Temporal entropy and the complexity of computing the expectation value of local operators after a quench

We study the computational complexity of simulating the time-dependent expectation value of a local operator in a one-dimensional quantum system by using temporal matrix product states(MPSs) and argue that it is intimately related to that of encoding temporal transition matrices and their partial tr...

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Detalles Bibliográficos
Autores: Carignano, Stefano, Ramos Marimón, Carlos, Tagliacozzo, Luca
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/412130
Acceso en línea:https://hdl.handle.net/2117/412130
https://dx.doi.org/10.1103/PhysRevResearch.6.033021
Access Level:acceso abierto
Palabra clave:Quantum computers
Quantum quench
Quantum statistical mechanics
Quantum Information
Science & Technology
Statistical Physics & Thermodynamics
Simulació per ordinador
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeria
Descripción
Sumario:We study the computational complexity of simulating the time-dependent expectation value of a local operator in a one-dimensional quantum system by using temporal matrix product states(MPSs) and argue that it is intimately related to that of encoding temporal transition matrices and their partial traces. We show that we can upper-bound the rank of these reduced transition matrices by one of the Heisenberg evolution of local operators, thus making aconnection between two apparently different quantities, the temporal entanglement and the local operator entanglement(OE). As a result, whenever the local OE grows slower than linearly in time, we show that computing time-dependent expectation values of local operators using temporal MPSs is likely advantageous with respect to computing the same quantities using standard MPS techniques.