Reuse Method for Quantum Circuit Synthesis

Abstract

The algebraic decomposition of a unitary operator is a key operation in the synthesis of quantum circuits. If most methods factorize the matrix into products, there exists a method that allows to reuse already existing optimized circuits to implement linear combinations of them. This paper presents an attempt to extend this method to a general framework of circuit synthesis. The method needs to find suitable groups for the implementation of new quantum circuits. We identify key points necessary for the construction of a comprehensive method and we test potential group candidates.

Quantum Software Engineering: Landscapes and Horizons

“…Allouche et al [7] attempted to extend further the design-byreuse method proposed by Klappenecker and Rötteler [150] to a general framework to support circuit synthesis through reusing the existing quantum circuits. In their extension, the approach needs to find suitable groups for the implementation of new quantum circuits.…”

“…At this phase, developers start coding based on the requirements and design discussed in the previous phases. Developers also perform the unit testing for each component to test the new code they write, review the code for each other, create builds, and deploy Reusing the computation of another quantum algorithm (6) Uncompute (aka unentangling aka copy-uncompute) Removing entanglement that resulted from a computation (7) Phase shift Distinguishing important aspects of a state efficiently (8) Amplitude amplification…”

The decomposition of an arbitrary $2^w\times 2^w$ unitary matrix into signed permutation matrices

“…The matrix set {M 0 , M 6 , M 1 , M 7 } forms a cyclic subgroup of D. The matrix set {M 0 , M 2 , M 4 , M 6 } does not form a group; it does form a projective group. The decomposition properties of both this projective group and the group D itself have been studied by Allouche et al [8].…”