An Automated Approach to the Collatz Conjecture

Yolcu, Emre; Aaronson, Scott; Heule, Marijn J. H.

doi:10.48550/arxiv.2105.14697

Cited by 2 publications

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“…The test states have different entanglement properties quantified by the Schmidt Rank Vector (SRV) [27], a different number of parties n, and a different number of basis elements. In particular, we look for the graphs for the GHZ(n,d) states GHZ(4,3) and GHZ(6,2), and states with SRV equal to (5,4,4), (6,4,4), (6,5,4) and (9,5,5). The wave functions of these states are written explicitly in App.…”

Section: Benchmarksmentioning

confidence: 99%

“…The recent advances in SAT solvers have allowed the automatic resolution of extremely complex problems involving thousands of variables [4]. Long-standing conjectures such as the Boolean Pythagorean triples problem [5], the Keller's conjecture (unresolved for 90 years) [6], among others [7,8,9] have been solved using logic AI providing, in some cases, intricate, long [10] but correct deduction steps.…”

Section: Introductionmentioning

confidence: 99%

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Design of quantum optical experiments with logic artificial intelligence

Cervera-Lierta

Krenn

Aspuru‐Guzik

2022

Quantum

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Logic Artificial Intelligence (AI) is a subfield of AI where variables can take two defined arguments, True or False, and are arranged in clauses that follow the rules of formal logic. Several problems that span from physical systems to mathematical conjectures can be encoded into these clauses and solved by checking their satisfiability (SAT). In contrast to machine learning approaches where the results can be approximations or local minima, Logic AI delivers formal and mathematically exact solutions to those problems. In this work, we propose the use of logic AI for the design of optical quantum experiments. We show how to map into a SAT problem the experimental preparation of an arbitrary quantum state and propose a logic-based algorithm, called Klaus, to find an interpretable representation of the photonic setup that generates it. We compare the performance of Klaus with the state-of-the-art algorithm for this purpose based on continuous optimization. We also combine both logic and numeric strategies to find that the use of logic AI significantly improves the resolution of this problem, paving the path to developing more formal-based approaches in the context of quantum physics experiments.

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Section: Benchmarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design of quantum optical experiments with logic artificial intelligence

Cervera-Lierta

Krenn

Aspuru‐Guzik

2022

Quantum

View full text Add to dashboard Cite

show abstract

“…Other open problems are approaching their resolution by using automatic reasoning strategies. For instance, the computation of Heesch numbers of non-tiling polyforms [9] or the Collatz conjecture [10], an 80 year old open problem in number theory about which Paul Erdős said that "mathematics may not be ready for such problems" [11]. In the end, any NP problem can be encoded into a SAT, thus the advances in SAT solving will immediately impact the resolution of many of these problems.…”

Section: Introductionmentioning

confidence: 99%

Design of quantum optical experiments with logic artificial intelligence

Cervera-Lierta¹,

Krenn²,

Aspuru‐Guzik³

2021

Preprint

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Logic artificial intelligence (AI) is a subfield of AI where variables can take two defined arguments, True or False, and are arranged in clauses that follow the rules of formal logic. Several problems that span from physical systems to mathematical conjectures can be encoded into these clauses and be solved by checking their satisfiability (SAT). Recently, SAT solvers have become a sophisticated and powerful computational tool capable, among other things, of solving long-standing mathematical conjectures. In this work, we propose the use of logic AI for the design of optical quantum experiments. We show how to map into a SAT problem the experimental preparation of an arbitrary quantum state and propose a logic-based algorithm, called Klaus, to find an interpretable representation of the photonic setup that generates it. We compare the performance of Klaus with the state-of-the-art algorithm for this purpose based on continuous optimization. We also combine both logic and numeric strategies to find that the use of logic AI improves significantly the resolution of this problem, paving the path to develop more formal-based approaches in the context of quantum physics experiments.

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An Automated Approach to the Collatz Conjecture

Cited by 2 publications

References 0 publications

Design of quantum optical experiments with logic artificial intelligence

Design of quantum optical experiments with logic artificial intelligence

Design of quantum optical experiments with logic artificial intelligence

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