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Quantum Computing Harnessing quantum mechanics for information technology

Quantum Computing Harnessing quantum mechanics for information technology. Andrew Fisher UCL. Overview. What’s different about a quantum computer? How can quantum mechanics help with information processing? How can “quantum parallelism” make a difference to the way computations are done?

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Quantum Computing Harnessing quantum mechanics for information technology

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  1. Quantum ComputingHarnessing quantum mechanics for information technology Andrew Fisher UCL Event Horizon, 24 Nov 2003

  2. Overview • What’s different about a quantum computer? • How can quantum mechanics help with information processing? • How can “quantum parallelism” make a difference to the way computations are done? • How might a quantum computer actually be built? • What are we doing at UCL? Event Horizon, 24 Nov 2003

  3. Overview • What’s different about a quantum computer? • How can quantum mechanics help with information processing? • How can “quantum parallelism” make a difference to the way computations are done? • How might a quantum computer actually be built? • What are we doing at UCL? Event Horizon, 24 Nov 2003

  4. Why we need quantum mechanics for “more of the same” • Moore’s Law (doubling of # transitors per chip every ~2 years) already takes mainstream electronics into regions where quantum mechanics is important • Transistors with “gate lengths” of 10nm can already be fabricated • Wave-like quantum properties of electrons become important on this lengthscale • Transistors switchable by a single electron predicted by 2015 or so Quantum mechanics is crucial - but this is not what we mean by quantum computing Event Horizon, 24 Nov 2003

  5. How is quantum mechanics different? A classical system is always (in principle) in a definite state; we “just” have to specify which one. For example, to give a complete specification of the system of N particles, we “just” have to specify the positions and velocities (or positions and momenta) of all of them: 6N variables in all. But for a quantum system this is not true… Event Horizon, 24 Nov 2003

  6. How is quantum mechanics different? (2) The state of a quantum system can involve many different possibilities simultaneously. Examples: A double slit experiment: particles pass through both slits to create interference pattern A particle moving in a potential well: has a probability of being found at many different positions The “spin” of a particle – for example an electron – can be both “up” and “down” simultaneously Event Horizon, 24 Nov 2003

  7. Quantum mechanics and kets Mathematically, represent state of the system using kets (a notation introduced by Dirac). A ket represents the state of a system, independently of the details of what coordinate system we use. “Basis kets” – represent a complete set of possible states for system Compare a two-dimensional vector: “Basis vectors” – represent a complete set of possible directions Event Horizon, 24 Nov 2003

  8. Quantum mechanics and information What does all this have to do with information processing? Information is physics. It is not useful to separate abstract statements about information content and information processing from the physical representation of that information. For example: we now know that computer science classification of problems into hard and easy depends on the physical laws used to process the information. Event Horizon, 24 Nov 2003

  9. What is quantum computing? Classical bits: Quantum bits: Superposition of 0 and 1 (qubits) A quantum computer performs manipulations on information represented as quantum bits, just as a classical computer performs manipulations on information represented as classical bits. A quantum computer could perform certain tasks (much) more efficiently than using any known algorithm on a classical computer. It would mark the transition from passively observing the quantum regime, to controlling it. Event Horizon, 24 Nov 2003

  10. Overview • What’s different about a quantum computer? • How can quantum mechanics help with information processing? • How can “quantum parallelism” make a difference to the way computations are done? • How might a quantum computer actually be built? • What are we doing at UCL? Event Horizon, 24 Nov 2003

  11. Why the advantage? Have to specify much more information to give the state of a quantum system than of its classical analogue. E.g. Three qubits: Specifying general classical state requires three binary numbers Specifying general quantum state of N qubits requires 2Nnumbers: Since quantum mechanics is linear, operations can, in effect, be performed on each member of this superposition in parallel. Event Horizon, 24 Nov 2003

  12. Quantum parallelism Event Horizon, 24 Nov 2003

  13. Quantum gates The bits are processed by means of logical gates QUANTUM CLASSICAL X Y “Exclusive or” or “controlled not” gate: And… Event Horizon, 24 Nov 2003

