Qubiter Algorithm Modification, Expressing Unstructured Unitary Matrices with Fewer CNOTs

TL;DR

This paper improves the Qubiter quantum compiler to reduce the number of CNOT gates needed for unstructured unitary matrices, matching the current best efficiency record.

Contribution

It introduces modifications to Qubiter that lower the CNOT count, achieving state-of-the-art efficiency in quantum compilation.

Findings

Reduced CNOT count to match world record

Enhanced Qubiter's efficiency for unstructured matrices

Demonstrated practical improvements in quantum compilation

Abstract

A quantum compiler is a software program for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). The author of this paper is also the author of a quantum compiler called Qubiter. Qubiter uses a matrix decomposition called the Cosine-Sine Decomposition (CSD) that is well known in the field of Computational Linear Algebra. One way of measuring the efficiency of a quantum compiler is to measure the number of CNOTs it uses to express an unstructured unitary matrix (a unitary matrix with no special symmetries). We will henceforth refer to this number as $\epsilon$. In this paper, we show how to improve $\epsilon$ for Qubiter so that it matches the current world record for $\epsilon$, which is held by another quantum compiling algorithm based on CSD.