Regensburg 2022 – wissenschaftliches Programm

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QI: Fachverband Quanteninformation

QI 12: Quantum Computing and Algorithms

QI 12.8: Vortrag

Donnerstag, 8. September 2022, 17:00–17:15, H8

Exploiting symmetry in variational quantum machine learningJohannes Jakob Meyer1, Marian Mularski1,2, Elies Gil-Fuster1,3, •Antonio Anna Mele1, Francesco Arzani1, Alissa Wilms1,2, and Jens Eisert1,3,41Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany — 2Porsche Digital GmbH, 71636 Ludwigsburg, Germany — 3Fraunhofer Heinrich Hertz Institute, 10587 Berlin, Germany — 4Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany

Variational quantum machine learning is an extensively studied NISQ application. The success of variational quantum learning models crucially depends on finding a suitable parametrization of the model that encodes an inductive bias relevant to the learning task. However, little is known about guiding principles for constructing suitable parametrizations. We explore when and how symmetries of the learning problem can be exploited to construct quantum learning models with outcomes invariant under the symmetry of the learning task. Using tools from representation theory, we show how a standard gateset can be transformed into an equivariant one that respects the symmetries of the problem through a process of symmetrization. We benchmark the proposed methods on two toy problems that feature a non-trivial symmetry and observe a substantial increase in generalization performance. As our tools can also be applied in a straightforward way to other variational problems with symmetric structure, we show how equivariant gatesets can be used in variational quantum eigensolvers.

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