  14. What could it do? • A quantum computer could: • Factor large integers in a time exponentially faster than any known classical algorithm, thereby making known public-key cryptography protocols vulnerable to attack • Search a database of N items in a time proportional to • Efficiently simulate the behaviour of another quantum system • Possibly run totally new algorithms that we cannot yet conceive because they have no classical analogue • Lead to a new understanding of the transition between quantum and classical physics: • When can a macroscopic system be put into a superposition of quantum states? • The nature of quantum entanglement and nonlocality Event Horizon, 24 Nov 2003

  15. H What do we need? Ability to perform any transformation on the state of the quantum bits (like any “rotation” of a vector). Needs, for example: At least one two-qubit manipulation that is “non-trivial” in the sense that it produces quantum correlations (entanglement) between the qubits + Arbitrary one-qubit manipulations (“Hadamard” gate) …all before decoherence sets in…. Event Horizon, 24 Nov 2003

  16. A simple example Is a particular coin we are given “fair” (heads on one side, tails on the other) or not (both sides the same)? Equivalent to asking… Is a particular binary function that we are given “balanced” (equally likely to give 0 or 1) or “constant” (always gives same result) Balanced: Constant: Classically: must look at both sides of coin (evaluate function twice) Event Horizon, 24 Nov 2003

  17. H H H The Deutsch-Josza algorithm Measure: 0→constant 1→balanced …with just one function evaluation! Event Horizon, 24 Nov 2003

  18. Overview • What’s different about a quantum computer? • How can quantum mechanics help with information processing? • How can “quantum parallelism” make a difference to the way computations are done? • How might a quantum computer actually be built? • What are we doing at UCL? Event Horizon, 24 Nov 2003

  19. The ‘DiVincenzo Checklist’ Must be able to • Characterise well-defined set of quantum states to use as qubits • Prepare suitable states within this set • Carry out desired quantum evolution (i.e. the computation) • Avoid decoherence for long enough to compute • Read out the results And ideally • Transport qubits • Interconvert stationary and flying qubits Event Horizon, 24 Nov 2003

  20. Some actual or proposed quantum computers Liquid-state NMR (“quantum computing in a coffee cup” - has factored 15) Bose-Einstein condensates Lattices of cold atoms Atom/photon interactions in cavities (“cavity QED”) Ion traps Superconducting circuits Event Horizon, 24 Nov 2003

  21. 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 Event Horizon, 24 Nov 2003

  22. 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 And ideally • Transport qubits • Interconvert stationary and flying qubits Event Horizon, 24 Nov 2003

  23. 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 Event Horizon, 24 Nov 2003

  24. 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) Event Horizon, 24 Nov 2003

  25. 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 Event Horizon, 24 Nov 2003

  26. 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 Event Horizon, 24 Nov 2003

  27. 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) Event Horizon, 24 Nov 2003

  28. Engineering the quantum states Vion et al Science 296 886 (2002) By working at “saddle-point” where system is insensitive to noise… …get quantum quality factor Q~25,000 Entanglement of two qubits recently demonstrated in a similar system (Mooij et al, Delft) Event Horizon, 24 Nov 2003

  29. 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 Magnetic field Si Event Horizon, 24 Nov 2003

  30. 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 + + + + Magnetic field Si Event Horizon, 24 Nov 2003

  31. 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 Event Horizon, 24 Nov 2003

  32. 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 Event Horizon, 24 Nov 2003

  33. 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 Event Horizon, 24 Nov 2003

  34. 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 Event Horizon, 24 Nov 2003

  35. Nuclear spins - the Kane proposal 20 nm A-gates J-gates Now good progress on some fabrication issues (Clark et al 2002) Event Horizon, 24 Nov 2003

  36. Overview • What’s different about a quantum computer? • How can quantum mechanics help with information processing? • How can “quantum parallelism” make a difference to the way computations are done? • How might a quantum computer actually be built? • What are we doing at UCL? Event Horizon, 24 Nov 2003

  37. 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 And ideally • Transport qubits • Interconvert stationary and flying qubits Event Horizon, 24 Nov 2003

  38. Excited state (interaction present) Ground state (no interaction) Is there another way? Would really like to control coupling of qubits without presence of nearby electrodes and associated electromagnetic fluctuations Our proposal (Stoneham et al., UCL): use real transitions in a localized state to drive gate: Exploit properties of point defect systems conveniently occurring in Si Event Horizon, 24 Nov 2003

