2004)

• Das Sarma (2004)
• Qubit shallow donor electron spin in Si
• Unitary Evolution Free evolution (of
  Hamiltonian) along with g-factor shift
• Initial state preparation Strong B-field
• Qubit interaction long range electron-electron
  magnetic dipolar coupling
• Read-out single electron spin measurements
• Strong inhomogeneous B-field required
• Dipolar coupling only extends to 4th neighbor
  effectively. Unwanted coupling or recoupling can
  be cancelled by applying ? pulses
• Residual exchange coupling treated as gate error
  ? quantum error correction to amend
• Magnetic coupling requires donor spacing of 30nm

(R de Sousa)
R de Sousa et al, PR A, 70 052304 (2004)
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Physical Realization of a Si QC

• Regardless of the specific implementation scheme,
  some common features that must be realized in a
  Si QC are
• Array of single, activated 31P atoms
• Top-down Highly charged single ion implantation
  of P (T Schenkel, LBNL)
• Bottom-up Hydrogen Lithography with STM tip (TC
  Shen, Utah State RG Clark, UNSW)
• Single-spin state read-out
• Single electron transistors
• Spin-dependent transport of aMOS
• Integrated control gates
• Must use pure 28Si substrate to avoid 29Si
  nuclear-donor magnetic coupling

SJ Part et al, Microelec. Eng., 73-74 695 (2004)
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Donor Array The Top-Down Approach

• Single Ion Implantation
• KE of P ions must be low for controllability of
  implantation profile
• Use highly charged P ions (12-15) to increase
  secondary electron yield for impact detection
  to compensate for the low KE
• Shoot ions through a 5nm aperture of AFM tip for
  dopant location control
• Current placement resolution 5nm
• Potential problems
• High charge states might enhance defect
  formation. Increased thermal budget for damage
  repair and activation.
• Extent of straggle? 5nm depth below barrier is
  optimum for adiabatic ionization of donors by
  A-gates. gt10nm depth results in non-adiabatic
  ionization under uniform E-field

T Schenkel et al, Nuclear Inst. And Methods in
Phy. Res. B, 219-220 200 (2004) T Schenkel et al,
APR, 94(11) 7017 (2003) T Schenkel et al, J. Vac.
Sci. Technol. B, 20(6) 2819 (2002)
AS Martins et al, PR B, 69 085320 (2004)
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Donor Array The Bottom-Up Approach

• Hydrogen Lithography
• Prepare atomically clean, Hydrogen-terminated Si
  surface
• Use STM tip to desorb H atoms at specific sites ?
  pattern formation
• Adsorption of phosphine (PH3) molecules to Si
  dangling bonds at surface
• Thermal removal of H resist layer, then perform
  RT Si epitaxy to encapsulate P atoms
• Recent Development
• P-donor lines 30nm-90nm wide and 750-900nm long
  fabricated and characterized

JL OBrien et al, Smart Mater. Struct., 11 741
(2002)
TC Shen et al, J. Vac. Sci. B, 22(6) 3182 (2004)
FJ Ruess et al, Nano Letters, 4(10) 1969 (2004)
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Read-out Control gates

• Ill save this for next time

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Challenges for Si QC

• In additional to the obvious technological
  challenges of fabricating atomically-precise
  devices as required for QC, scalability is a big
  issue
• Silicon specific problems
• Each device is unique, due to
• Temperature gradients in substrate
• Uneven depletion of reagents
• Different thermal expansion of materials ? strain
• Patterns and interconnections ? inhomogeneous
  strain in substrate
• Strain in Si
• Can alter electronic wavefunction substantially
• Uncertainty over control of donor electron
• Variability of process, donor placement
• Large-scale QCs in general
• Error correction by redundancy ? increases
  overhead by a factor of 10 100
• Control of qubit-qubit interactions
• Integration of these nano-devices with
  conventional electronics is also a big challenge!

RW Keyes, IEEE Com. Sci. Eng (2005)
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QIST Roadmap (v.2 2004)
http//qist.lanl.gov
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(V) Summary and Conclusions
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Summary

• QC new physics (QM) leads to new algorithms for
  computation ? potential in computational speed-up
  
• Superposition of states and entanglement are the
  new tools that we make use of in a QC
• Requirements for realizing a QC extremely
  technologically challenging
• Several Si based QC schemes have been proposed,
  all make use of P donors in Si
• QC operation is done by manipulation of E and B
  fields to influence the donor electron.
• Experimental work is still at the stage of
  infancy
• Ability for donor array placement has been
  demonstrated (top-down and bottom-up approaches)
• Spin control architecture not yet demonstrated
• Spin-state measurement of individual electrons is
  still a challenge

37
The Road Ahead

• QIST Roadmap (v.2 2004) Solid-state Quantum
  Computing

http//qist.lanl.gov
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The End

• Id also like to thank Gilbert and Yu-chih for
  taking the time to train me in Microlab

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Answer to Moores Law?

• Death of Silicon in the coming decades
• Is QC the answer to the continuation of Moores
  Law beyond conventional microelectronics?
• Extremely stringent requirements for construction
  ? cost, cost, cost!
• Speed-ups are for limited number of specific
  tasks only (so far), so general users wont
  benefit from a QC too much
• Molecular electronics/DNA/CNT have better
  potentials as replacement technologies
• BUT, the ability to efficiently simulate quantum
  mechanical systems alone is enough to make things
  exciting!!!

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Other exciting possibilities

• With the ability to pattern atomic scale
  circuits, we can also develop
• Single electron transistor (SET) circuitry
• Quantum Cellular Automata (QCA) circuits
• Spintronics

JR Tucker and TC Shen, Int. J. of Circuitry
Theory and App., 28 553 (2000)