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Implementation of Quantum Computing

Implementation of Quantum Computing. With emphasis on the Kane quantum computer. Ethan Brown Devin Harper. Overview. Motivation DiVincenzo Criteria Kane Quantum Computer. What makes it so Cool?. Binary 1’s and 0’s replaced by two-level system allowing for infinite superpositions of states

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Implementation of Quantum Computing

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  1. Implementation of Quantum Computing With emphasis on the Kane quantum computer Ethan Brown Devin Harper

  2. Overview • Motivation • DiVincenzo Criteria • Kane Quantum Computer

  3. What makes it so Cool? • Binary 1’s and 0’s replaced by two-level system allowing for infinite superpositions of states • Overcomes size limit of classical computing • Factoring 100-digit number • Classically : >lifetime of universe • Quantum: matter of seconds

  4. DiVincenzo Criteria • A scalable physical system with well-characterized qubits • The ability to initialize the state of the qubits to a simple fiducial state • Long decoherence times relative to the time of gate operations • A universal set of quantum gates • A qubit-specific measurement capability David DiVincenzo http://www.physics2005.iop.org

  5. Well-Characterized qubits What is a qubit? • Quantum two-level system a|0> + b|1> • States fill a two dimensional vector space • Two qubits: a|00> + b|01> + c|10> + d|11> • States fill a 22 dimensional vector space • N qubits fills a 2n dimensional complex vector space Bloch Sphere with qubit superpositions http://www.esat.kuleuven.ac.be/sista-cosic-docarch

  6. Well-Characterized qubits What is well-characterized? • Known physical parameters • Internal hamiltonian • Presence of and couplings to other states of the qubit • Interactions with other qubits • Couplings to external fields • Control of higher energy states Qubits in IBM NMR http://domino.research.ibm.com/

  7. Well-Characterized Qubits What is scalable? • Preskill’s estimate • 106 qubits with 10-6 probability of error • Selectivity • Pinpoint single qubits • Differentiate qubits Charge density maps in solid state quantum computer.

  8. Initialization Initialization • take all qubits to initial known state (|000000…>) Continual zeroing • Needed for quantum error correcting Approaches • Cooling • qubit taken to ground state of hamiltonian • Projection • Initialized through measurement Continued controlled transport of five Cs atoms with "conveyor belt“ http://www.iap.uni-bonn.de/ag_meschede/english/singleatoms_eng.html

  9. Decoherence times What is decoherence? • The change from a given quantum state into a mixture of states • Decay into classical behavior Appropriate length • Long enough for quantum features to come into play • Short enough to maintain quantum characterization decoherence times and gate operation times I. Chuang

  10. Universal Quantum Gates What is “universal”? • implies all operations may be derived from a series of given gates or unitary operations Example: cNOT Truth table Input Output |00> |00> |01> |01> |10> |11> |11> |10> Unitary operator for cNOT I. Chuang

  11. Measurement • Determine state of qubit after computation • Gives outcome “0” with probability p and “1” with probability 1-p • Specific measurement for specific qubits • If zeroed because of measurement, accomplished requirement 2. • Tm should be on order of Top Superposition of qubit states http://physics.syr.edu/~bplourde Superposition of qubit states http://www.qtc.ecs.soton.ac.uk/lecture2/

  12. Kane Quantum Computer • Semiconductor substrate with embedded electron donors (31P) • Electron wave functions manipulated by changing gate voltages • Most easily scalable Cross-section of Kane Quantum Computer www.lanl.gov/physics/quantum/i Potential wells in Kane Quantum Computer MRS, February 2005, Kane

  13. Kane Quantum Computer: qubits P nucleus • Spin mediated by electron spin through hyperfine interaction • Controlled and measured by varying voltages in top gates • Long decoherence times ~1018 s Cross-sections of Kane Quantum Computer www.lanl.gov/physics/quantum/i

  14. Kane Quantum Computer Initialization (AFP) Adiabatic Fast Passage • Bac turned off • Nuclear spin measured • Bias A-gate • Bac turned on • A gate-bias swept through prescribed voltage interval • Bac turned off • Nuclear spin measure • Repeat with smaller prescribed voltage interval • Do similar process for J-gate Cross-section of Kane Quantum Computer Nature May 1998, Kane

  15. Kane Quantum Computer Logic Gates Universal gates: • Classical NOT: Single qubit operation • Bias A-gate above P • Distort electron wave function • Switch of nuclear spin • Sqrt(SWAP): Two qubit operation • Bias J-gate • Distort electron wave functions • Entanglement SWAP operation performed on two qubits MRS Bulletin, February 2005, Kane

  16. Kane Quantum Computer Measurement Measurement: • Both electrons bound to same donor • Differential voltage in A-gates results in charge motion • Current measured via capacitive techniques • Signal lasts entire decoherence time • Measurement of single qubit via magnetic field Cross-section of Kane Quantum Computer Nature May 1998, Kane

  17. Kane Quantum Computer Difficulties • Incorporation of donor array in Si • 100 Å below barrier layer • Even if off by 1 lattice site, effect on exchange interaction can be on the order of 100% • Zero-spin, zero-impurity material necessary • Gate Construction • ~100 Å apart, patterned

  18. Kane Quantum Computer Future • Further research into semiconductor materials • Smaller technology while approaching limit by Moore’s law http://qso.lanl.gov/qc

  19. References DiVincenzo, David P. The Physical Implementation of Quantum Computation. April 13, 2005 Kane, B.E. Can We Build a Large-Scale Quantum Computer Using Semiconductor Materials? MRS Bulletin, February 2005. Kane, B.E. A Silicon-Based Nuclear Spin Quantum Computer. Nature, May 1998. Chuang, I.L., Michael A. Nielsen. Quantum Computation and Quantum Information. Cambridge, 2000.

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