Uncertainty Quantification for Quantum Computing

• URL: http://arxiv.org/abs/2603.25039v1
• Date: Thu, 26 Mar 2026 05:21:39 GMT
• Title: Uncertainty Quantification for Quantum Computing
• Abstract summary: This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ)<n>We highlight how intrinsic mathematical tools can directly address error propagation and reliability challenges in today's quantum devices.<n>The purpose is to narrow the conceptual divide between applied mathematics, scientific computing and quantum information sciences.
• Score: 0.8699280339422538
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for understanding how noise and intrinsic randomness shape quantum computational outcomes in the language of mathematics. By grounding quantum computation in statistical inference, we highlight how mathematical tools such as probabilistic modeling, stochastic analysis, Bayesian inference, and sensitivity analysis, can directly address error propagation and reliability challenges in today's quantum devices. We also connect these methods to key scientific priorities in the field, including scalable uncertainty-aware algorithms and characterization of correlated errors. The purpose is to narrow the conceptual divide between applied mathematics, scientific computing and quantum information sciences, demonstrating how mathematically rooted UQ methodologies can guide validation, error mitigation, and principled algorithm design for emerging quantum technologies, in order to address challenges and opportunities present in modern-day quantum high performance and fault-tolerant quantum computing paradigms.

Related papers

• Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms [50.573955644831386]
  Quantum-enhanced Computer Vision (QeCV) is a new research field at the intersection of computer vision, machine learning and quantum computing.<n>It has high potential to transform how visual signals are processed and interpreted with the help of quantum computing.<n>This survey contributes to the existing literature on QeCV with a holistic review of this research field.
  arXiv  Detail & Related papers  (2025-10-08T17:59:51Z)
• Digital quantum simulation of many-body systems: Making the most of intermediate-scale, noisy quantum computers [51.56484100374058]
  This thesis is centered around simulating quantum dynamics on quantum devices.<n>We present an overview of the most relevant quantum algorithms for quantum dynamics.<n>We identify relevant problems within quantum dynamics that could benefit from quantum simulation in the near future.
  arXiv  Detail & Related papers  (2025-08-29T10:37:19Z)
• Distinguishing Quantum Software Bugs from Hardware Noise: A Statistical Approach [4.00671924018776]
  We propose a statistical approach to differentiate between quantum software bugs and hardware noise.<n>We evaluate our methodology using well-known quantum algorithms, including Grover's algorithm, Deutsch-Jozsa algorithm, and Simon's algorithm.
  arXiv  Detail & Related papers  (2025-07-28T02:21:39Z)
• Quantum-Accelerated Wireless Communications: Concepts, Connections, and Implications [59.0413662882849]
  Quantum computing is poised to redefine the algorithmic foundations of communication systems.<n>This article outlines the fundamentals of quantum computing in a style familiar to the communications society.<n>We highlight a mathematical harmony between quantum and wireless systems, which makes the topic more enticing to wireless researchers.
  arXiv  Detail & Related papers  (2025-06-25T22:25:47Z)
• An Introduction to Variational Quantum Eigensolver Applied to Chemistry [0.0]
  Variational Quantum Algorithms (VQAs) stand out as a feasible approach to demonstrating advantages over classical methods in the near term.<n>We present the application of quantum mechanics to the study of molecules, provide an introduction to the fundamentals of quantum computing, and explore the integration of these fields by employing the VQE in molecular simulations.
  arXiv  Detail & Related papers  (2025-05-07T19:46:15Z)
• A Review of Quantum Scientific Computing Algorithms for Engineering Problems [0.0]
  Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology. This paper systematically explores the foundational concepts of quantum mechanics and their implications for computational advancements.
  arXiv  Detail & Related papers  (2024-08-25T21:40:22Z)
• Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning [47.991114317813555]
  Quantum models implement implicit probabilistic predictors that produce multiple random decisions for each input through measurement shots. This paper proposes to leverage such randomness to define prediction sets for both classification and regression that provably capture the uncertainty of the model.
  arXiv  Detail & Related papers  (2023-04-06T22:05:21Z)
• Quantum Machine Learning: from physics to software engineering [58.720142291102135]
  We show how classical machine learning approach can help improve the facilities of quantum computers. We discuss how quantum algorithms and quantum computers may be useful for solving classical machine learning tasks.
  arXiv  Detail & Related papers  (2023-01-04T23:37:45Z)
• Assessing the Stability of Noisy Quantum Computation [0.40611352512781856]
  We frame the concepts of computational accuracy, result, device reliability and program stability in the context of quantum computation. Our assessment highlights the continuing need for statistical analyses of quantum computing program to increase our confidence in the burgeoning field of quantum information science.
  arXiv  Detail & Related papers  (2022-08-11T00:05:14Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• An Introduction to Quantum Computing for Statisticians [2.3757641219977392]
  Quantum computing has the potential to revolutionise and change the way we live and understand the world. This review aims to provide an accessible introduction to quantum computing with a focus on applications in statistics and data analysis.
  arXiv  Detail & Related papers  (2021-12-13T12:08:28Z)
• An Application of Quantum Annealing Computing to Seismic Inversion [55.41644538483948]
  We apply a quantum algorithm to a D-Wave quantum annealer to solve a small scale seismic inversions problem. The accuracy achieved by the quantum computer is at least as good as that of the classical computer.
  arXiv  Detail & Related papers  (2020-05-06T14:18:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.