75,511 research outputs found
Error tolerance in an NMR Implementation of Grover's Fixed-Point Quantum Search Algorithm
We describe an implementation of Grover's fixed-point quantum search
algorithm on a nuclear magnetic resonance (NMR) quantum computer, searching for
either one or two matching items in an unsorted database of four items. In this
new algorithm the target state (an equally weighted superposition of the
matching states) is a fixed point of the recursive search operator, and so the
algorithm always moves towards the desired state. The effects of systematic
errors in the implementation are briefly explored.Comment: 5 Pages RevTex4 including three figures. Changes made at request of
referees; now in press at Phys Rev
A different kind of quantum search
The quantum search algorithm consists of an alternating sequence of selective
inversions and diffusion type operations, as a result of which it can find a
target state in an unsorted database of size N in only sqrt(N) queries. This
paper shows that by replacing the selective inversions by selective phase
shifts of Pi/3, the algorithm gets transformed into something similar to a
classical search algorithm. Just like classical search algorithms this
algorithm has a fixed point in state-space toward which it preferentially
converges. In contrast, the original quantum search algorithm moves uniformly
in a two-dimensional state space. This feature leads to robust search
algorithms and also to conceptually new schemes for error correction.Comment: 13 pages, 4 figure
Fixed-point quantum search with an optimal number of queries
Grover's quantum search and its generalization, quantum amplitude
amplification, provide quadratic advantage over classical algorithms for a
diverse set of tasks, but are tricky to use without knowing beforehand what
fraction of the initial state is comprised of the target states. In
contrast, fixed-point search algorithms need only a reliable lower bound on
this fraction, but, as a consequence, lose the very quadratic advantage that
makes Grover's algorithm so appealing. Here we provide the first version of
amplitude amplification that achieves fixed-point behavior without sacrificing
the quantum speedup. Our result incorporates an adjustable bound on the failure
probability, and, for a given number of oracle queries, guarantees that this
bound is satisfied over the broadest possible range of .Comment: 4 pages plus references, 2 figure
A quantum genetic algorithm with quantum crossover and mutation operations
In the context of evolutionary quantum computing in the literal meaning, a
quantum crossover operation has not been introduced so far. Here, we introduce
a novel quantum genetic algorithm which has a quantum crossover procedure
performing crossovers among all chromosomes in parallel for each generation. A
complexity analysis shows that a quadratic speedup is achieved over its
classical counterpart in the dominant factor of the run time to handle each
generation.Comment: 21 pages, 1 table, v2: typos corrected, minor modifications in
sections 3.5 and 4, v3: minor revision, title changed (original title:
Semiclassical genetic algorithm with quantum crossover and mutation
operations), v4: minor revision, v5: minor grammatical corrections, to appear
in QI
Performance of Equal Phase-Shift Search for One Iteration
Grover presented the phase-shift search by replacing the selective inversions
by selective phase shifts of . In this paper, we investigate the
phase-shift search with general equal phase shifts. We show that for small
uncertainties, the failure probability of the Phase- search is smaller
than the general phase-shift search and for large uncertainties, the success
probability of the large phase-shift search is larger than the Phase-
search. Therefore, the large phase-shift search is suitable for large-size of
databases.Comment: 10 pages, 4 figure
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