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arXiv:2608.19249

Adaptive Error Budget Allocation for Fault-Tolerant Quantum Resource Estimation: A Metaheuristic Approach

Asif Akhtab Ronggon, Tasnuva Farheen

quant-phSubmitted Aug 16, 2026• Announced Aug 18, 2026• 0 citations
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Abstract

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.

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A Game Theoretic Approach for Optimizing Quantum Error Budget Distribution

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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.

quant-pharXiv:2604.15603•Apr 20, 2026•0 citations

Price and Payoff: Non-Determinism in Fault Tolerant Quantum Computation

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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 $R_z$ 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.

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Fault-tolerant quantum computation enables the deployment of practical quantum algorithms but incurs substantial overhead from error correction, making resource estimation a central concern. Beyond case-by-case analyses, existing quantum programming languages either require programmers to manipulate low-level hardware details, rendering fault-tolerant implementations cumbersome, or abstract away the underlying error-correction schemes, reducing the effectiveness of resource utilization and estimation. To address these limitations while preserving programmability, we present a quantum programming language that enables efficient resource utilization, together with a resource-estimation framework for comprehensive resource analysis. Our framework features programmer-visible abstractions of error-correction schemes and cross-layer program-hardware analysis, allowing systematic exploration of resource trade-offs. We evaluate our approach on detailed fault-tolerant implementations of practical large-scale quantum algorithms, including components typically treated as black boxes in existing frameworks. The results demonstrate that our framework enables substantial resource savings while delivering detailed, fine-grained, and accurate resource estimates for fault-tolerant quantum programs.

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Improving Hardware Requirements for Fault-Tolerant Quantum Computing by Optimizing Error Budget Distributions

Tobias V. Forster, Nils Quetschlich, Mathias Soeken +1 more

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 of$\mathbf{1 5. 6 \%}$, including cases without improvement, and a maximum reduction of$\mathbf{7 7. 7 \%}$.

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Tobias V. Forster, Nils Quetschlich, Robert Wille

Quantum computing has made significant advancements in the last years in both hardware and software. Unfortunately, the currently available Noisy Intermediate-Scale Quantum (NISQ) hardware is still heavily affected by noise. Many optimization techniques have been developed to reduce the negative effects thereof, which, however, only works up to a certain point. Therefore, scaling quantum applications from currently considered small research examples to industrial applications requires error-correction techniques to execute quantum circuits in a fault-tolerant fashion and enter the Fault-Tolerant Quantum Computing (FTQC) era. These error-correction techniques introduce dramatic qubit overheads, leading to the requirement of tens of thousands of qubits already for toy-sized examples. Hence, quantum circuit optimization that reduces qubit overheads when shifting from the NISQ to the FTQC era is essential. This raises the question, whether we need to start from scratch, or whether current state-of-the-art optimization techniques can be used as a basis for this. To approach this question, this work investigates the effects of different optimization passes on a representative selection of quantum circuits. Since hardly any tools to automatically design and evaluate FTQC quantum circuits exist yet, we utilize resource estimation to compare the (potential) benefits gained by applying NISQ quantum circuit optimization to estimated FTQC resource requirements. The Results indicate that, indeed, the estimated resource requirements for FTQC can be improved by applying NISQ quantum circuit optimization techniques. At the same time, more detailed investigations show what techniques lead to more benefits for FTQC compared to others, providing guidelines for the transfer of NISQ optimization techniques to the FTQC era.

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AutoQuREO: A Framework for Automated Quantum Resource Estimation and Optimization

Harshkumar Oza, Aritra Sarkar, Syed Naqi Abbas +4 more

As quantum computing progresses from proof-of-principle demonstrations toward practical utility, a significant impediment is the need to augment algorithmic feasibility with system-level optimization across heterogeneous hardware and software stacks. Quantum resource estimation (QRE) plays a central role in this transition, yet existing approaches remain largely compilation-heavy or domain-knowledge-guided symbolic annotations, and tightly coupled to long-term fault-tolerant assumptions, limiting their topical applicability. In this work, we introduce AutoQuREO, an Automated framework for full-stack Quantum Resource Estimation and Optimization. AutoQuREO is built around four core novelties: (i) a flexible, user-defined abstraction of the quantum computing stack; (ii) a modular library of reusable stack components enabling rapid full-stack prototyping; (iii) surrogate modeling of layer-wise resources via algorithmic profiling and neuro-symbolic learning; and (iv) integrated multi-objective optimization that embeds QRE directly into deployment pipelines. Together, these design choices enable AutoQuREO to serve as a digital twin for quantum computing stacks, supporting the tractable exploration of complex design spaces. We demonstrate the capabilities of AutoQuREO through representative co-design case studies, including early-fault-tolerant quantum algorithms, small error correction codes, gate decomposition and variational training of parametric quantum circuits. These examples illustrate how AutoQuREO enables systematic discovery of unexploited resource trade-offs that are computationally intractable or abstruse using existing QRE tools. AutoQuREO is positioned as a general-purpose platform for advancing quantum technology readiness.

