Computational complexity continuum within Ising formulation of NP problems
Publication Date
2022-12Journal Title
Communications Physics
ISSN
2399-3650
Publisher
Springer Science and Business Media LLC
Volume
5
Issue
1
Language
en
Type
Article
This Version
VoR
Metadata
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Kalinin, K., & Berloff, N. (2022). Computational complexity continuum within Ising formulation of NP problems. Communications Physics, 5 (1) https://doi.org/10.1038/s42005-021-00792-0
Description
Funder: Julian Schwinger Foundation JSF-19-02-0005
Funder: Cambridge Trust and NPIF EPSRC Doctoral grant EP/R512461/1
Abstract
<jats:title>Abstract</jats:title><jats:p>A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem yet not all problem instances are equivalently hard to optimise. Given that the operational principles of Ising machines are suited to the structure of some problems but not others, we propose to identify computationally simple instances with an ‘optimisation simplicity criterion’. Neuromorphic architectures based on optical, photonic, and electronic systems can naturally operate to optimise instances satisfying this criterion, which are therefore often chosen to illustrate the computational advantages of new Ising machines. As an example, we show that the Ising model on the Möbius ladder graph is ‘easy’ for Ising machines. By rewiring the Möbius ladder graph to random 3-regular graphs, we probe an intermediate computational complexity between P and NP-hard classes with several numerical methods. Significant fractions of polynomially simple instances are further found for a wide range of small size models from spin glasses to maximum cut problems. A compelling approach for distinguishing easy and hard instances within the same NP-hard class of problems can be a starting point in developing a standardised procedure for the performance evaluation of emerging physical simulators and physics-inspired algorithms.</jats:p>
Keywords
Article, /639/624/400/2797, /639/705/1042, article
Sponsorship
Engineering and Physical Sciences Research Council (EP/R512461/1)
Identifiers
s42005-021-00792-0, 792
External DOI: https://doi.org/10.1038/s42005-021-00792-0
This record's URL: https://www.repository.cam.ac.uk/handle/1810/333014
Rights
Licence:
http://creativecommons.org/licenses/by/4.0/
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