90,835 research outputs found
Adiabatic quantum search algorithm for structured problems
The study of quantum computation has been motivated by the hope of finding
efficient quantum algorithms for solving classically hard problems. In this
context, quantum algorithms by local adiabatic evolution have been shown to
solve an unstructured search problem with a quadratic speed-up over a classical
search, just as Grover's algorithm. In this paper, we study how the structure
of the search problem may be exploited to further improve the efficiency of
these quantum adiabatic algorithms. We show that by nesting a partial search
over a reduced set of variables into a global search, it is possible to devise
quantum adiabatic algorithms with a complexity that, although still
exponential, grows with a reduced order in the problem size.Comment: 7 pages, 0 figur
Quantum games via search algorithms
We build new quantum games, similar to the spin flip game, where as a novelty
the players perform measurements on a quantum system associated to a continuous
time search algorithm. The measurements collapse the wave function into one of
the two possible states. These games are characterized by a continuous space of
strategies and the selection of a particular strategy is determined by the
moments when the players measure.Comment: 4 pages, 3 figure
Robust quantum spatial search
Quantum spatial search has been widely studied with most of the study
focusing on quantum walk algorithms. We show that quantum walk algorithms are
extremely sensitive to systematic errors. We present a recursive algorithm
which offers significant robustness to certain systematic errors. To search N
items, our recursive algorithm can tolerate errors of size O(1/\sqrt{\ln N})
which is exponentially better than quantum walk algorithms for which tolerable
error size is only O(\ln N/\sqrt{N}). Also, our algorithm does not need any
ancilla qubit. Thus our algorithm is much easier to implement experimentally
compared to quantum walk algorithms
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