quant-pharXiv:2608.12936•Aug 14, 2026•0 citations
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.
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.
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 RzR_zRz​ 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.
Fault-tolerant quantum computation enables the deployment of practical quantum algorithms but incurs substantial overhead from error correction, making resource estimation a central concern. Beyond case-by-case analyses, existing quantum programming languages either require programmers to manipulate low-level hardware details, rendering fault-tolerant implementations cumbersome, or abstract away the underlying error-correction schemes, reducing the effectiveness of resource utilization and estimation. To address these limitations while preserving programmability, we present a quantum programming language that enables efficient resource utilization, together with a resource-estimation framework for comprehensive resource analysis. Our framework features programmer-visible abstractions of error-correction schemes and cross-layer program-hardware analysis, allowing systematic exploration of resource trade-offs. We evaluate our approach on detailed fault-tolerant implementations of practical large-scale quantum algorithms, including components typically treated as black boxes in existing frameworks. The results demonstrate that our framework enables substantial resource savings while delivering detailed, fine-grained, and accurate resource estimates for fault-tolerant quantum programs.
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%\mathbf{1 5. 6 \%}15.6%, including cases without improvement, and a maximum reduction of77.7%\mathbf{7 7. 7 \%}77.7%.
Quantum computing has made significant advancements in the last years in both hardware and software. Unfortunately, the currently available Noisy Intermediate-Scale Quantum (NISQ) hardware is still heavily affected by noise. Many optimization techniques have been developed to reduce the negative effects thereof, which, however, only works up to a certain point. Therefore, scaling quantum applications from currently considered small research examples to industrial applications requires error-correction techniques to execute quantum circuits in a fault-tolerant fashion and enter the Fault-Tolerant Quantum Computing (FTQC) era. These error-correction techniques introduce dramatic qubit overheads, leading to the requirement of tens of thousands of qubits already for toy-sized examples. Hence, quantum circuit optimization that reduces qubit overheads when shifting from the NISQ to the FTQC era is essential. This raises the question, whether we need to start from scratch, or whether current state-of-the-art optimization techniques can be used as a basis for this. To approach this question, this work investigates the effects of different optimization passes on a representative selection of quantum circuits. Since hardly any tools to automatically design and evaluate FTQC quantum circuits exist yet, we utilize resource estimation to compare the (potential) benefits gained by applying NISQ quantum circuit optimization to estimated FTQC resource requirements. The Results indicate that, indeed, the estimated resource requirements for FTQC can be improved by applying NISQ quantum circuit optimization techniques. At the same time, more detailed investigations show what techniques lead to more benefits for FTQC compared to others, providing guidelines for the transfer of NISQ optimization techniques to the FTQC era.
As quantum computing progresses from proof-of-principle demonstrations toward practical utility, a significant impediment is the need to augment algorithmic feasibility with system-level optimization across heterogeneous hardware and software stacks. Quantum resource estimation (QRE) plays a central role in this transition, yet existing approaches remain largely compilation-heavy or domain-knowledge-guided symbolic annotations, and tightly coupled to long-term fault-tolerant assumptions, limiting their topical applicability. In this work, we introduce AutoQuREO, an Automated framework for full-stack Quantum Resource Estimation and Optimization. AutoQuREO is built around four core novelties: (i) a flexible, user-defined abstraction of the quantum computing stack; (ii) a modular library of reusable stack components enabling rapid full-stack prototyping; (iii) surrogate modeling of layer-wise resources via algorithmic profiling and neuro-symbolic learning; and (iv) integrated multi-objective optimization that embeds QRE directly into deployment pipelines. Together, these design choices enable AutoQuREO to serve as a digital twin for quantum computing stacks, supporting the tractable exploration of complex design spaces. We demonstrate the capabilities of AutoQuREO through representative co-design case studies, including early-fault-tolerant quantum algorithms, small error correction codes, gate decomposition and variational training of parametric quantum circuits. These examples illustrate how AutoQuREO enables systematic discovery of unexploited resource trade-offs that are computationally intractable or abstruse using existing QRE tools. AutoQuREO is positioned as a general-purpose platform for advancing quantum technology readiness.