Quantum Circuit Synthesis Using an Exact T Library

TL;DR

This paper introduces an exact T gate synthesis method for fault-tolerant quantum circuits, optimizing T counts by canonicalizing Boolean functions and precomputing implementations, leading to significant reductions in T gate usage.

Contribution

It formulates an exact T synthesis problem, canonicalizes Boolean functions under Clifford equivalence, and precomputes T-optimal implementations to improve T gate efficiency.

Findings

Reduced T count by up to 14.3% on benchmarks

Improved T counts of cryptographic modules by up to 40%

Developed a customized mapper for T optimization

Abstract

In fault-tolerant quantum circuit synthesis, T gates supplied via magic states dominate space-time cost, while Clifford gates incur negligible overhead. Conventional flows minimize AND count in an {XOR, AND, NOT} basis as a proxy for T, which neglects phase cancellation and can be far from T-optimal. We instead formulate an exact T synthesis problem and canonicalize Boolean functions under Clifford equivalence. By precomputing T-optimal implementations up to seven variables and developing a customized mapper, we reduce the T count by up to 14.3% on EPFL benchmarks and improve the T counts of several cryptographic modules by up to 40%.