Implementation of Quantum Computing With emphasis on the

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

Overview • Motivation • Di. Vincenzo 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 • Overcomes size limit of classical computing • Factoring 100 -digit number – Classically : >lifetime of universe – Quantum: matter of seconds

Di. Vincenzo Criteria David Di. Vincenzo http: //www. physics 2005. iop. org • A scalable physical system with wellcharacterized 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

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 2 n dimensional complex vector space Bloch Sphere with qubit superpositions http: //www. esat. kuleuven. ac. be/sista-cosic-docarch

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/

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.

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

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

Universal Quantum Gates What is “universal”? - implies all operations may be derived from a series of given gates or unitary operations Example: c. NOT Truth table Input Output |00> |01> |10> |11> |10> Unitary operator for c. NOT I. Chuang

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/lecture 2/

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

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

Kane Quantum Computer Initialization Adiabatic Fast Passage (AFP) 1. Bac turned off 2. Nuclear spin measured 3. Bias A-gate 4. Bac turned on 5. A gate-bias swept through prescribed voltage interval 6. Bac turned off 7. Nuclear spin measure 8. Repeat with smaller prescribed voltage interval 9. Do similar process for J-gate Cross-section of Kane Quantum Computer Nature May 1998, Kane

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

Kane Quantum Computer Measurement: • Both electrons bound to same donor • Differential voltage in Agates 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

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

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

References Di. Vincenzo, 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.