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Crystal Bray Dylan Gorman Justin Jeet C191 December 9, 2008
Crystal BrayDylan Gorman
Justin Jeet
C191 December 9, 2008
Adiabatic Theorem Adiabatic QC (AQC) ~ Standard QC (SQC)
Intuition AQC with Feynam’s “Global Clock Particle” AQC with Ground State QC (GSQC)
Experimental Implementation Factorization Algorithm
Theory Evolution of Hamiltonians
Implementation Diethyl-fluoromalonate Pulse sequences
Results
2/15
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
A physical system remains in its instantaneouseigenstate if a given perturbation is acting on it slowly enough and if there is a gap betweenthe eigenvalue and the rest of the Hamiltonian’s Spectrum.
3/15
Ehrenfest, Ann. Phys., 51, 327 (1916)Born et. al, Phys., 51, 165 (1928)A, Messiah, Quantum Mechanics (Wiley, New York,1976)
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
4/15Acknowledgements: Professor B. Whaley and Professor U. VaziraniKempe et. al, arXiv: quant-ph/0406180v2
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
Equivlalence Universal gates
Single qubit gates, e.g. Hadamard gate Two qubit gate, e.g. CNOT gate Correspond to unitary operators
Gates correspond to Hamiltonians
5/15Landau et. al, arXiv:quant-ph/0405098
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
AQC + Clock Two-body interactions
2-local Hamiltonians Global Clock Particle
Unary bit registration tensored to the state Measurement of clock yields result
Polynomially equivalent to Circuit model Running time = O(N11) N = # of single- and two- qubit gates
6/15Landau et. al, arXiv:quant-ph/0405098
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
7/15Landau et. al, arXiv:quant-ph/0405098Acknowledgements: Professor U. Vazirani
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
AQC + GSQC Physically and mathematically transparent Easy to implement Running time = O((MN)2)
M = # qubits N = # of single- and two-qubit gates
Needs energy gap Measure the qubit on the last row
Quantum dot scenario
8/15Mizel et al., Phys. Rev. Lett., 99, 70502 (2007)Mizel et al., Phys. Rev. A, 63, 040302 (2001)
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
9/15*-Mizel et. Al, Phys. Rev. Lett., 99, 70502 (2007)Mizel et al., Phys. Rev. A, 63, 040302 (2001)
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
“ In GSQC, one executes an algorithm by producing a ground state that spatially
encodes the entire temporal trajectory of the algorithm, from input to output” *
Single - Qubit Gates
Single- and Two- Qubit Gates
Mizel et. Al, Phys. Rev. Lett., 99, 70502 (2007)Peng et. al, Phys. Rev. Lett., 101, 220405 (2008) 10/15
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
11/15Peng et. al, Phys. Rev. Lett., 101, 220405 (2008)
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
12/15Peng et. al, PRL, 101, 220405 (2008)
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
Optimization Algorithm for Factoring
13/15Peng et. al, PRL, 101, 220405 (2008)
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
Initialize
Evolve Hamiltonian Selective Qubit
Control
Advanced Pulse Sequences
Diethyl-fluoromalonate
Adiabatic Condition Satisfied Total Evolution Time =
0.168s M = 5 discrete steps
Factoring |z 1z 2z 3 > = |111> P = 2z1 + 1 = 3 q = 4z2 + 2z3 + 1=7 N = 3 x 7
90% probability
Peng et. al, PRL, 101, 220405 (2008) 14/15
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
Shor why NOT
15/15
Outline
Adiabatic Theorem
AQC~SQC
Intuition
AQC + Clock GSQC + AQC
Experiment
Theory
Methods/ Materials
Results
