A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits

TL;DR

This paper introduces a meet-in-the-middle algorithm that efficiently finds depth-optimal quantum circuit decompositions, demonstrated by a Toffoli gate implementation with reduced T-depth.

Contribution

The paper presents a novel meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits, improving over brute force methods.

Findings

Achieved a T-depth of 3 for the Toffoli gate, reducing previous best by 40%.

Demonstrated the algorithm's effectiveness on small quantum circuits.

Provided a practical approach for depth optimization in quantum circuit synthesis.

Abstract

We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speed-up over simple brute force algorithms. As an illustration of our method we implemented this algorithm and found factorizations of the commonly used quantum logical operations into elementary gates in the Clifford+T set. In particular, we report a decomposition of the Toffoli gate over the set of Clifford and T gates. Our decomposition achieves a total T-depth of 3, thereby providing a 40% reduction over the previously best known decomposition for the Toffoli gate. Due to the size of the search space the algorithm is only practical for small parameters, such as the number of qubits, and the number of gates in an optimal implementation.