Linear-Time T-Gate Optimization via Random Abstraction

TL;DR

This paper introduces a linear-time randomized algorithm for T-gate optimization in quantum circuits, significantly improving scalability and speed over existing tools, enabling efficient optimization of large-scale quantum computations.

Contribution

The paper presents a novel linear-time randomized static analysis for T-gate optimization and an implementation, TZAP, that outperforms existing tools in speed while maintaining comparable T-count reductions.

Findings

TZAP is several orders of magnitude faster than state-of-the-art tools.

TZAP can optimize circuits with millions of gates within seconds.

The static analysis approximates reachable quantum states with high probability.

Abstract

Quantum computers promise exponential speedups for problems in cryptography, chemistry, and optimization. Realizing this promise requires fault tolerance: physical qubits are noisy, so logical qubits must be encoded redundantly across many physical ones using quantum error-correcting codes. In most practical fault-tolerance schemes, T gates cannot be implemented transversally and instead require costly magic-state distillation protocols involving a complex set of operations. As a result, T-gate count can dominate the resource budget of large-scale quantum computations, making T-count minimization a central bottleneck on the path to quantum advantage. Existing T-count optimization tools, however, do not scale to the circuits that quantum advantage demands. We present theoretical and practical results on T-gate optimization. On the theoretical side, we give a linear-time randomized algorithm for phase folding, based on a novel randomized static analysis. Our static analysis soundly approximates the set of reachable quantum states with an arbitrarily high probability. Our key insight is a static analysis that does not track symbolic expressions, but propagates constant-width bitstrings down the circuit. On the practical side, our implementation, TZAP, is multiple orders of magnitude faster than state-of-the-art tools -- such as PyZX, VOQC, and Feynman -- closely matches their T-count reductions on standard benchmarks, and within seconds on a laptop computer can optimize circuits with millions of gates.