Characterizing barren plateaus in quantum ansätze with the adjoint representation
Fontana, Enrico and Herman, Dylan and Chakrabarti, Shouvanik and Kumar, Niraj and Yalovetzky, Romina and Heredge, Jamie and Sureshbabu, Shree Hari and Pistoia, Marco (2024) Characterizing barren plateaus in quantum ansätze with the adjoint representation. Nature Communications, 15 (1). 7171. ISSN 2041-1723 (https://doi.org/10.1038/s41467-024-49910-w)
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Abstract
Variational quantum algorithms, a popular heuristic for near-term quantum computers, utilize parameterized quantum circuits which naturally express Lie groups. It has been postulated that many properties of variational quantum algorithms can be understood by studying their corresponding groups, chief among them the presence of vanishing gradients or barren plateaus, but a theoretical derivation has been lacking. Using tools from the representation theory of compact Lie groups, we formulate a theory of barren plateaus for parameterized quantum circuits whose observables lie in their dynamical Lie algebra, covering a large variety of commonly used ansätze such as the Hamiltonian Variational Ansatz, Quantum Alternating Operator Ansatz, and many equivariant quantum neural networks. Our theory provides, for the first time, the ability to compute the exact variance of the gradient of the cost function of the quantum compound ansatz, under mixing conditions that we prove are commonplace.
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Item type: Article ID code: 90325 Dates: DateEvent22 August 2024Published25 June 2024Accepted13 October 2023SubmittedSubjects: Science > Mathematics > Electronic computers. Computer science > Quantum computers Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 23 Aug 2024 10:44 Last modified: 25 Sep 2024 15:13 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/90325