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 DiVincenzohttp://www.physics2005.iop.org

Well-Characterized qubitsWhat 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 superpositionshttp://www.esat.kuleuven.ac.be/sista-cosic-docarch

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 NMRhttp://domino.research.ibm.com/

What is scalable?– Preskill’s estimate

• 106 qubits with 10-6 probability of error

– Selectivity• Pinpoint single qubits• Differentiate qubits

Well-Characterized Qubits

Charge density maps in solid state quantum computer.

InitializationInitialization

– 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 timesWhat 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 timesI. 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 tableInput Output|00> |00>|01> |01>|10> |11>|11> |10>

Unitary operator for cNOTI. 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 stateshttp://physics.syr.edu/~bplourde

Superposition of qubit stateshttp://www.qtc.ecs.soton.ac.uk/lecture2/

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 Computerwww.lanl.gov/physics/quantum/i Potential wells in Kane Quantum Computer

MRS, February 2005, Kane

Kane Quantum Computer: qubitsP 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 Computerwww.lanl.gov/physics/quantum/i

Kane Quantum Computer InitializationAdiabatic Fast Passage 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 ComputerNature 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 qubitsMRS 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

http://qso.lanl.gov/qc

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.