Optimum-Preserving QUBO Parameter Compression

• URL: http://arxiv.org/abs/2307.02195v1
• Date: Wed, 5 Jul 2023 10:42:05 GMT
• Title: Optimum-Preserving QUBO Parameter Compression
• Authors: Sascha M\"ucke and Thore Gerlach and Nico Piatkowski
• Abstract summary: We study the implications of solving Quadratic unconstrained binary optimization problems under limited precision. We show that the problem's dynamic range has a crucial impact on the problem's robustness against distortions. We introduce techniques to reduce the dynamic range of a given QUBO instance based on theoretical bounds of the minimal energy value.
• Score: 0.9281671380673306
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quadratic unconstrained binary optimization (QUBO) problems are well-studied, not least because they can be approached using contemporary quantum annealing or classical hardware acceleration. However, due to limited precision and hardware noise, the effective set of feasible parameter values is severely restricted. As a result, otherwise solvable problems become harder or even intractable. In this work, we study the implications of solving QUBO problems under limited precision. Specifically, it is shown that the problem's dynamic range has a crucial impact on the problem's robustness against distortions. We show this by formalizing the notion of preserving optima between QUBO instances and explore to which extend parameters can be modified without changing the set of minimizing solutions. Based on these insights, we introduce techniques to reduce the dynamic range of a given QUBO instance based on theoretical bounds of the minimal energy value. An experimental evaluation on random QUBO instances as well as QUBO-encoded Binary Clustering and Subset Sum problems show that our theoretical findings manifest in practice. Results on quantum annealing hardware show that the performance can be improved drastically when following our methodology.

Related papers

• Adaptive Graph Shrinking for Quantum Optimization of Constrained Combinatorial Problems [4.266376725904727]
  We propose a hybrid classical--quantum framework based on graph shrinking to reduce the number of variables and constraints in QUBO formulations of optimization problems.<n>Our approach improves solution feasibility, reduces repair complexity, and enhances quantum optimization quality on hardware-limited instances.
  arXiv  Detail & Related papers  (2025-06-17T07:11:48Z)
• Scalability Challenges in Variational Quantum Optimization under Stochastic Noise [0.0]
  Variational Quantum Algorithms (VQAs) have gained significant attention as promising candidates. We investigate how state-of-the-art classical hardwares minimize well-behaved quantum loss functions for random QUBO problem instances. Our results raise serious doubts about the feasibility of achieving a practical quantum advantage in optimization using VQAs.
  arXiv  Detail & Related papers  (2025-03-18T20:00:19Z)
• Bayesian Quantum Amplitude Estimation [49.1574468325115]
  We present BAE, a problem-tailored and noise-aware Bayesian algorithm for quantum amplitude estimation.<n>In a fault tolerant scenario, BAE is capable of saturating the Heisenberg limit; if device noise is present, BAE can dynamically characterize it and self-adapt.<n>We propose a benchmark for amplitude estimation algorithms and use it to test BAE against other approaches.
  arXiv  Detail & Related papers  (2024-12-05T18:09:41Z)
• Solving QUBOs with a quantum-amenable branch and bound method [0.3749861135832072]
  We describe and experimentally validate an exact classical branch and bound solver for quadratic unconstrained binary optimization problems. Our solver leverages cheap-to-implement bounds from the literature previously proposed for Ising models. We detail a variety of techniques from high-performance computing and operations research used to boost solver performance.
  arXiv  Detail & Related papers  (2024-07-29T17:13:01Z)
• Enhancing Hypergradients Estimation: A Study of Preconditioning and Reparameterization [49.73341101297818]
  Bilevel optimization aims to optimize an outer objective function that depends on the solution to an inner optimization problem. The conventional method to compute the so-called hypergradient of the outer problem is to use the Implicit Function Theorem (IFT) We study the error of the IFT method and analyze two strategies to reduce this error.
  arXiv  Detail & Related papers  (2024-02-26T17:09:18Z)
• Quantum Annealing Solutions for the Closest String Problem with D-Wave Systems [0.0]
  Closest String Problem is an NP-complete problem which appears more commonly in bioinformatics and coding theory. Two QUBO formulations have been proposed, with one being a slight modification over the other. DWave annealers have been used, while providing guidelines for optimality on certain platform-specific concerns.
  arXiv  Detail & Related papers  (2023-10-19T16:03:25Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Hybrid Quantum Algorithms integrating QAOA, Penalty Dephasing and Zeno Effect for Solving Binary Optimization Problems with Multiple Constraints [5.259170150405252]
  This paper presents a hybrid framework that combines the use of standard Ising Hamiltonians to solve a subset of the constraints. The resolution of these non-Ising constraints is achieved through either penalty dephasing or the quantum Zeno effect.
  arXiv  Detail & Related papers  (2023-05-14T03:49:10Z)
• No-Regret Constrained Bayesian Optimization of Noisy and Expensive Hybrid Models using Differentiable Quantile Function Approximations [0.0]
  Constrained Upper Quantile Bound (CUQB) is a conceptually simple, deterministic approach that avoids constraint approximations. We show that CUQB significantly outperforms traditional Bayesian optimization in both constrained and unconstrained cases.
  arXiv  Detail & Related papers  (2023-05-05T19:57:36Z)
• Learning to Optimize with Stochastic Dominance Constraints [103.26714928625582]
  In this paper, we develop a simple yet efficient approach for the problem of comparing uncertain quantities. We recast inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses apparent intractability. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.
  arXiv  Detail & Related papers  (2022-11-14T21:54:31Z)
• Constrained Optimization via Quantum Zeno Dynamics [23.391640416533455]
  We introduce a technique that uses quantum Zeno dynamics to solve optimization problems with multiple arbitrary constraints, including inequalities. We show that the dynamics of quantum optimization can be efficiently restricted to the in-constraint subspace on a fault-tolerant quantum computer.
  arXiv  Detail & Related papers  (2022-09-29T18:00:40Z)
• 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)
• Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing [58.720142291102135]
  We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions.
  arXiv  Detail & Related papers  (2021-08-18T09:26:17Z)
• The Variational Method of Moments [65.91730154730905]
  conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables. Motivated by a variational minimax reformulation of OWGMM, we define a very general class of estimators for the conditional moment problem. We provide algorithms for valid statistical inference based on the same kind of variational reformulations.
  arXiv  Detail & Related papers  (2020-12-17T07:21:06Z)

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.