Multi-qubit controlled gate with optimal T-count

TL;DR

This paper presents an optimized method for approximating multi-qubit controlled SU(2) gates with minimal T-count, achieving near-optimal resource efficiency for quantum computing applications.

Contribution

It introduces a T-count bound for approximating multi-qubit controlled gates, matching the lower bound under certain restrictions, and provides practical synthesis methods.

Findings

T-count of 3 log2(1/ε) + o(log(1/ε)) for approximating controlled SU(2)s

Matching lower bound on T-count when almost controlled gates are disallowed

Efficient synthesis methods for controlled gates and SU(4) gates

Abstract

Controlled gates are key components in various quantum algorithms. Improving on the prior work of Gosset et al., we show that, for an allowed error $\varepsilon$, $3\log_2(1/\varepsilon) + o(\log(1/\varepsilon))$ $T$ gates are sufficient to approximate most multi-qubit controlled SU(2)s. We also show that this T-count matches the lower bound when the use of an almost controlled gate is prohibited. As an application, general controlled gate synthesis and efficient SU(4) gate synthesis are given.