Efficient Characterization of Quantum Evolutions via a Recommender System

Priya Batra, Anukriti Singh, and T. S. Mahesh

Department of Physics and NMR Research Center, Indian Institute of Science Education and Research, Pune 411008, India

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We demonstrate characterizing quantum evolutions via matrix factorization algorithm, a particular type of the recommender system (RS). A system undergoing a quantum evolution can be characterized in several ways. Here we choose (i) quantum correlations quantified by measures such as entropy, negativity, or discord, and (ii) state-fidelity. Using quantum registers with up to 10 qubits, we demonstrate that an RS can efficiently characterize both unitary and nonunitary evolutions. After carrying out a detailed performance analysis of the RS in two qubits, we show that it can be used to distinguish a clean database of quantum correlations from a noisy or a fake one. Moreover, we find that the RS brings about a significant computational advantage for building a large database of quantum discord, for which no simple closed-form expression exists. Also, RS can efficiently characterize systems undergoing nonunitary evolutions in terms of quantum discord reduction as well as state-fidelity. Finally, we utilize RS for the construction of discord phase space in a nonlinear quantum system.

Confused about choosing a product? Probably, the Recommender System (RS) might help. RS is a type of algorithm that is being used by online platforms to recommend products to consumers. They use the past history of an individual along with the similar choices of other consumers. Given a sparse database of the rating matrix, RS can fill out the remaining elements with pretty high accuracy. Here we use RS to complete a sparse quantum database of correlations, gate fidelities, etc. Interestingly, we found that RS can even predict quantum discord, a kind of quantum correlation that has no analytical expression. While one can think of many applications of such a prediction, here we demonstrate completing a sparse phase-space diagram of a nonlinear quantum system.

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[2] Kavita Dorai and Arvind, "NMR Quantum Information Processing: Indian Contributions and Perspectives", Journal of the Indian Institute of Science 103 2, 569 (2023).

[3] Priya Batra, M. Harshanth Ram, and T.S. Mahesh, "Recommender system expedited quantum control optimization", Physics Open 14, 100127 (2023).

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