The automatic resource estimation tools provided by Azure Quantum and Microsoft Quantum Development Kit are described, which enable the evaluation of the resources required to run algorithms on fault-tolerant quantum computers. An example is given of obtaining resource estimates for quantum fault-tolerant implementations of several multiplication algorithms.
The automatic resource estimation tools provided by Azure Quantum and Microsoft Quantum Development Kit are described, which enable the evaluation of the resources required to run algorithms on fault-tolerant quantum computers. An example is given of obtaining resource estimates for quantum fault-tolerant implementations of several multiplication algorithms.
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.
As quantum computers progress towards a larger scale, it is imperative that the “top” of the computing-technology stack is improved. This project investigates the quantum resources required to compute primitive arithmetic algorithms, particularly multiplication. By using various quantum resource estimators, like Microsoft's Azure Quantum Resource Estimator, one can determine the resources required for numerous quantum algorithms [8]. In this paper, we will provide a comprehensive resource analysis of numerous quantum multiplication algorithms such as Karatsuba, schoolbook, and windowed arithmetic for different qubit platforms (trapped ion, superconducting, and Majorana) using the new Azure Quantum Resource Estimator.
Estimates of the quantum resources needed to run fault-tolerant algorithms are almost always reported as single numbers, even though they rest on uncertain hardware parameters and on cost models that disagree. We present an open, tool-agnostic framework that propagates evidence-based priors over fault-tolerant hardware parameters through five surface-code cost models, adds correlated-input sensitivity analysis, and evaluates the resulting intervals with a pre-registered three-layer protocol. Applied to RSA-2048, ECC-256, AES-256, and a Hubbard-model simulation on a superconducting surface-code architecture, it produces three coupled findings that together undermine the single-number convention. Propagating the error rates hardware has actually demonstrated, whose median across five large-array devices is about 4 x 10^-3 rather than the conventional 10^-3, widens the 90% physical-qubit interval to roughly forty times and lifts its median about 4.6 times above the conventional point estimate. Against the same inputs, five independently structured cost models, including two third-party estimators (the Azure Quantum Resource Estimator and Qualtran) that agree with each other to within about ten percent, disagree by a stable factor of two, a structural uncertainty that no single tool reveals. Most consequentially, both third-party estimators exceed their representable envelope for 80 to 100 percent of the evidence-based parameter space, and the AES-256 gate count overflows one tool's counter outright, so these workloads cannot be represented at measured error rates at all. The optimistic convention conceals every one of these effects. The uncertainty machinery we use is standard. The contribution is its evidence-based application, the pre-registered evaluation, and the finding that standard tools break down precisely where hardware operates.
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.
It is widely recognized that quantum computing has profound impacts on multiple fields, including but not limited to cryptography, machine learning, materials science, and so on. To run quantum algorithms, it is essential to develop scalable quantum hardware with low noise levels and to design efficient fault-tolerant quantum computing (FTQC) schemes. Currently, various FTQC schemes have been developed for different hardware platforms. However, a comprehensive framework for the analysis and evaluation of these schemes is still lacking. In this work, we propose Quantum Logical Operations Per Second (QLOPS) as a metric for assessing the performance of FTQC schemes on quantum hardware platforms. This benchmarking framework will integrate essential relevant factors, e.g., the code rates of quantum error-correcting codes, the accuracy, throughput, and latency of the decoder. Through a resource analysis of factoring RSA-2048, we demonstrate that QLOPS reflects the practical requirements of quantum algorithm execution. This framework will enable the identification of bottlenecks in quantum hardware, providing potential directions for their development. Moreover, our results will help establish a comparative framework for evaluating FTQC designs. As this benchmarking approach considers practical applications, it may assist in estimating the hardware resources needed to implement quantum algorithms and offers preliminary insights into potential timelines.
As quantum computing technology advances, the need for optimized arithmetic circuits continues to grow. This paper presents the implementation and resource estimation of a library of quantum arithmetic algorithms, including addition, multiplication, division, and modular exponentiation. Using the Azure Quantum Resource Estimator, we evaluate runtime, qubit usage, and space-time trade-offs and identify the best-performing algorithm for each arithmetic operation. We explore the design space for division, optimize windowed modular exponentiation, and identify the tipping point between multipliers, demonstrating effective applications of resource estimation in quantum research. Additionally, we highlight the impact of parallelization, reset operations, and uncomputation techniques on implementation and resource estimation. Our findings provide both a practical library and a valuable knowledge base for selecting and optimizing quantum arithmetic algorithms in real-world applications.