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Quantum optimization with linear Ising penalty functions for customer data science [dataset] Open Access

Constrained combinatorial optimization problems, which are ubiquitous in industry, can be solved by quantum algorithms such as quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA). In these quantum algorithms, constraints are typically implemented with quadratic penalty functions. This penalty method can introduce large energy scales and make interaction graphs much more dense. These effects can result in worse performance of quantum optimization, particularly on near-term devices that have sparse hardware graphs and other physical limitations. In this work, we consider linear Ising penalty functions, which are applied with local fields in the Ising model, as an alternative method for implementing constraints that makes more efficient use of physical resources. We study the behaviour of the penalty method in the context of quantum optimization for customer data science problems. Our theoretical analysis and numerical simulations of QA and the QAOA indicate that this penalty method can lead to better performance in quantum optimization than the quadratic method. However, the linear Ising penalty method is not suitable for all problems as it cannot always exactly implement the desired constraint. In cases where the linear method is not successful in implementing all constraints, we propose that schemes involving both quadratic and linear Ising penalties can be effective.

Descriptions

Resource type

Dataset

Contributors

Data collector: Mirkarimi, Puya ¹
Creator: Mirkarimi, Puya ¹
Contact person: Mirkarimi, Puya ¹
Editor: Mirkarimi, Puya ¹
Data curator: Mirkarimi, Puya ¹
Data collector: Shukla, Ishaan ¹
Creator: Shukla, Ishaan ¹
Creator: Hoyle, David C. ²
Creator: Williams, Ross ²
Creator: Chancellor, Nicholas ³

¹ Durham University, United Kingdom
² dunnhumby, United Kingdom
³ Newcastle University, United Kingdom

Funder

Engineering and Physical Sciences Research Council
dunnhumby

Research methods

Computer assisted numerical calculations

Other description

Keyword

quantum computing
quantum annealing
quantum approximate optimization algorithm
combinatorial optimization

Subject

Quantum computing

Location

Language

English

Cited in

doi:10.48550/arXiv.2404.05467

Identifier

ark:/32150/r2fq977t82m
doi:10.15128/r2fq977t82m

Rights

Creative Commons Attribution 4.0 International (CC BY)

Publisher

Durham University

Date Created

2024-05-10

File Details

Depositor

P. Mirkarimi

Date Uploaded

10 May 2024, 11:05:05

Date Modified

13 May 2024, 10:05:14

Audit Status

Audits have not yet been run on this file.

Characterization

File format: zip (ZIP Format)

Mime type: application/zip

File size: 275404604

Last modified: 2024:05:10 12:31:14+01:00

Filename: QuantumLinearPenalty.zip

Original checksum: cb8e7501e92b2d9084849a0cb7b184a7