Quantum Compiling with Approximation of Multiplexors
Abstract
Description
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.
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
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