T Count as a Numerically Solvable Minimization Problem

TL;DR

This paper introduces a numerically solvable approach to find minimal T-Count quantum circuits by formulating it as a continuous minimization problem and demonstrates its effectiveness on small and large circuits.

Contribution

The authors present a novel formulation of T-Count optimization as a binary search over continuous problems, enabling practical numerical solutions for larger quantum circuits.

Findings

Successfully reproduces best-known small circuit results

Extends optimization to larger circuits via circuit partitioning

Demonstrates practical numerical solvability of the problem

Abstract

We present a formulation of the problem of finding the smallest T -Count circuit that implements a given unitary as a binary search over a sequence of continuous minimization problems, and demonstrate that these problems are numerically solvable in practice. We reproduce best-known results for synthesis of circuits with a small number of qubits, and push the bounds of the largest circuits that can be solved for in this way. Additionally, we show that circuit partitioning can be used to adapt this technique to be used to optimize the T -Count of circuits with large numbers of qubits by breaking the circuit into a series of smaller sub-circuits that can be optimized independently.