RT info:eu-repo/semantics/article
T1 Finding eigenvectors with a quantum variational algorithm
A1 García Escartín, Juan Carlos
K1 Computación cuántica
K1 Fotónica
K1 Quantum algorithms
K1 Variational algorithms
K1 Hybrid quantum algorithms
K1 Eigenvectors
K1 Quantum principal component analysis
K1 SWAP test
K1 2210.23 Teoría Cuántica
K1 1203 Ciencia de Los Ordenadores
K1 2209 Óptica
AB 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 theSWAP 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 reproducethe found approximation to the eigenstate on demand. This variational eigenvectorfinder can be adapted to solve the generalized eigenvalue problem, to find the eigen-vectors of normal matrices and to perform quantum principal component analysis onunknown input mixed states. These algorithms can all be run with low-depth quantumcircuits, suitable for an efficient implementation on noisy intermediate-scale quantumcomputers and, with some restrictions, on linear optical systems. In full-scale quan-tum computers, where there might be optimization problems due to barren plateausin larger systems, the proposed algorithms can be used as a primitive to boost knownquantum algorithms. Limitations and potential applications are discussed.
PB Springer
YR 2024
FD 2024
LK https://uvadoc.uva.es/handle/10324/75146
UL https://uvadoc.uva.es/handle/10324/75146
LA eng
NO Quantum Information Processing, 2024, vol. 23, n. 7
NO Producción Científica
DS UVaDOC
RD 10-abr-2025