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Abbreviated Journal Title

Phys. Rev. A

Keywords

Polynomials; Optics; Physics; Atomic; Molecular & Chemical

Abstract

Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row or column, and these entries are efficiently computable. One can formulate a model of computation based on the composition of sparse unitaries which includes the quantum Turing machine model, the quantum circuit model, anyonic models, permutational quantum computation, and discrete time quantum walks as special cases. Thus, we obtain a simple unified proof that these models are all contained in BQP. Furthermore, our general method for implementing sparse unitaries simplifies several existing quantum algorithms.

Journal Title

Physical Review A

Volume

80

Issue/Number

6

Publication Date

1-1-2009

Document Type

Article

Language

English

First Page

4

WOS Identifier

WOS:000273233800033

ISSN

1050-2947

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