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

Quantum Error Correction (QEC) is essential for realizing practical Fault-Tolerant Quantum Computing (FTQC) but comes with substantial resource overhead. Quantum circuits must be compiled into the Clifford+T gate set, where the non-transversal nature of the T-gates necessitates costly magic distillation. As circuit complexity grows, so does the T-depth: the sequential T-gate layers, due to the decomposition of arbitrary rotations, further increasing the QEC demands. Optimizing T-depth poses two key challenges: it is NP-hard and existing solutions like greedy or brute-force algorithms are either suboptimal or computationally expensive. We address this by framing the problem as a search task and propose a Genetic Algorithm (GA)-based approach to discover near-optimal T-gate merge patterns across circuit layers. To improve upon convergence and solution quality, we incorporate a mathematical expansion scheme that facilitates reordering layers to identify better merge opportunities, along with a greedy initialization strategy based on T-gate density. Our method achieves up to 79.23% T-depth reduction and 41.86% T-count reduction in large circuits (90-100 qubits). Compared to state-of-the-art methods like the lookahead-based approach, our framework yields an average improvement of 1.2x across varying circuit sizes and T-gate densities. Our approach is hardware-agnostic making it compatible with diverse QEC architectures such as surface codes and QLDPCs, resulting in a scalable and practical optimization framework for near-term fault-tolerant quantum computing.