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QI: Fachverband Quanteninformation
QI 30: Quantum Algorithms
QI 30.4: Talk
Thursday, March 9, 2023, 15:30–15:45, B305
Purified-Ensembles Variational Quantum Algorithm for Excited States — •Cheng-Lin Hong1, Lexin Ding1, Carlos L. Benavides-Riveros2,3, Luis Colmenarez2, and Christian Schilling1 — 1LMU Munich, Munich, Germany — 2Max Planck Institute for the Physics of Complex Systems, Dresden, Germany — 3INO-CNR BEC Center,Trento, Italy
Variational quantum algorithms (VQA) can obtain an approximation ground state of the target Hamiltonian. Methods based on VQA for calculating excited states currently involve high-depth unitary implementation or specific previously-found ground states. To directly extend the VQA framework to excited states, we propose an algorithm based on the purification of weighted ensemble states. This algorithm uses the Gross-Oliveira-Kohn (GOK) variational principle and chooses the appropriate set of weights to construct a BCS-like state; the exponential form of the BCS-like state allows efficient implementation on near-term quantum devices. Combined with variational quantum circuits, we can obtain all excited states we want.