Approaching the theoretical limit in quantum gate decomposition

TL;DR

This paper introduces a numerical method for decomposing general quantum programs into single- and two-qubit gates, achieving gate counts close to theoretical lower bounds, adaptable to current quantum hardware architectures.

Contribution

It presents a new optimization-based approach for quantum gate decomposition that minimizes CNOT gates and is suitable for sparse connectivity architectures.

Findings

Decomposes 3-qubit unitaries with 15 CNOTs

Decomposes 4-qubit unitaries with 63 CNOTs

High numerical accuracy close to theoretical limits

Abstract

In this work we propose a novel numerical approach to decompose general quantum programs in terms of single- and two-qubit quantum gates with a $CNOT$ gate count very close to the current theoretical lower bounds. In particular, it turns out that $15$ and $63$ $CNOT$ gates are sufficient to decompose a general $3$- and $4$-qubit unitary, respectively, with high numerical accuracy. Our approach is based on a sequential optimization of parameters related to the single-qubit rotation gates involved in a pre-designed quantum circuit used for the decomposition. In addition, the algorithm can be adopted to sparse inter-qubit connectivity architectures provided by current mid-scale quantum computers, needing only a few additional $CNOT$ gates to be implemented in the resulting quantum circuits.