Lie-algebraic classical simulations for variational quantum computing

• URL: http://arxiv.org/abs/2308.01432v1
• Date: Wed, 2 Aug 2023 21:08:18 GMT
• Title: Lie-algebraic classical simulations for variational quantum computing
• Authors: Matthew L. Goh, Martin Larocca, Lukasz Cincio, M. Cerezo, Fr\'ed\'eric Sauvage
• Abstract summary: Methods relying on the Lie-algebraic structure of quantum dynamics have received relatively little attention. We present a framework that we call "$mathfrakg$sim", and showcase their efficient implementation in several paradigmatic variational quantum computing tasks. Specifically, we perform Lie-algebraic simulations to train and parametrized quantum circuits, design enhanced parameter strategies, solve tasks of quantum circuit synthesis, and train a quantum-phase synthesis.
• Score: 0.755972004983746
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity, and in the development of quantum technologies. Compared to other techniques for efficient classical simulations, methods relying on the Lie-algebraic structure of quantum dynamics have received relatively little attention. At their core, these simulations leverage the underlying Lie algebra - and the associated Lie group - of a dynamical process. As such, rather than keeping track of the individual entries of large matrices, one instead keeps track of how its algebraic decomposition changes during the evolution. When the dimension of the algebra is small (e.g., growing at most polynomially in the system size), one can leverage efficient simulation techniques. In this work, we review the basis for such methods, presenting a framework that we call "$\mathfrak{g}$-sim", and showcase their efficient implementation in several paradigmatic variational quantum computing tasks. Specifically, we perform Lie-algebraic simulations to train and optimize parametrized quantum circuits, design enhanced parameter initialization strategies, solve tasks of quantum circuit synthesis, and train a quantum-phase classifier.

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