Non-trivial symmetries in quantum landscapes and their resilience to quantum noise
Fontana, Enrico and Cerezo, M. and Arrasmith, Andrew and Rungger, Ivan and Coles, Patrick J. (2022) Non-trivial symmetries in quantum landscapes and their resilience to quantum noise. Quantum, 6. 804. ISSN 2521-327X (https://doi.org/10.22331/q-2022-09-15-804)
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Abstract
Very little is known about the cost landscape for parametrized Quantum Circuits (PQCs). Nevertheless, PQCs are employed in Quantum Neural Networks and Variational Quantum Algorithms, which may allow for near-term quantum advantage. Such applications require good optimizers to train PQCs. Recent works have focused on quantum-aware optimizers specifically tailored for PQCs. However, ignorance of the cost landscape could hinder progress towards such optimizers. In this work, we analytically prove two results for PQCs: (1) We find an exponentially large symmetry in PQCs, yielding an exponentially large degeneracy of the minima in the cost landscape. Alternatively, this can be cast as an exponential reduction in the volume of relevant hyperparameter space. (2) We study the resilience of the symmetries under noise, and show that while it is conserved under unital noise, non-unital channels can break these symmetries and lift the degeneracy of minima, leading to multiple new local minima. Based on these results, we introduce an optimization method called Symmetry-based Minima Hopping (SYMH), which exploits the underlying symmetries in PQCs. Our numerical simulations show that SYMH improves the overall optimizer performance in the presence of non-unital noise at a level comparable to current hardware. Overall, this work derives large-scale circuit symmetries from local gate transformations, and uses them to construct a noise-aware optimization method.
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Item type: Article ID code: 82674 Dates: DateEvent2022Published15 September 2022Published Online1 September 2022AcceptedSubjects: Science > Physics Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 11 Oct 2022 13:04 Last modified: 18 Sep 2024 00:53 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/82674