Modeling Linear Inequality Constraints in Quadratic Binary Optimization for Variational Quantum Eigensolver

• URL: http://arxiv.org/abs/2007.13245v3
• Date: Wed, 25 Nov 2020 23:03:16 GMT
• Title: Modeling Linear Inequality Constraints in Quadratic Binary Optimization for Variational Quantum Eigensolver
• Authors: Miguel Paredes Quinones and Catarina Junqueira
• Abstract summary: This paper introduces the use of tailored variational forms for variational quantum eigensolver. Four constraints that usually appear in several optimization problems are modeled. The main advantage of the proposed methodology is that the number of parameters on the variational form remain constant.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces the use of tailored variational forms for variational quantum eigensolver that have properties of representing certain constraints on the search domain of a linear constrained quadratic binary optimization problem solution. Four constraints that usually appear in several optimization problems are modeled. The main advantage of the proposed methodology is that the number of parameters on the variational form remain constant and depend on the number of variables that appear on the constraints. Moreover, this variational form always produces feasible solutions for the represented constraints differing from penalization techniques commonly used to translate constrained problems into unconstrained one. The methodology is implemented in a real quantum computer for two known optimization problems: the Facility Location Problem and the Set Packing Problem. The results obtained for this two problems with VQE using 2-Local variational form and a general QAOA implementation are compared, and indicate that less quantum gates and parameters were used, leading to a faster convergence.

Related papers

• Optimized QUBO formulation methods for quantum computing [0.4999814847776097]
  We show how to apply our techniques in case of an NP-hard optimization problem inspired by a real-world financial scenario. We follow by submitting instances of this problem to two D-wave quantum annealers, comparing the performances of our novel approach with the standard methods used in these scenarios.
  arXiv  Detail & Related papers  (2024-06-11T19:59:05Z)
• Variational Quantum Eigensolver with Constraints (VQEC): Solving Constrained Optimization Problems via VQE [0.0]
  Variational quantum approaches have shown great promise in finding near-optimal solutions to computationally challenging tasks. This work proposes a hybrid quantum-classical algorithmic paradigm termed VQEC to handle optimization with constraints.
  arXiv  Detail & Related papers  (2023-11-14T19:49:09Z)
• Improving Performance in Combinatorial Optimization Problems with Inequality Constraints: An Evaluation of the Unbalanced Penalization Method on D-Wave Advantage [0.0]
  A new method known as unbalanced penalization has been presented to avoid using slack variables. This work tests the unbalanced penalization method using real quantum hardware on D-Wave Advantage for the traveling salesman problem (TSP) The results show that the unbalanced penalization method outperforms the solutions found using slack variables.
  arXiv  Detail & Related papers  (2023-05-30T05:40:50Z)
• 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)
• Multiobjective variational quantum optimization for constrained problems: an application to Cash Management [45.82374977939355]
  We introduce a new method for solving optimization problems with challenging constraints using variational quantum algorithms. We test our proposal on a real-world problem with great relevance in finance: the Cash Management problem. Our empirical results show a significant improvement in terms of the cost of the achieved solutions, but especially in the avoidance of local minima.
  arXiv  Detail & Related papers  (2023-02-08T17:09:20Z)
• Symmetric Tensor Networks for Generative Modeling and Constrained Combinatorial Optimization [72.41480594026815]
  Constrained optimization problems abound in industry, from portfolio optimization to logistics. One of the major roadblocks in solving these problems is the presence of non-trivial hard constraints which limit the valid search space. In this work, we encode arbitrary integer-valued equality constraints of the form Ax=b, directly into U(1) symmetric networks (TNs) and leverage their applicability as quantum-inspired generative models.
  arXiv  Detail & Related papers  (2022-11-16T18:59:54Z)
• Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization [44.96576908957141]
  We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linear iterations problems on quantum computers.
  arXiv  Detail & Related papers  (2022-03-23T18:00:03Z)
• A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors [60.489902135153415]
  This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement.
  arXiv  Detail & Related papers  (2021-11-26T06:33:29Z)
• 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)
• Conditional gradient methods for stochastically constrained convex minimization [54.53786593679331]
  We propose two novel conditional gradient-based methods for solving structured convex optimization problems. The most important feature of our framework is that only a subset of the constraints is processed at each iteration. Our algorithms rely on variance reduction and smoothing used in conjunction with conditional gradient steps, and are accompanied by rigorous convergence guarantees.
  arXiv  Detail & Related papers  (2020-07-07T21:26:35Z)
• 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.