Adaptive Error Budget Allocation for Fault-Tolerant Quantum Resource Estimation: A Metaheuristic Approach
System-level resource estimation is a key component of fault-tolerant quantum computing (FTQC) toolchains. Its efficiency depends on how global error tolerance is allocated across logical operations, T-state distillation, and rotation synthesis to minimize physical resource overhead. The commonly used uniform-allocation strategy ignores circuit-specific structure and can overprovision inactive or less critical subsystems, leading to inflated space-time estimates. Prior work aims to address this limitation using supervised models trained on offline-generated datasets. However, this approach incurs additional data-generation costs and limits deployment flexibility. To overcome these drawbacks, we propose a training-free optimization framework that performs derivative-free search directly on the Azure Quantum Resource Estimator (AQRE), enabling instance-specific error budget allocation for previously unseen circuits without requiring offline training data. To evaluate robustness to optimizer choice, we instantiate the framework with two structurally distinct metaheuristics, simulated annealing and quantum particle swarm optimization. We evaluate our framework across 433 circuits spanning 2 to 91 qubits from 31 families in the MQT Bench suite. Across the benchmark suite, both methods reduce space-time cost by more than 33\% on average and agree within 1.34\% points, indicating that the gains are stable across different metaheuristic search strategies. Our analysis further finds that the optimization benefit is driven primarily by error-profile asymmetry rather than circuit scale, and the metric, Gini coefficient of optimized allocation, provides an interpretable diagnostic of expected improvement. Together, these results position adaptive error budget allocation as a system-software optimization layer for FTQC resource estimation pipeline.