Linear-Time T-Gate Optimization via Random Abstraction
This work addresses the scalability bottleneck of T-count minimization for large-scale quantum computations, which is critical for achieving fault-tolerant quantum advantage.
The authors present a linear-time randomized algorithm for T-gate optimization in quantum circuits, achieving multiple orders of magnitude speedup over existing tools while closely matching their T-count reductions on standard benchmarks, and can optimize circuits with millions of gates in seconds.
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.