Computing at the quantum edge

1
The challenge of quantum computation in solids

• Andrew Fisher
• UCL
• (University College London)
• http//www.cmmp.ucl.ac.uk/

2
The solid state pros and cons for quantum
computing

• Potential advantages
• Scalability
• Silicon compatibility
• Microfabrication (and nanofabrication)
• Possibility of engineering structures
• Interaction with light (quantum communication)
• Potential disadvantage
• Much stronger contact of qubits with environment,
  so (usually) much more rapid decoherence

3
The DiVincenzo Checklist

• Must be able to
• Characterise well-defined set of quantum states
  to use as qubits
• Prepare suitable pure states within this set
• Carry out desired quantum evolution
• Avoid decoherence for long enough to compute
• Read out the results

4
The DiVincenzo Checklist

• Must be able to
• Characterise well-defined set of quantum states
  to use as qubits
• Prepare suitable pure states within this set
• Carry out desired quantum evolution
• Avoid decoherence for long enough to compute
• Read out the results

5
What are the qubits?

• Many different particles in solids (electrons and
  nuclei) whose states can be used
• There are also collective excitations that only
  occur in many-particle systems
• Possible systems for qubits include
• Nuclear spins
• Nuclear (atomic) displacements
• Electron spins
• Electron charges
• Correlated many-electron states

6
Timescales

• Can arrange these roughly according to strength
  of the qubit interactions with one another (and
  with the environment)

7
Qubits

• Nuclear spins
• Electron spins
• Electron charges
• Correlated many-electron states

8
Nuclear spins - the Kane proposal

• Qubit is spin of 31P nucleus embedded in silicon
  crystal
• Evolution and measurement of qubits performed by
  controlling individual electron states nearby

V0
Si
Magnetic field
9
Nuclear spins - the Kane proposal

• Qubit is spin of 31P nucleus embedded in silicon
  crystal
• Evolution and measurement of qubits performed by
  controlling individual electron states nearby

Vgt0

Si
Magnetic field
10
Nuclear spins - the Kane proposal

• Qubit is spin of 31P nucleus embedded in silicon
  crystal
• Evolution and measurement of qubits performed by
  controlling individual electron states nearby

VJlt0
- - - - -
Si
11
Nuclear spins - the Kane proposal

• Qubit is spin of 31P nucleus embedded in silicon
  crystal
• Evolution and measurement of qubits performed by
  controlling individual electron states nearby

VJgt0

Si
12
Nuclear spins - the Kane proposal

• Readout performed by transferring qubits to
  electrons and measuring small changes in the
  shape of the electron distribution

- - - - -
Electron cannot transfer
Si
13
Nuclear spins - the Kane proposal

• Readout performed by transferring qubits to
  electrons and measuring small changes in the
  shape of the electron distribution

- - - - -
Electron transfers
Si
14
Nuclear spins - the Kane proposal
20 nm
A-gates
J-gates
15
Qubits

• Nuclear spins
• Electron spins
• Electron charges
• Correlated many-electron states

16
Electron spins - the Loss DiVincenzo proposal

• Represent qubit by spin of single extra electron
  in an artificial atom in a semiconductor
  (quantum dot)
• Coupling of spins controlled by tuning transfer
  of electrons between the dots

17
Electron spins - the Loss DiVincenzo proposal

• Represent qubit by spin of single extra electron
  in an artificial atom in a semiconductor
  (quantum dot)
• Coupling of spins controlled by tuning transfer
  of electrons between the dots

Transfer possible ? spins rotate
Low barrier
18
Electron spins - the Loss DiVincenzo proposal

• Represent qubit by spin of single extra electron
  in an artificial atom in a semiconductor
  (quantum dot)
• Coupling of spins controlled by tuning transfer
  of electrons between the dots

Transfer possible ? spins rotate
Low barrier
19
Electron spins - the Loss DiVincenzo proposal

• Represent qubit by spin of single extra electron
  in an artificial atom in a semiconductor
  (quantum dot)
• Coupling of spins controlled by tuning transfer
  of electrons between the dots

Transfer impossible ? no rotation
X
High barrier
20
Electron spins - the Barnes et al. proposal

• Qubits are spins of individual electrons carried
  by troughs of surface acoustic wave through
  narrow channels

Channel 1
Channel 2
Barnes et al. Phys Rev B 62 8410 (2000)
Motion
21
Electron spins - the Barnes et al. proposal

• Control interactions between qubits by changing
  separation of channels

Channel 1
Channel 2
Barnes et al. Phys Rev B 62 8410 (2000)
Motion
22
Spins in fullerenes
(Image courtesy of Mark Welland see
http//planck.thphys.may.ie/QIPDDF/)
Alternative idea replace nuclear spins in Kane
proposal by endohedral spins in fullerenes (e.g.
N_at_C60)
23
Electron spins - magnetic clusters

• Use spin of a single magnetic nanoparticle to
  represent whole quantum computer
• Manipulate spin of particle by series of radio
  pulses in order to make efficient data search

2S1 gtgt2 states
Leuenberger and Loss Nature 410 789 (2001)
24
Qubits

• Nuclear spins
• Electron spins
• Electron charges
• Correlated many-electron states

25
Electrons in quantum dots

• Can coherently combine exciton states with
  different electron charge distributions in a
  quantum dot
• Could use this as a basis for a qubit with
  extremely rapid switching

Bonadeo et al. Science 282 1473 (1998)
26
Entangled excitons in nanostructuresan
all-optical proposal (Johnson et al.)

• Qubits based on excitons in multi-dot arrays
• Entanglement and logic operations generated using
  current femtosecond laser technology
• Possible realisable in semiconductors, organics,
  biological systems (e.g. photosynthesis)
• Decoherence calculations support feasibility

27
Qubits

• Nuclear spins
• Electron spins
• Electron charges
• Correlated many-electron states

28
Many-particle states superconductors

• Superconductors are an example of a macroscopic
  quantum state
• Coherence extending over large distances
• Use magnetic field (flux) through a
  superconducting ring as the qubit.

Superconducting loop with small weak link of
normal material (SQUID)
Field
Field
29
Many-particle states superconductors

• Superconductors are an example of a macroscopic
  quantum state
• Coherence extending over large distances
• or use a small Cooper pair box containing
  variable number of superconducting electrons

Box connected to reservoir of superconducting
electrons by weak link

N electrons
(N2) electrons
30
Coherence of qubits in superconductors
Oscillating population of single Cooper pair
box as two quantum processes interfere
Nakamura et al. Nature 398 786 (1999)
31
Summary

• Several very promising proposals for solid-state
  qubits
• Experiments at an early stage, but coherent
  behaviour of candidate qubits is established
• Demonstration of (controlled) entanglement in the
  solid state will itself be a significant
  milestone
• Hardest parts seem likely to be
• Controlling initialisation and decoherence
• Readout

32
Conclusions and prospects

• A very fertile and exciting field, and one that
  is being heavily funded abroad
• Numerous promising proposals, but no clear winner
  at this stage
• Major opportunity to define a new technology for
  group(s) who can demonstrate experimentally
  feasibility of a proposal

33
The need for collaboration
Collaboration involving people and facilities
from different backgrounds needed to take up this
challenge
34
Thanks to...

• Gabriel Aeppli
• James Annett
• Crispin Barnes
• Simon Benjamin
• Andrew Briggs
• Mark Fox
• Peter de Groot
• Rasmus Hansen
• John Jefferson

• Neil Johnson
• David Mowbray
• Doug Paul
• Mike Pepper
• Maurice Skolnick
• Tim Spiller
• Marshall Stoneham
• Mark Welland
• David Williams