Current fault-tolerant quantum compilers allocate error budgets uniformly during resource estimation, causing suboptimal physical resource overhead. We optimize this allocation using a potential game formulation, where Nash Equilibrium yields a Pareto-optimal distribution across logical operations, T-state distillation, and rotation synthesis. An iterated best response (IBR) algorithm converges to this equilibrium through monotonic descent of the shared cost function. Evaluation across 433 MQT benchmarks demonstrates an average reduction of 30.22\% in physical resource requirements relative to uniform baselines, with peak improvements of 97.81\% for specific circuit instances. This establishes a game-theoretic foundation for strategic error budget optimization in fault-tolerant quantum design automation.
Current fault-tolerant quantum compilers allocate error budgets uniformly during resource estimation, causing suboptimal physical resource overhead. We optimize this allocation using a potential game formulation, where Nash Equilibrium yields a Pareto-optimal distribution across logical operations, T-state distillation, and rotation synthesis. An iterated best response (IBR) algorithm converges to this equilibrium through monotonic descent of the shared cost function. Evaluation across 433 MQT benchmarks demonstrates an average reduction of 30.22% in physical resource requirements relative to uniform baselines, with peak improvements of 97.81% for specific circuit instances. This establishes a game-theoretic foundation for strategic error budget optimization in fault-tolerant quantum design automation.
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.
Despite significant progress in quantum computing in recent years, executing quantum circuits for practical problems remains challenging due to error-prone quantum hardware. Hence, quantum error correction becomes essential but induces significant overheads in qubits and execution time, often by orders of magnitude. Obviously, these overheads must be reduced. Since many quantum applications can tolerate some noise, end users can provide a maximum tolerated error, the error budget, to be considered during compilation and execution. This error budget, or, more precisely, its distribution, can be a key factor in achieving the overhead reduction. Conceptually, an errorcorrected quantum circuit can be divided into different parts that each have a specific purpose. Errors can happen in any of these parts and their errors sum up to the mentioned error budget-but how to distribute it among them actually constitutes a degree of freedom. This work is based on the idea that some of the circuit parts can compensate for errors more efficiently than others. Consequently, these parts should contribute more to satisfy the total error budget than the parts where it is more costly. However, this poses the challenge of finding optimal distributions. We address this challenge not only by providing general guidelines on distributing the error budget, but also a method that automatically determines resource-efficient distributions for arbitrary circuits by training a machine learning model on an accumulated dataset. The approach is evaluated by analyzing the machine learning model's predictions on so far unseen data, reducing the estimated space-time costs for more than 75% of the considered quantum circuits, with an average reduction of15.6%, including cases without improvement, and a maximum reduction of77.7%.
Fault-tolerance is the future of quantum computing, ensuring error-corrected quantum computation that can be used for practical applications. Resource requirements for fault-tolerant quantum computing (FTQC) are daunting, and hence, compilation techniques must be designed to ensure resource efficiency. There is a growing need for compilation strategies tailored to the early FTQC regime, which refers to the first generation of fault-tolerant machines operating under stringent resource constraints of fewer physical qubits and limited distillation capacity. Present-day compilation techniques are largely focused on overprovisioning of routing paths and make liberal assumptions regarding the availability of distillation factories. Our work develops compilation techniques that are tailored to the needs of early FTQC systems, including distillation-adaptive qubit layouts and routing techniques. In particular, we show that simple greedy heuristics are extremely effective for this problem, offering up to 60% reduction in the number of qubits compared to prior works. Our techniques offer results with an average overhead of 1.2X in execution time for a 53% reduction in qubits against the theoretical lower bounds. As the industry develops early FTQC systems with tens to hundreds of logical qubits over the coming years, our work has the potential to be widely useful for optimising program executions.