  39. Dopants Silicon Our proposal: basic idea • Qubits are S=1/2 electron spins which must be controlled by one- and two-qubit gates • The spins are associated with dopants (desirable impurities) • Chosen so they do not ionise thermally at the working temperatures (“deep donors”) • The dopants are spaced 7-10nm to have negligible interactions in the “off” state

  40. Dopants Silicon Basic Ideas (Continued)… • The new concept is to control the spins producing the A-gates and J-gates using laser pulses • Another major new concept is separation of the storing of Quantum information from the control of Quantum interactions • Uniquely, the distribution of dopant atoms is disordered • A disordered distribution is desirable for system reasons • Dopants do not have to be placed at precise sites

  41. ALL GATES OFF ONE GATE ON Controlling Spins Control gate by laser-induced electron transfer Gate addressed by combination of position and energy Silicon Donors carrying Qubit Spins Source of Control Electron

  42. ALL GATES OFF ALL GATES OFF ONE GATE ON Many different charge transfer events possible Different laser wavelengths allow discrimination Controlling Spins Control gate by laser-induced electron transfer Gate addressed by combination of position and energy Silicon Donors carrying Qubit Spins Source of Control Electron

  43. Configuring the Device… • Some qubit atoms will be too close to use as gates • - These may be useful to move quantum information around When we have made a device… • Some qubit atoms will be at useful spacings • Some qubit atoms will be too distant (hence useless) …we shall not know in advance which are which! The solution… We shall configure each device, just as hard disks are configured There are also analogies with communications networks Dopants Silicon

  44. Can one achieve entanglement? • Experimental demonstrations for related systems: • Optically-induced many-spin entanglement demonstrated in quantum wells: • Bao, Bragas, Furdyna, Merlin 2003 Nature Materials2 175 (also 2003 Sol State Comm127 771) • Entanglement demonstrated in bulk spin systems via macroscopic properties: • Ghosh, Rosenbaum, Aeppli, Coppersmith 2003 Nature 425 48. Event Horizon, 24 Nov 2003

  45. Macroscopic properties (magnetic susceptibility) of LiHo0.045Y0.955F4 showing effects of entanglement. Ghosh, Rosenbaum, Aeppli, Coppersmith 2003 Nature 425 48 Event Horizon, 24 Nov 2003

  46. Advantages: Compatibility with CMOS Coupling mechanism does not rely on a small energy scale, so potential for high-temperature operation if single-qubit decoherence OK An interface with photons (“flying qubits”) built in from the beginning Take advantage of natural inhomogeneity to address individual gates Challenges: Initialization cannot be done using B-field if operate at high T Must ensure no ‘residual’ entanglement between control particle and qubits (gate timing) Readout mechanisms Connectivity of gates Fabrication and demonstration experiments (London Centre for Nanotechnology) Advantages and challenges New £3.5M Basic Technology project at UCL, 2003-7 Event Horizon, 24 Nov 2003

  47. To watch • The Basic Technology project • Other quantum-information related projects in the CMMP group and in the new London Centre for Nanotechnology • The new IRC in Quantum Information Processing (CMMP group and Sougato Bose involved) Event Horizon, 24 Nov 2003

  48. Thanks: • Several colleagues at UCL: • Marshall Stoneham • Thornton Greenland • Gabriel Aeppli • Joe Gittings • Robbie Rodriguez • Members of informal ‘quantum logic gate club’ (Oxford/Cambridge/HP/UCL/IC/Bristol…) • EPSRC and Basic Technology programme (£) Event Horizon, 24 Nov 2003

  49. To find out more… • About the field in general: • Gerald Milburn “The Feynman Processor” (Perseus 1998) • “Feynman lectures on computation” (Penguin 1999) • Michael Nielsen and Isaac Chuang “Quantum computation and quantum information” (CUP 2000; for the serious – and advanced – student!) • About our Basic Technology project: • Our paper: Stoneham, Fisher and Greenland J. Phys. Cond. Matt. 15 L447 (2003) (find it on http://www.iop.org) • Nature news article (31 July 2003 – see also http://www.nature.com)) • About the LCN: • LCN website http://www.london-nano.ucl.ac.uk Event Horizon, 24 Nov 2003

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