How to Approximate any Objective Function via Quadratic Unconstrained Binary Optimization

• URL: http://arxiv.org/abs/2204.11035v1
• Date: Sat, 23 Apr 2022 09:43:06 GMT
• Title: How to Approximate any Objective Function via Quadratic Unconstrained Binary Optimization
• Authors: Thomas Gabor, Marian Lingsch Rosenfeld, Sebastian Feld, Claudia Linnhoff-Popien
• Abstract summary: We present a toolkit of methods to transform almost arbitrary problems to Quadratic unconstrained binary optimization (QUBO) We showcase the usage of our approaches on two example problems (ratio cut and logistic regression)
• Score: 11.095381943951539
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quadratic unconstrained binary optimization (QUBO) has become the standard format for optimization using quantum computers, i.e., for both the quantum approximate optimization algorithm (QAOA) and quantum annealing (QA). We present a toolkit of methods to transform almost arbitrary problems to QUBO by (i) approximating them as a polynomial and then (ii) translating any polynomial to QUBO. We showcase the usage of our approaches on two example problems (ratio cut and logistic regression).

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)
• Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates [49.84541884653309]
  A current standard approach to solving convex discrete optimization problems is the use of cutting-plane algorithms. Despite the existence of a number of general-purpose cut-generating algorithms, large-scale discrete optimization problems continue to suffer from intractability. We propose a method for accelerating cutting-plane algorithms via reinforcement learning.
  arXiv  Detail & Related papers  (2023-07-17T20:11:56Z)
• Solving (Max) 3-SAT via Quadratic Unconstrained Binary Optimization [10.156623881772362]
  We introduce a novel approach to translate arbitrary 3-SAT instances to Quadratic Unconstrained Binary Optimization (QUBO) Our approach requires fewer couplings and fewer physical qubits than the current state-of-the-art, which results in higher solution quality.
  arXiv  Detail & Related papers  (2023-02-07T15:38:29Z)
• 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)
• 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)
• Polynomial unconstrained binary optimisation inspired by optical simulation [52.11703556419582]
  We propose an algorithm inspired by optical coherent Ising machines to solve the problem of unconstrained binary optimization. We benchmark the proposed algorithm against existing PUBO algorithms, and observe its superior performance. The application of our algorithm to protein folding and quantum chemistry problems sheds light on the shortcomings of approxing the electronic structure problem by a PUBO problem.
  arXiv  Detail & Related papers  (2021-06-24T16:39:31Z)
• Solving Quadratic Unconstrained Binary Optimization with divide-and-conquer and quantum algorithms [0.0]
  We apply the divide-and-conquer approach to reduce the original problem to a collection of smaller problems. This technique can be applied to any QUBO instance and leads to either an all-classical or a hybrid quantum-classical approach.
  arXiv  Detail & Related papers  (2021-01-19T19:00:40Z)
• 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)
• 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)
• Multi-block ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers [3.04585143845864]
  We present a decomposition-based approach to extend the applicability of current approaches to "quadratic plus convex" mixed binary optimization problems. We show that the alternating direction method of multipliers (ADMM) can split the MBO into a binary unconstrained problem (that can be solved with quantum algorithms) The validity of the approach is then showcased by numerical results obtained on several optimization problems via simulations with VQE and QAOA on the quantum circuits implemented in Qiskit.
  arXiv  Detail & Related papers  (2020-01-07T14:43:13Z)

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.