762,635 research outputs found
Period Finding with Adiabatic Quantum Computation
We outline an efficient quantum-adiabatic algorithm that solves Simon's
problem, in which one has to determine the `period', or xor-mask, of a given
black-box function. We show that the proposed algorithm is exponentially faster
than its classical counterpart and has the same complexity as the corresponding
circuit-based algorithm. Together with other related studies, this result
supports a conjecture that the complexity of adiabatic quantum computation is
equivalent to the circuit-based computational model in a stronger sense than
the well-known, proven polynomial equivalence between the two paradigms. We
also discuss the importance of the algorithm and its theoretical and
experimental implications for the existence of an adiabatic version of Shor's
integer factorization algorithm that would have the same complexity as the
original algorithm.Comment: 6 page
Realizable Quantum Adiabatic Search
Grover's unstructured search algorithm is one of the best examples to date
for the superiority of quantum algorithms over classical ones. Its
applicability, however, has been questioned by many due to its oracular nature.
We propose a mechanism to carry out a quantum adiabatic variant of Grover's
search algorithm using a single bosonic particle placed in an optical lattice.
By studying the scaling of the gap and relevant matrix element in various
spatial dimensions, we show that a quantum speedup can already be gained in
three dimensions. We argue that the suggested scheme is realizable with
present-day experimental capabilities.Comment: 6 pages, 4 figure
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