Quantum Compiling with Approximation of Multiplexors

2004/12/09 by Robert R. Tucci, Tucci, Robert R.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0412072

Ver1:18 pages (files: 1 .tex, 1 .sty, 7 .eps); Ver2:26 pages (files: 1 .tex, 1 .sty, 7 .eps, 7 .m) Ver2 = Ver1 + new material, including 7 Octave/Matlab m-files

arxiv created 2005/02/09 · arxiv updated 2009/12/01

Abstract

A quantum compiling algorithm is an algorithm for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). Suppose U_in is an \nb-bit unstructured unitary matrix (a unitary matrix with no special symmetries) that we wish to compile. For \nb>10, expressing U_in as a SEO requires more than a million CNOTs. This calls for a method for finding a unitary matrix that: (1)approximates U_in well, and (2) is expressible with fewer CNOTs than U_in. The purpose of this paper is to propose one such approximation method. Various quantum compiling algorithms have been proposed in the literature that decompose an arbitrary unitary matrix into a sequence of U(2)-multiplexors, each of which is then decomposed into a SEO. Our strategy for approximating U_in is to approximate these intermediate U(2)-multiplexors. In this paper, we will show how one can approximate a U(2)-multiplexor by another U(2)-multiplexor that is expressible with fewer CNOTs.

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