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Volumn 76, Issue 4, 2007, Pages

Quantum speedup of classical mixing processes

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; DIMERS; ENERGY GAP; MARKOV PROCESSES; MIXING; MONOMERS;

EID: 34948855496     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.76.042306     Document Type: Article
Times cited : (80)

References (42)
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    • Alagic and Russell exhibit a decoherent quantum walk on the hypercube which converges to the uniform distribution and preserves the quantum mixing speedup proven by Moore and Russell, but in contrast to our work, it is their single (carefully chosen) final measurement that forces uniform convergence, not the decoherence itself (which only adds "noise" that if small enough does not destroy the speedup).
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    • Similarly, we can retrieve a good approximation to π by generating and then measuring a good approximation to the ground state |π = xS π (x) |x of the Hamiltonian H=DP D-1.
    • Similarly, we can retrieve a good approximation to π by generating and then measuring a good approximation to the ground state |π = xS π (x) |x of the Hamiltonian H=DP D-1.
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    • For a walk on the symmetric group Sn, Gerhardt and Watrous showed that 1 2 Π-u 1† 1 1 n - 1 nn! (2n-2 n-1); for a walk on the hypercube Z2n, Moore and Russell showed that there exists an >0 such that 1 2 Π-u 1† 1
    • For a walk on the symmetric group Sn, Gerhardt and Watrous showed that 1 2 Π-u 1† 1 1 n - 1 nn! (2n-2 n-1); for a walk on the hypercube Z2n, Moore and Russell showed that there exists an >0 such that 1 2 Π-u 1† 1 =.
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    • Π is also positive semidefinite: it is the Gram matrix of { fs } with fs (kl): = s| k l |s if λk = λl, 0 otherwise.
    • Π is also positive semidefinite: it is the Gram matrix of { fs } with fs (kl): = s| k l |s if λk = λl, 0 otherwise.
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    • For d=1 it does not; the Grover walk on Zn with measurement ω= ν̄ mixes perfectly in T=n time steps.
    • For d=1 it does not; the Grover walk on Zn with measurement ω= ν̄ mixes perfectly in T=n time steps.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.