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oai:uvadoc.uva.es:10324/751462025-03-11T09:54:15Zcom_10324_1191com_10324_931com_10324_894col_10324_1379

Finding eigenvectors with a quantum variational algorithm García Escartín, Juan Carlos Computación cuántica Fotónica Producción Científica This paper presents a hybrid variational quantum algorithm that finds a random eigen- vector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum circuit. The eigenvec- tor is described by a compact set of classical parameters that can be used to reproduce the found approximation to the eigenstate on demand. This variational eigenvector finder can be adapted to solve the generalized eigenvalue problem, to find the eigen- vectors of normal matrices and to perform quantum principal component analysis on unknown input mixed states. These algorithms can all be run with low-depth quantum circuits, suitable for an efficient implementation on noisy intermediate-scale quantum computers and, with some restrictions, on linear optical systems. In full-scale quan- tum computers, where there might be optimization problems due to barren plateaus in larger systems, the proposed algorithms can be used as a primitive to boost known quantum algorithms. Limitations and potential applications are discussed. 2025-02-26T14:04:54Z 2025-02-26T14:04:54Z 2024 info:eu-repo/semantics/article Quantum Information Processing, 2024, vol. 23, n. 7 https://uvadoc.uva.es/handle/10324/75146 10.1007/s11128-024-04461-3 7 Quantum Information Processing 23 1573-1332 eng https://link.springer.com/article/10.1007/s11128-024-04461-3 info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/4.0/ © 2024 The Author(s) Atribución 4.0 Internacional Springer SI