Elementary Proof of QAOA Convergence

• URL: http://arxiv.org/abs/2302.04968v1
• Date: Thu, 9 Feb 2023 22:57:59 GMT
• Title: Elementary Proof of QAOA Convergence
• Authors: Lennart Binkowski, Gereon Ko{\ss}mann, Timo Ziegler, Ren\'e Schwonnek
• Abstract summary: We provide a rigorous proof of convergence for the Quantum Alternating Operator Ansatz (QAOA) The proof involves retracing the connection between the Quantum Adiabatic Algorithm and the QAOA, and naturally suggests a refined definition of the phase separator' and mixer' keywords.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Quantum Alternating Operator Ansatz (QAOA) and its predecessor, the Quantum Approximate Optimization Algorithm, are one of the most widely used quantum algorithms for solving combinatorial optimization problems. However, as there is yet no rigorous proof of convergence for the QAOA, we provide one in this paper. The proof involves retracing the connection between the Quantum Adiabatic Algorithm and the QAOA, and naturally suggests a refined definition of the `phase separator' and `mixer' keywords.

Related papers

• A quantum algorithm for Khovanov homology [42.6618666851542]
  Khovanov homology is a knot that categorifies the Jones topological invariant, recognizes the unknot, and is conjectured to appear as an observable in $4D$ supersymmetric Yang-Mills theory. Despite its rich mathematical and physical significance, the computational complexity of Khovanov homology remains largely unknown.
  arXiv  Detail & Related papers  (2025-01-21T18:54:59Z)
• Optimization by Decoded Quantum Interferometry [43.55132675053983]
  We introduce a quantum algorithm for reducing classical optimization problems to classical decoding problems. We show that DQI achieves a better approximation ratio than any quantum-time classical algorithm known to us.
  arXiv  Detail & Related papers  (2024-08-15T17:47:42Z)
• Bias-field digitized counterdiabatic quantum optimization [39.58317527488534]
  We call this protocol bias-field digitizeddiabatic quantum optimization (BF-DCQO) Our purely quantum approach eliminates the dependency on classical variational quantum algorithms. It achieves scaling improvements in ground state success probabilities, increasing by up to two orders of magnitude.
  arXiv  Detail & Related papers  (2024-05-22T18:11:42Z)
• Solving Combinatorial Optimization Problems with a Block Encoding Quantum Optimizer [0.0]
  Block ENcoding Quantum (BEQO) is a hybrid quantum solver that uses block encoding to represent the cost function. Our findings confirm that BENQO performs significantly better than QAOA and competes with VQE across a variety of performance metrics.
  arXiv  Detail & Related papers  (2024-04-22T10:10:29Z)
• A Faster Algorithm for the Free Energy in One-Dimensional Quantum Systems [0.0]
  We consider the problem of approximating the free energy density of a translation-invariant, one-dimensional quantum spin system with finite range. While the complexity of this problem is nontrivial due to its close connection to problems with known hardness results, a classical subpolynomial-time algorithm has recently been proposed. We propose an algorithm outperforming this resultally and give rigorous bounds on its runtime.
  arXiv  Detail & Related papers  (2024-02-29T10:42:18Z)
• 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)
• An introduction to variational quantum algorithms for combinatorial optimization problems [0.0]
  This tutorial provides a mathematical description of the class of Variational Quantum Algorithms. We introduce precisely the key aspects of these hybrid algorithms on the quantum side and the classical side. We devote a particular attention to QAOA, detailing the quantum circuits involved in that algorithm, as well as the properties satisfied by its possible guiding functions.
  arXiv  Detail & Related papers  (2022-12-22T14:27:52Z)
• Monte Carlo Tree Search based Hybrid Optimization of Variational Quantum Circuits [7.08228773002332]
  We propose a new variational quantum algorithm called MCTS-QAOA. It combines a Monte Carlo tree search method with an improved natural policy gradient solver to optimize the discrete and continuous variables in the quantum circuit. We find that MCTS-QAOA has excellent noise-resilience properties and outperforms prior algorithms in challenging instances of the generalized QAOA.
  arXiv  Detail & Related papers  (2022-03-30T23:15:21Z)
• Quantum Error Mitigation Relying on Permutation Filtering [84.66087478797475]
  We propose a general framework termed as permutation filters, which includes the existing permutation-based methods as special cases. We show that the proposed filter design algorithm always converges to the global optimum, and that the optimal filters can provide substantial improvements over the existing permutation-based methods.
  arXiv  Detail & Related papers  (2021-07-03T16:07:30Z)
• An adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer [0.0]
  The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves optimization problems. We develop an iterative version of QAOA that is problem-tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the standard QAOA.
  arXiv  Detail & Related papers  (2020-05-20T18:00:01Z)

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.