Crystal Bray Dylan Gorman Justin Jeet C191 December 9, 2008
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
Related Documents
