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Implementation of Quantum Computing
Ethan Brown
Devin Harper
With emphasis on the 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.