Implementation of Quantum Computing

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.