Variational quantum optimization with multibasis encodings
Abstract
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate a realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization landscapes. We tackle these challenges by introducing a variational quantum algorithm that benefits from two innovations: multibasis graph encodings using single-qubit expectation values and nonlinear activation functions. Our technique results in increased observed optimization performance and a factor-of-two reduction in requisite qubits. While the classical simulation of many qubits with traditional quantum formalism is impossible due to its exponential scaling, we mitigate this limitation with exact circuit representations using factorized tensor rings. In particular, the shallow circuits permitted by our technique, combined with efficient factorized tensor-based simulation, enable us to successfully optimize the MaxCut of the 512-vertex DIMACS library graphs on a single GPU. By improving the performance of quantum optimization algorithms while requiring fewer quantum resources and utilizing shallower, more error-resistant circuits, we offer tangible progress for variational quantum optimization.
Additional Information
This work was done during T.L.P.'s internship at NVIDIA. At CalTech, A.A. is supported in part by the Bren endowed chair, and Microsoft, Google, Adobe faculty fellowships. S.F.Y. thanks the AFOSR and the NSF for funding. The authors would like to thank Brucek Khailany, Johnnie Gray, Garnet Chan, Andreas Hehn, and Adam Jedrych for conversations.Additional details
- Eprint ID
- 116869
- Resolver ID
- CaltechAUTHORS:20220909-232706000
- Air Force Office of Scientific Research (AFOSR)
- NSF
- Bren Professor of Computing and Mathematical Sciences
- Microsoft Faculty Fellowship
- Google Faculty Research Award
- Adobe
- Created
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2022-10-29Created from EPrint's datestamp field
- Updated
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2022-11-01Created from EPrint's last_modified field