Warm-starting quantum optimization

• URL: http://arxiv.org/abs/2009.10095v4
• Date: Wed, 16 Jun 2021 16:12:13 GMT
• Title: Warm-starting quantum optimization
• Authors: Daniel J. Egger, Jakub Marecek, Stefan Woerner
• Abstract summary: We discuss how to warm-start quantum optimization with an initial state corresponding to the solution of a relaxation of an optimization problem. This allows the quantum algorithm to inherit the performance guarantees of the classical algorithm. It is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.
• Score: 6.832341432995627
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: There is an increasing interest in quantum algorithms for problems of integer programming and combinatorial optimization. Classical solvers for such problems employ relaxations, which replace binary variables with continuous ones, for instance in the form of higher-dimensional matrix-valued problems (semidefinite programming). Under the Unique Games Conjecture, these relaxations often provide the best performance ratios available classically in polynomial time. Here, we discuss how to warm-start quantum optimization with an initial state corresponding to the solution of a relaxation of a combinatorial optimization problem and how to analyze properties of the associated quantum algorithms. In particular, this allows the quantum algorithm to inherit the performance guarantees of the classical algorithm. We illustrate this in the context of portfolio optimization, where our results indicate that warm-starting the Quantum Approximate Optimization Algorithm (QAOA) is particularly beneficial at low depth. Likewise, Recursive QAOA for MAXCUT problems shows a systematic increase in the size of the obtained cut for fully connected graphs with random weights, when Goemans-Williamson randomized rounding is utilized in a warm start. It is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.

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)
• Randomized Benchmarking of Local Zeroth-Order Optimizers for Variational Quantum Systems [65.268245109828]
  We compare the performance of classicals across a series of partially-randomized tasks. We focus on local zeroth-orders due to their generally favorable performance and query-efficiency on quantum systems.
  arXiv  Detail & Related papers  (2023-10-14T02:13:26Z)
• 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)
• Enhancing Quantum Algorithms for Quadratic Unconstrained Binary Optimization via Integer Programming [0.0]
  In this work, we integrate the potentials of quantum and classical techniques for optimization. We reduce the problem size according to a linear relaxation such that the reduced problem can be handled by quantum machines of limited size. We present numerous computational results from real quantum hardware.
  arXiv  Detail & Related papers  (2023-02-10T20:12:53Z)
• 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)
• Prog-QAOA: Framework for resource-efficient quantum optimization through classical programs [0.0]
  Current quantum optimization algorithms require representing the original problem as a binary optimization problem, which is then converted into an equivalent Ising model suitable for the quantum device. We propose to design classical programs for computing the objective function and certifying the constraints, and later compile them to quantum circuits. This results in a new variant of the Quantum Approximate Optimization Algorithm (QAOA), which we name the Prog-QAOA.
  arXiv  Detail & Related papers  (2022-09-07T18:01:01Z)
• 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)
• Twisted hybrid algorithms for combinatorial optimization [68.8204255655161]
  Proposed hybrid algorithms encode a cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. We show that for levels $p=2,ldots, 6$, the level $p$ can be reduced by one while roughly maintaining the expected approximation ratio.
  arXiv  Detail & Related papers  (2022-03-01T19:47:16Z)
• Progress towards analytically optimal angles in quantum approximate optimisation [0.0]
  The Quantum Approximate optimisation algorithm is a $p$ layer, time-variable split operator method executed on a quantum processor. We prove that optimal parameters for $p=1$ layer reduce to one free variable and in the thermodynamic limit, we recover optimal angles. We moreover demonstrate that conditions for vanishing gradients of the overlap function share a similar form which leads to a linear relation between circuit parameters, independent on the number of qubits.
  arXiv  Detail & Related papers  (2021-09-23T18:00:13Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)
• 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.