Quantum Circuit Synthesis Using an Exact T Library

We formulate exact T-count synthesis by canonicalizing Boolean functions under Clifford equivalence, precompute T-optimal implementations up to seven variables, and build a customized mapper — reducing T count by up to 14.3% on EPFL benchmarks and up to 40% on cryptographic modules. DAC 2026.

Hanyu Wang, Mingfei Yu, Xinrui Wu, Jason Cong · DAC 2026 · arXiv:2605.15476

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%.

Plain-language summary

Running programs on a fault-tolerant quantum computer is expensive mainly because of one gate type: the T gate, which must be “fed” by costly magic states. Standard toolchains do not minimize T gates directly — they minimize AND gates in a classical logic representation and hope the T count follows. This misses cancellation effects that only exist in the quantum domain. This work builds a library of provably T-optimal circuits for all small Boolean functions (up to seven inputs), grouped by Clifford equivalence so the library stays compact, and then maps large circuits onto that library with a mapper designed for T-count cost. The result is a synthesis flow that targets the true cost metric of fault-tolerant quantum computing instead of a proxy.

Key contributions

  • An exact T-count synthesis formulation, rather than minimizing AND count as a proxy.
  • Canonicalization of Boolean functions under Clifford equivalence, making a precomputed T-optimal library (up to 7 variables) tractable.
  • A customized technology mapper that rewrites large circuits using the T-optimal library.

Key results

Benchmark Metric Improvement
EPFL benchmarks T count up to 14.3% reduction
Cryptographic modules T count up to 40% reduction

Resources

How to cite

@inproceedings{wang2026exactt,
  author    = {Wang, Hanyu and Yu, Mingfei and Wu, Xinrui and Cong, Jason},
  title     = {Quantum Circuit Synthesis Using an Exact T Library},
  booktitle = {63rd ACM/IEEE Design Automation Conference (DAC)},
  year      = {2026}
}