1,354 research outputs found
A Quantitative Measure of Interference
We introduce an interference measure which allows to quantify the amount of
interference present in any physical process that maps an initial density
matrix to a final density matrix. In particular, the interference measure
enables one to monitor the amount of interference generated in each step of a
quantum algorithm. We show that a Hadamard gate acting on a single qubit is a
basic building block for interference generation and realizes one bit of
interference, an ``i-bit''. We use the interference measure to quantify
interference for various examples, including Grover's search algorithm and
Shor's factorization algorithm. We distinguish between ``potentially
available'' and ``actually used'' interference, and show that for both
algorithms the potentially available interference is exponentially large.
However, the amount of interference actually used in Grover's algorithm is only
about 3 i-bits and asymptotically independent of the number of qubits, while
Shor's algorithm indeed uses an exponential amount of interference.Comment: 13 pages of latex; research done at http://www.quantware.ups-tlse.fr
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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