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Bulletin of the American Physical Society

The quantum computing stack: From quantum algorithms to optimized resource estimates

Thomas Häner, Damian S. Steiger, Matthias Troyer

Published Mar 5, 2019• 0 citations
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Quantum computing and algorithms

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•Dec 3, 2025•0 citations
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.
Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for evaluating functions that are often encountered in the quantum algorithm literature. This includes Gaussians, hyperbolic tangent, sine/cosine, inverse square root, arcsine, and exponentials. We use insights from classical high-performance computing in order to optimize our circuits and implement a quantum software stack module which allows to automatically generate circuits for evaluating piecewise smooth functions in the computational basis. Our circuits enable more detailed cost analyses of various quantum algorithms, allowing to identify concrete applications of future quantum computing devices. Furthermore, our resource estimates may guide future research aiming to reduce the costs or even the need for arithmetic in the computational basis altogether.
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.