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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.<\/jats:p>","DOI":"10.22331\/q-2022-09-15-804","type":"journal-article","created":{"date-parts":[[2022,9,15]],"date-time":"2022-09-15T10:22:16Z","timestamp":1663237336000},"page":"804","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["Non-trivial symmetries in quantum landscapes and their resilience to quantum noise"],"prefix":"10.22331","volume":"6","author":[{"given":"Enrico","family":"Fontana","sequence":"first","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"},{"name":"Department of Computer and Information Sciences, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK"},{"name":"National Physical Laboratory, Teddington TW11 0LW, UK"}]},{"given":"M.","family":"Cerezo","sequence":"additional","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"},{"name":"Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA"}]},{"given":"Andrew","family":"Arrasmith","sequence":"additional","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}]},{"given":"Ivan","family":"Rungger","sequence":"additional","affiliation":[{"name":"National Physical Laboratory, Teddington, UK"}]},{"given":"Patrick J.","family":"Coles","sequence":"additional","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}]}],"member":"9598","published-online":{"date-parts":[[2022,9,15]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. 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