Design of quantum optical experiments with logic artificial intelligence

Alba Cervera-Lierta1,2,3, Mario Krenn1,2,4,5, and Alán Aspuru-Guzik1,2,4,6

1Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Canada.
2Department of Computer Science, University of Toronto, Canada.
3Barcelona Supercomputing Center, Barcelona, Spain
4Vector Institute for Artificial Intelligence, Toronto, Canada.
5Max Planck Institute for the Science of Light (MPL), Erlangen, Germany
6Canadian Institute for Advanced Research (CIFAR) Lebovic Fellow, Toronto, Canada

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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.

We propose a new methodology to generate a quantum experimental setup in this work. In particular, we present an algorithm capable of constructing a photonic-based experiment that generates interesting quantum states. The algorithm, called Klaus, is based on Logic Artificial Intelligence (AI), 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. This way, we can encode the properties of the quantum states we want to generate with photons into a set of logical statements. Photonic experimental setups can be represented using graphs, which allow us to encode all these properties into logical clauses. Then, we check if these clauses are fulfilled and try to minimize the experimental requirement as much as possible by asking Klaus to remove graph edges and check iteratively if all constraints are still fulfilled. We compared the performance of Klaus with other state-of-the-art algorithms based on different methodologies, and we found significant improvements.
Problems spanning physical systems to mathematical conjectures can be solved using Logic AI. This work represents the first application to the design of quantum experiments.

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Cited by

[1] Anna Dawid, Julian Arnold, Borja Requena, Alexander Gresch, Marcin Płodzień, Kaelan Donatella, Kim A. Nicoli, Paolo Stornati, Rouven Koch, Miriam Büttner, Robert Okuła, Gorka Muñoz-Gil, Rodrigo A. Vargas-Hernández, Alba Cervera-Lierta, Juan Carrasquilla, Vedran Dunjko, Marylou Gabrié, Patrick Huembeli, Evert van Nieuwenburg, Filippo Vicentini, Lei Wang, Sebastian J. Wetzel, Giuseppe Carleo, Eliška Greplová, Roman Krems, Florian Marquardt, Michał Tomza, Maciej Lewenstein, and Alexandre Dauphin, "Modern applications of machine learning in quantum sciences", arXiv:2204.04198.

[2] Carlos Ruiz-Gonzalez, Sören Arlt, Jan Petermann, Sharareh Sayyad, Tareq Jaouni, Ebrahim Karimi, Nora Tischler, Xuemei Gu, and Mario Krenn, "Digital Discovery of 100 diverse Quantum Experiments with PyTheus", arXiv:2210.09980.

[3] Mario Krenn, Jonas Landgraf, Thomas Foesel, and Florian Marquardt, "Artificial Intelligence and Machine Learning for Quantum Technologies", arXiv:2208.03836.

[4] Moshe Y. Vardi and Zhiwei Zhang, "Quantum-Inspired Perfect Matching under Vertex-Color Constraints", arXiv:2209.13063.

[5] L. Sunil Chandran and Rishikesh Gajjala, "Perfect Matchings and Quantum Physics: Progress on Krenn's Conjecture", arXiv:2202.05562.

[6] Sören Arlt, Carlos Ruiz-Gonzalez, and Mario Krenn, "Digital Discovery of a Scientific Concept at the Core of Experimental Quantum Optics", arXiv:2210.09981.

The above citations are from SAO/NASA ADS (last updated successfully 2022-11-30 08:33:03). The list may be incomplete as not all publishers provide suitable and complete citation data.

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