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...
| Autores: | , , |
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| 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 |
| 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. |
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