Recursive Quantum Approximate Optimization Algorithm for the MAX-CUT problem on Complete graphs

• URL: http://arxiv.org/abs/2211.15832v1
• Date: Mon, 28 Nov 2022 23:51:02 GMT
• Title: Recursive Quantum Approximate Optimization Algorithm for the MAX-CUT problem on Complete graphs
• Authors: Eunok Bae and Soojoon Lee
• Abstract summary: Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum applications, it has been known that quantum approximate optimization algorithms have limitations for certain instances to solve the MAX-CUT problem.
• Score: 1.90365714903665
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum applications, it has been known that quantum approximate optimization algorithms have limitations for certain instances to solve the MAX-CUT problem, at any constant level $p$. Recently, the recursive quantum approximate optimization algorithm, which is a non-local version of quantum approximate optimization algorithm, has been proposed to overcome these limitations. However, it has been shown by mostly numerical evidences that the recursive quantum approximate optimization algorithm outperforms the original quantum approximate optimization algorithm for specific instances. In this work, we analytically prove that the recursive quantum approximate optimization algorithm is more competitive than the original one to solve the MAX-CUT problem for complete graphs with respect to the approximation ratio.

Related papers

• Sum-of-Squares inspired Quantum Metaheuristic for Polynomial Optimization with the Hadamard Test and Approximate Amplitude Constraints [76.53316706600717]
  Recently proposed quantum algorithm arXiv:2206.14999 is based on semidefinite programming (SDP) We generalize the SDP-inspired quantum algorithm to sum-of-squares. Our results show that our algorithm is suitable for large problems and approximate the best known classicals.
  arXiv  Detail & Related papers  (2024-08-14T19:04:13Z)
• Iterative Quantum Algorithms for Maximum Independent Set: A Tale of Low-Depth Quantum Algorithms [0.0]
  We study a new class of hybrid approaches to quantum optimization, termed Iterative Maximum Quantum Algorithms. We show that for QAOA with depth $p=1$, this algorithm performs exactly the same operations and selections as the classical greedy algorithm for MIS.
  arXiv  Detail & Related papers  (2023-09-22T18:00:03Z)
• 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)
• Ising formulation of integer optimization problems for utilizing quantum annealing in iterative improvement strategy [1.14219428942199]
  We propose an Ising formulation of integer optimization problems to utilize quantum annealing in the iterative improvement strategy. We analytically show that a first-order phase transition is successfully avoided for a fully connected ferro Potts model if the overlap between a ground state and a candidate solution exceeds a threshold.
  arXiv  Detail & Related papers  (2022-11-08T02:12:49Z)
• Stochastic optimization algorithms for quantum applications [0.0]
  We review the use of first-order, second-order, and quantum natural gradient optimization methods, and propose new algorithms defined in the field of complex numbers. The performance of all methods is evaluated by means of their application to variational quantum eigensolver, quantum control of quantum states, and quantum state estimation.
  arXiv  Detail & Related papers  (2022-03-11T16:17:05Z)
• Quantum algorithm for stochastic optimal stopping problems with applications in finance [60.54699116238087]
  The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in optimal stopping theory. We propose a quantum LSM based on quantum access to a process, on quantum circuits for computing the optimal stopping times, and on quantum techniques for Monte Carlo.
  arXiv  Detail & Related papers  (2021-11-30T12:21:41Z)
• Quantum optimisation via maximally amplified states [0.0]
  This paper presents a novel quantum algorithm for optimisation in the restricted circuit depth context of near-term quantum computing. The Maximum Amplification optimisation algorithm (MAOA) performs considerably better than other near-term quantum algorithms.
  arXiv  Detail & Related papers  (2021-11-01T09:43:53Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Improving the Quantum Approximate Optimization Algorithm with postselection [0.0]
  Combinatorial optimization is among the main applications envisioned for near-term and fault-tolerant quantum computers. We consider a well-studied quantum algorithm for optimization: the Quantum Approximate Optimization Algorithm (QAOA) applied to the MaxCut problem on 3-regular graphs. We derive theoretical upper and lower bounds showing that a constant (though small) increase of the fraction of satisfied edges is indeed achievable.
  arXiv  Detail & Related papers  (2020-11-10T22:17:50Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• 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.