Scalable quantum computation is expected to rely on fault-tolerant quantum computation (FTQC), in which quantum error correction (QEC) suppresses physical errors sufficiently to support reliable logical operations. This requires quantum compilation to move beyond general-purpose circuit optimization toward encoding-aware and protocol-structured compilation across the full stack of fault-tolerant quantum computers. Beyond circuit synthesis and hardware mapping, an FTQC compiler must lower algorithm-level operations into the logical gate set supported by the chosen code, coordinate encoded data and ancilla resources, realize logical operations together with repeated syndrome extraction under hardware constraints, and provide the resulting measurement stream to real-time decoding.
This survey presents a full-stack view of compiler design for QEC-protected quantum computation. We organize existing work into three interacting layers: logical-level QEC compilation, physical-level QEC realization, and decoder runtime integration. At the logical level, we review surface-code lattice-surgery compilers, beyond-surface-code code-surgery frameworks including emerging qLDPC approaches, and compilation support for non-Clifford operations such as magic-state distillation and code switching. At the physical level, we survey hardware-aware QEC realization on superconducting, trapped-ion, and neutral-atom platforms. We further examine decoder models, real-time decoding systems, and frame-management mechanisms that close the feedback loop during fault-tolerant execution. Finally, we identify open challenges in cross-layer optimization, qLDPC compilation, compiler-decoder co-design, runtime adaptivity, and the development of integrated and benchmarkable FTQC compilation stacks. An actively maintained paper list is available at: github.com/chenghongz/QEC-compiler-design.
Fault-tolerance is the future of quantum computing, ensuring error-corrected quantum computation that can be used for practical applications. Resource requirements for fault-tolerant quantum computing (FTQC) are daunting, and hence, compilation techniques must be designed to ensure resource efficiency. There is a growing need for compilation strategies tailored to the early FTQC regime, which refers to the first generation of fault-tolerant machines operating under stringent resource constraints of fewer physical qubits and limited distillation capacity. Present-day compilation techniques are largely focused on overprovisioning of routing paths and make liberal assumptions regarding the availability of distillation factories. Our work develops compilation techniques that are tailored to the needs of early FTQC systems, including distillation-adaptive qubit layouts and routing techniques. In particular, we show that simple greedy heuristics are extremely effective for this problem, offering significant reduction in the number of qubits compared to prior works. Our techniques offer results with an average overhead of 1.2× in execution time for a 53 % reduction in qubits against the theoretical lower bounds. As the industry develops early FTQC systems with tens to hundreds of logical qubits over the coming years, our work has the potential to be widely useful for optimising program executions.
A promising approach to achieving scalable fault-tolerant quantum computation is the use of quantum error correction (QEC) codes augmented with magic states i.e. resource states produced via distillation, cultivation, or Rz synthesis and teleported into the circuit as needed. Because magic-state production dominates the space-time volume of fault-tolerant programs, system architects must decide how many production units to allocate. Current approaches rely on deterministic analysis that either provisions for worst-case peak demand (wasting valuable qubit resources on factories that are never simultaneously utilized) or assumes average demand, which increases execution time. In this work, we build a simulation framework that couples circuit scheduling with different stochastic magic state production models, and use it to quantify the impact of non-determinism on circuit execution. We show that non-determinism has a dual effect that deterministic models cannot capture: it inflates total execution time (the price), while deflating peak per-cycle resource demand (the payoff). For distillation-based architectures, this demand smoothing shifts the space-time-optimal provisioning point: fewer factories are needed to minimize space-time volume than deterministic analysis predicts. Across benchmarks, stochastic-aware provisioning reduces space-time volume by up to 27% compared to the deterministic optimum for distillation, while requiring up to 30% fewer factories. We characterize these effects across each preparation mechanism, map the resulting design-space tradeoffs, and demonstrate that static resource estimation systematically mis-characterizes the cost of fault-tolerant execution. Our results establish that stochastic-aware analysis is necessary for right-sizing the factory allocations and should replace deterministic heuristics as the standard methodology for FTQC resource planning.