Survival of the Optimized: An Evolutionary Approach to T-depth Reduction

Abstract

Quantum Error Correction (QEC) is the cornerstone of practical Fault-Tolerant Quantum Computing (FTQC), but incurs enormous resource overheads. Circuits must decompose into Clifford+T gates, and the non-transversal T gates demand costly magic-state distillation. As circuit complexity grows, sequential T-gate layers ("T-depth") increase, amplifying the spatiotemporal overhead of QEC. Optimizing T-depth is NP-hard, and existing greedy or brute-force strategies are either inefficient or computationally prohibitive. We frame T-depth reduction as a search optimization problem and present a Genetic Algorithm (GA) framework that approximates optimal layer-merge patterns across the non-convex search space. We introduce a mathematical formulation of the circuit expansion for systematic layer reordering and a greedy initial merge-pair selection, accelerating the convergence and enhancing the solution quality. In our benchmark with ~90-100 qubits, our method reduces T-depth by 79.23% and overall T-count by 41.86%. Compared to the reversible circuit benchmarks, we achieve a 2.58x improvement in T-depth over the state-of-the-art methods, demonstrating its viability for near-term FTQC.