Ising Machines for Diophantine Problems in Physics

Abel, Steven; Nutricati, Luca

doi:10.48550/arxiv.2206.09956

Cited by 2 publications

(2 citation statements)

References 63 publications

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“…This sidesteps the difficulty of encoding the problem directly onto the annealer (for recent discussions in the Physics context see ref. [25] and also ref. [26]).…”

Section: The Genetic Algorithm and Quantum Annealingmentioning

confidence: 67%

Decoding Nature with Nature's Tools: Heterotic Line Bundle Models of Particle Physics with Genetic Algorithms and Quantum Annealing

Abel,

Constantin,

Harvey

et al. 2023

Fortschritte der Physik

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The string theory landscape may include a multitude of ultraviolet embeddings of the Standard Model, but identifying these has proven difficult due to the enormous number of available string compactifications. Genetic Algorithms (GAs) represent a powerful class of discrete optimisation techniques that can efficiently deal with the immensity of the string landscape, especially when enhanced with input from quantum annealers. In this letter, we focus on geometric compactifications of the heterotic string theory compactified on smooth Calabi‐Yau threefolds with Abelian bundles. We make use of analytic formulae for bundle‐valued cohomology to impose the entire range of spectrum requirements, something that has not been possible so far. For manifolds with a relatively low number of Kähler parameters, we compare the GA search results with results from previous systematic scans, showing that GAs can find nearly all the viable solutions while visiting only a tiny fraction of the solution space. Moreover, we carry out GA searches on manifolds with a larger numbers of Kähler parameters where systematic searches are not feasible.

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“…This sidesteps the difficulty of encoding the problem directly onto the annealer (for recent discussions in the Physics context see ref. [25] and also ref. [26]).…”

Section: The Genetic Algorithm and Quantum Annealingmentioning

confidence: 67%

Decoding Nature with Nature's Tools: Heterotic Line Bundle Models of Particle Physics with Genetic Algorithms and Quantum Annealing

Abel,

Constantin,

Harvey

et al. 2023

Fortschritte der Physik

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show abstract

“…Such methods, including genetic algorithms, reinforcement learning and quantum annealing have been used to solve similar Diophantine equations in refs. [32][33][34][35][36][37][38][39][40][41]. These results show that a good fraction of the solutions can be found by checking a tiny sample of the search space, provided a non-trivial number of solutions exists.…”

Section: Other Approaches and Extensionsmentioning

confidence: 99%

Enumerating Calabi‐Yau Manifolds: Placing Bounds on the Number of Diffeomorphism Classes in the Kreuzer‐Skarke List

Chandra,

Constantin,

Fraser‐Taliente

et al. 2024

Fortschritte der Physik

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The diffeomorphism class of simply connected smooth Calabi‐Yau threefolds with torsion‐free cohomology is determined via certain basic topological invariants: the Hodge numbers, the triple intersection form, and the second Chern class. In the present paper, we shed some light on this classification by placing bounds on the number of diffeomorphism classes present in the set of smooth Calabi‐Yau threefolds constructed from the Kreuzer‐Skarke (KS) list of reflexive polytopes up to Picard number six. The main difficulty arises from the comparison of triple intersection numbers and divisor integrals of the second Chern class up to basis transformations. By using certain basis‐independent invariants, some of which appear here for the first time, we are able to place lower bounds on the number of classes. Upper bounds are obtained by explicitly identifying basis transformations, using constraints related to the index of line bundles. Extrapolating our results, we conjecture that the favorable entries of the KS list of reflexive polytopes lead to some diffeomorphically distinct Calabi‐Yau threefolds.

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Ising Machines for Diophantine Problems in Physics

Cited by 2 publications

References 63 publications

Decoding Nature with Nature's Tools: Heterotic Line Bundle Models of Particle Physics with Genetic Algorithms and Quantum Annealing

Decoding Nature with Nature's Tools: Heterotic Line Bundle Models of Particle Physics with Genetic Algorithms and Quantum Annealing

Enumerating Calabi‐Yau Manifolds: Placing Bounds on the Number of Diffeomorphism Classes in the Kreuzer‐Skarke List

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