Low-depth Quantum Circuit Decomposition of Multi-controlled Gates

TL;DR

This paper presents a new low-depth decomposition method for multi-controlled quantum gates, significantly reducing circuit depth and improving efficiency for quantum algorithms, with open-source implementation available.

Contribution

It introduces an optimized divide-and-conquer decomposition that lowers the asymptotic depth of multi-controlled gates to 2.799 polylogarithmic, outperforming previous methods.

Findings

Achieved the lowest asymptotic depth for n-controlled gates in literature.

Reduced circuit depth for n-controlled SU(2) and U(2) gates.

Provided open-source code for reproducibility.

Abstract

Multi-controlled gates are fundamental components in the design of quantum algorithms, where efficient decompositions of these operators can enhance algorithm performance. The best asymptotic decomposition of an n-controlled X gate with one borrowed ancilla into single qubit and CNOT gates produces circuits with degree 3 polylogarithmic depth and employs a divide-and-conquer strategy. In this paper, we reduce the number of recursive calls in the divide-and-conquer algorithm and decrease the depth of n-controlled X gate decomposition to a degree of 2.799 polylogarithmic depth. With this optimized decomposition, we also reduce the depth of n-controlled SU(2) gates and approximate n-controlled U(2) gates. Decompositions described in this work achieve the lowest asymptotic depth reported in the literature. We also perform an optimization in the base of the recursive approach. Starting at 52 control qubits, the proposed n-controlled X gate with one borrowed ancilla has the shortest circuit depth in the literature. One can reproduce all the results with the freely available open-source code provided in a public repository.