Quantum Decoding Algorithms: Quantum Speedups in Optimization

• URL: http://arxiv.org/abs/2605.00312v1
• Date: Fri, 01 May 2026 00:47:15 GMT
• Title: Quantum Decoding Algorithms: Quantum Speedups in Optimization
• Abstract summary: A new approach to solving the max-LINSAT class of optimization problems has emerged, called Decoded Quantum Interferometry (DQI)<n>In DQI, a combination of techniques rooted in (classical) coding theory and interferometry are used to obtain the solution of max-LINSAT.<n>In the special problem instance of the optimal intersection (OPI) problem, strong evidence exists to show that an superpolynomial speedup exists.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Attaining a quantum speedup in solving practically useful optimization problems has been one of the holy grails in the field of quantum computing. While prior approaches have demonstrated speedups for certain structured problem classes, establishing a clear and scalable advantage on broadly useful practical optimization problems remains challenging. Recently, a new approach to solving the max-LINSAT class of optimization problems has emerged, called Decoded Quantum Interferometry (DQI). In DQI, a combination of techniques rooted in (classical) coding theory and interferometry are used to obtain the solution of max-LINSAT. In the special problem instance of the optimal polynomial intersection (OPI) problem, strong evidence exists to show that an superpolynomial speedup exists over the best classical methods in obtaining an approximate solution. In this review, we give a self-contained description of DQI and the necessary background to understand the algorithm. Specifically, we give the essentials of Galois fields, optimization problems such as max-LINSAT and OPI, and coding theory, followed by a step-by-step walkthrough of the quantum algorithm and its operating principle.

Related papers

• An Introduction to the Quantum Approximate Optimization Algorithm [51.56484100374058]
  The tutorial begins by outlining variational quantum circuits and QUBO problems.<n>Next, it explores the QAOA in detail, covering its Hamiltonian formulation, gate decomposition, and example applications.<n>The tutorial extends these concepts to higher-order Hamiltonians and discussing the associated symmetries and circuit construction.
  arXiv  Detail & Related papers  (2025-11-23T09:54:20Z)
• Classical optimization with imaginary time block encoding on quantum computers: The MaxCut problem [1.354560757162539]
  We develop a new method, called ITE-BE, based on a recent imaginary time algorithm.<n>We demonstrate that our method can be successfully combined with other quantum algorithms.
  arXiv  Detail & Related papers  (2024-11-16T08:17:36Z)
• Optimization by Decoded Quantum Interferometry [38.063836468778895]
  We introduce Decoded Quantum Interferometry (DQI), a quantum algorithm that uses the quantum Fourier transform to reduce optimization problems to decoding problems.<n>For approximating optimal fits over finite fields, DQI achieves a superpolynomial speedup over known classical algorithms.
  arXiv  Detail & Related papers  (2024-08-15T17:47:42Z)
• Variational Quantum Algorithms for Combinatorial Optimization [0.571097144710995]
  Variational Algorithms (VQA) have emerged as one of the strongest candidates towards reaching practical applicability of NISQ systems. This paper explores the current state and recent developments of VQAs, emphasizing their applicability to Approximate optimization. We implement QAOA circuits with varying depths to solve the MaxCut problem on graphs with 10 and 20 nodes.
  arXiv  Detail & Related papers  (2024-07-08T22:02:39Z)
• A Review on Quantum Approximate Optimization Algorithm and its Variants [47.89542334125886]
  The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve intractable optimization problems. This comprehensive review offers an overview of the current state of QAOA, encompassing its performance analysis in diverse scenarios. We conduct a comparative study of selected QAOA extensions and variants, while exploring future prospects and directions for the algorithm.
  arXiv  Detail & Related papers  (2023-06-15T15:28:12Z)
• Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
  We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
  arXiv  Detail & Related papers  (2023-04-18T11:57:15Z)
• Efficient Use of Quantum Linear System Algorithms in Interior Point Methods for Linear Optimization [0.0]
  We develop an Inexact Infeasible Quantum Interior Point Method to solve linear optimization problems. We also discuss how can we get an exact solution by Iterative Refinement without excessive time of quantum solvers.
  arXiv  Detail & Related papers  (2022-05-02T21:30:56Z)
• Classically-Boosted Quantum Optimization Algorithm [0.0]
  We explore a natural approach to leveraging existing classical techniques to enhance quantum optimization. Specifically, we run a classical algorithm to find an approximate solution and then use a quantum circuit to search its "neighborhood" for higher-quality solutions. We demonstrate the applications of CBQOA to Max 3SAT and Max Bisection, and provide empirical evidence that it outperforms previous approaches on these problems.
  arXiv  Detail & Related papers  (2022-03-25T23:36:14Z)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA [68.11912614360878]
  Hybrid quantum-classical algorithms such as Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
  arXiv  Detail & Related papers  (2020-03-11T13:52:41Z)

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.