109,190 research outputs found
Quantum Effects in Algorithms
We discuss some seemingly paradoxical yet valid effects of quantum physics in
information processing. Firstly, we argue that the act of ``doing nothing'' on
part of an entangled quantum system is a highly non-trivial operation and that
it is the essential ingredient underlying the computational speedup in the
known quantum algorithms. Secondly, we show that the watched pot effect of
quantum measurement theory gives the following novel computational possibility:
suppose that we have a quantum computer with an on/off switch, programmed ready
to solve a decision problem. Then (in certain circumstances) the mere fact that
the computer would have given the answer if it were run, is enough for us to
learn the answer, even though the computer is in fact not run.Comment: 10 pages, Latex. For Proceedings of First NASA International
Conference on Quantum Computation and Quantum Communication (Palm Springs,
February 1998
Realization of quantum walks with negligible decoherence in waveguide lattices
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks. Since waveguide lattices are easily constructed at large scales and display negligible decoherence, they can serve as an ideal and versatile experimental playground for the study of quantum walks and quantum algorithms. We experimentally observe quantum walks in large systems (similar to 100 sites) and confirm quantum walks effects which were studied theoretically, including ballistic propagation, disorder, and boundary related effects
Realization of quantum walks with negligible decoherence in waveguide lattices
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks. Since waveguide lattices are easily constructed at large scales and display negligible decoherence, they can serve as an ideal and versatile experimental playground for the study of quantum walks and quantum algorithms. We experimentally observe quantum walks in large systems (similar to 100 sites) and confirm quantum walks effects which were studied theoretically, including ballistic propagation, disorder, and boundary related effects
Decoherence in Discrete Quantum Walks
We present an introduction to coined quantum walks on regular graphs, which
have been developed in the past few years as an alternative to quantum Fourier
transforms for underpinning algorithms for quantum computation. We then
describe our results on the effects of decoherence on these quantum walks on a
line, cycle and hypercube. We find high sensitivity to decoherence, increasing
with the number of steps in the walk, as the particle is becoming more
delocalised with each step. However, the effect of a small amount of
decoherence can be to enhance the properties of the quantum walk that are
desirable for the development of quantum algorithms, such as fast mixing times
to uniform distributions.Comment: 15 pages, Springer LNP latex style, submitted to Proceedings of DICE
200
Quantum Multiobservable Control
We present deterministic algorithms for the simultaneous control of an
arbitrary number of quantum observables. Unlike optimal control approaches
based on cost function optimization, quantum multiobservable tracking control
(MOTC) is capable of tracking predetermined homotopic trajectories to target
expectation values in the space of multiobservables. The convergence of these
algorithms is facilitated by the favorable critical topology of quantum control
landscapes. Fundamental properties of quantum multiobservable control
landscapes that underlie the efficiency of MOTC, including the multiobservable
controllability Gramian, are introduced. The effects of multiple control
objectives on the structure and complexity of optimal fields are examined. With
minor modifications, the techniques described herein can be applied to general
quantum multiobjective control problems.Comment: To appear in Physical Review
An Introduction to Quantum Computing for Non-Physicists
Richard Feynman's observation that quantum mechanical effects could not be
simulated efficiently on a computer led to speculation that computation in
general could be done more efficiently if it used quantum effects. This
speculation appeared justified when Peter Shor described a polynomial time
quantum algorithm for factoring integers.
In quantum systems, the computational space increases exponentially with the
size of the system which enables exponential parallelism. This parallelism
could lead to exponentially faster quantum algorithms than possible
classically. The catch is that accessing the results, which requires
measurement, proves tricky and requires new non-traditional programming
techniques.
The aim of this paper is to guide computer scientists and other
non-physicists through the conceptual and notational barriers that separate
quantum computing from conventional computing. We introduce basic principles of
quantum mechanics to explain where the power of quantum computers comes from
and why it is difficult to harness. We describe quantum cryptography,
teleportation, and dense coding. Various approaches to harnessing the power of
quantum parallelism are explained, including Shor's algorithm, Grover's
algorithm, and Hogg's algorithms. We conclude with a discussion of quantum
error correction.Comment: 45 pages. To appear in ACM Computing Surveys. LATEX file. Exposition
improved throughout thanks to reviewers' comment
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