Quantum approximate optimization for hard problems in linear algebra

The quantum approximate optimization algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for binary linear least squares (BLLS); a problem that can serve as a building block of several other hard probl...

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Autor principal:	Ajinkya Borle, Vincent E. Elfving, Samuel J. Lomonaco
Formato:	article
Lenguaje:	EN
Publicado:	SciPost 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/f4cd35313c20476585a2eeafa2ddea53
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spelling	oai:doaj.org-article:f4cd35313c20476585a2eeafa2ddea532021-11-30T15:47:53ZQuantum approximate optimization for hard problems in linear algebra2666-936610.21468/SciPostPhysCore.4.4.031https://doaj.org/article/f4cd35313c20476585a2eeafa2ddea532021-11-01T00:00:00Zhttps://scipost.org/SciPostPhysCore.4.4.031https://doaj.org/toc/2666-9366The quantum approximate optimization algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for binary linear least squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra, such as the non-negative binary matrix factorization (NBMF) and other variants of the non-negative matrix factorization (NMF) problem. Most of the previous efforts in quantum computing for solving these problems were done using the quantum annealing paradigm. For the scope of this work, our experiments were done on noiseless quantum simulators, a simulator including a device-realistic noise-model, and two IBM Q 5-qubit machines. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where trial solutions can be obtained directly as samples, rather than being amplitude-encoded in the quantum wavefunction. Our numerics show that even for a small number of steps, simulated annealing can outperform QAOA for BLLS at a QAOA depth of $p\leq3$ for the probability of sampling the ground state. Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on cloud-based quantum computers.Ajinkya Borle, Vincent E. Elfving, Samuel J. LomonacoSciPostarticlePhysicsQC1-999ENSciPost Physics Core, Vol 4, Iss 4, p 031 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Ajinkya Borle, Vincent E. Elfving, Samuel J. Lomonaco Quantum approximate optimization for hard problems in linear algebra
description	The quantum approximate optimization algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for binary linear least squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra, such as the non-negative binary matrix factorization (NBMF) and other variants of the non-negative matrix factorization (NMF) problem. Most of the previous efforts in quantum computing for solving these problems were done using the quantum annealing paradigm. For the scope of this work, our experiments were done on noiseless quantum simulators, a simulator including a device-realistic noise-model, and two IBM Q 5-qubit machines. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where trial solutions can be obtained directly as samples, rather than being amplitude-encoded in the quantum wavefunction. Our numerics show that even for a small number of steps, simulated annealing can outperform QAOA for BLLS at a QAOA depth of $p\leq3$ for the probability of sampling the ground state. Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on cloud-based quantum computers.
format	article
author	Ajinkya Borle, Vincent E. Elfving, Samuel J. Lomonaco
author_facet	Ajinkya Borle, Vincent E. Elfving, Samuel J. Lomonaco
author_sort	Ajinkya Borle, Vincent E. Elfving, Samuel J. Lomonaco
title	Quantum approximate optimization for hard problems in linear algebra
title_short	Quantum approximate optimization for hard problems in linear algebra
title_full	Quantum approximate optimization for hard problems in linear algebra
title_fullStr	Quantum approximate optimization for hard problems in linear algebra
title_full_unstemmed	Quantum approximate optimization for hard problems in linear algebra
title_sort	quantum approximate optimization for hard problems in linear algebra
publisher	SciPost
publishDate	2021
url	https://doaj.org/article/f4cd35313c20476585a2eeafa2ddea53
work_keys_str_mv	AT ajinkyaborlevincenteelfvingsamueljlomonaco quantumapproximateoptimizationforhardproblemsinlinearalgebra
_version_	1718406540234326016

Quantum approximate optimization for hard problems in linear algebra

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