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

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 Overcomes size limit of classical computing Factoring 100-digit number –Classically : >lifetime of universe –Quantum: matter of seconds

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

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 2 2 dimensional vector space –N qubits fills a 2 n dimensional complex vector space Bloch Sphere with qubit superpositions

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 Well-Characterized qubits Qubits in IBM NMR

What is scalable? –Preskill’s estimate 10 6 qubits with probability of error –Selectivity Pinpoint single qubits Differentiate qubits Well-Characterized 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“

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: cNOT Truth table InputOutput|00>|01> |10>|11> |11>|10> Unitary operator for cNOT 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. T m should be on order of T op Superposition of qubit states Superposition of qubit states

Kane Quantum Computer Semiconductor substrate with embedded electron donors ( 31 P) Electron wave functions manipulated by changing gate voltages Most easily scalable Cross-section of Kane Quantum Computer Potential wells in Kane Quantum Computer MRS, February 2005, Kane

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 ~10 18 s Cross-sections of Kane Quantum Computer

Kane Quantum Computer Initialization Adiabatic Fast Passage 1.B ac turned off 2.Nuclear spin measured 3.Bias A-gate 4.B ac turned on 5.A gate-bias swept through prescribed voltage interval 6.B ac 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 (AFP)

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 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

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

Further research into semiconductor materials Smaller technology while approaching limit by Moore’s law Kane Quantum Computer Future

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 Kane, B.E. A Silicon-Based Nuclear Spin Quantum Computer. Nature, May Chuang, I.L., Michael A. Nielsen. Quantum Computation and Quantum Information. Cambridge, 2000.