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The challenge of quantum computation in solids

The challenge of quantum computation in solids. Andrew Fisher UCL (University College London) http://www.cmmp.ucl.ac.uk/. The solid state: pros and cons for quantum computing. Potential advantages: Scalability Silicon compatibility Microfabrication (and nanofabrication)

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The challenge of quantum computation in solids

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  1. The challenge of quantum computation in solids Andrew Fisher UCL (University College London) http://www.cmmp.ucl.ac.uk/ Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  6. Weaker interactions Stronger interactions Electron spins Nuclear spins Collective electron excitations Electron charges Atomic motions Faster operation (good) Faster decoherence (bad) Timescales • Can arrange these roughly according to strength of the qubit interactions with one another (and with the environment) Computing at the quantum edge 31 May 2001

  7. Qubits • Nuclear spins • Electron spins • Electron charges • Correlated many-electron states Computing at the quantum edge 31 May 2001

  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 V=0 Si Magnetic field Computing at the quantum edge 31 May 2001

  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 V>0 + + + + Si Magnetic field Computing at the quantum edge 31 May 2001

  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 electronstates nearby VJ<0 - - - - - Si Computing at the quantum edge 31 May 2001

  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 VJ>0 + + + + Si Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  14. Nuclear spins - the Kane proposal 20 nm A-gates J-gates Computing at the quantum edge 31 May 2001

  15. Qubits • Nuclear spins • Electron spins • Electron charges • Correlated many-electron states Computing at the quantum edge 31 May 2001

  16. Transfer possible  spins rotate Low barrier 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 Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  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@C60) Computing at the quantum edge 31 May 2001

  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 2S+1 >>2 states Leuenberger and Loss Nature 410 789 (2001) Computing at the quantum edge 31 May 2001

  24. Qubits • Nuclear spins • Electron spins • Electron charges • Correlated many-electron states Computing at the quantum edge 31 May 2001

  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.Science282 1473 (1998) Computing at the quantum edge 31 May 2001

  26. Entangled excitons in nanostructures:an 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 Computing at the quantum edge 31 May 2001

  27. Qubits • Nuclear spins • Electron spins • Electron charges • Correlated many-electron states Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  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 (N+2) electrons Computing at the quantum edge 31 May 2001

  30. Experiment Theory Coherence of qubits in superconductors Oscillating population of ‘single Cooper pair box’ as two quantum processes interfere Nakamura et al.Nature398 786 (1999) Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  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 Computing at the quantum edge 31 May 2001

  33. Low temperature physics Quantum computation theory Optics Microfabrication and nanofabrication Magnetic resonance Magnetism Semiconductors The need for collaboration Collaboration involving people and facilities from different backgrounds needed to take up this challenge Computing at the quantum edge 31 May 2001

  34. 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 Thanks to... Computing at the quantum edge 31 May 2001

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