Quantum Circuit Synthesis Using an Exact T Library

• URL: http://arxiv.org/abs/2605.15476v1
• Date: Thu, 14 May 2026 23:34:01 GMT
• Title: Quantum Circuit Synthesis Using an Exact T Library
• Abstract summary: In fault-tolerant quantum synthesis circuit, T gates supplied via magic states dominate space-time cost, while Clifford gates incur negligible overhead.<n>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.<n>We instead formulate an exact T synthesis problem and canonicalize Boolean functions under Clifford equivalence.
• Score: 11.993614756390436
• License: http://creativecommons.org/licenses/by/4.0/
• 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%.

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