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