Preparation and verification of tensor network states

Autor(en)

Esther Cruz, Flavio Baccari, Jordi Tura, Norbert Schuch, J. Ignacio Cirac

Abstrakt

We consider a family of tensor network states defined on regular lattices that come with a natural definition of an adiabatic path to prepare them. This family comprises relevant classes of states, such as injective matrix product and projected entangled-pair states, and some corresponding to classical spin models. We show how uniform lower bounds to the gap of the parent Hamiltonian along the adiabatic trajectory can be efficiently computed using semidefinite programming. This allows one to check whether the adiabatic preparation can be performed efficiently with a scalable effort. We also derive a set of observables whose expectation values can be easily determined and that form a complete set, in the sense that they uniquely characterize the state. We identify a subset of those observables which can be efficiently computed if one has access to the quantum state and local measurements, and analyze how they can be used in verification procedures.

Organisation(en)

Institut für Mathematik, Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Max-Planck-Institut für Quantenoptik, Munich Center for Quantum Science and Technology (MCQST)

Journal

Physical Review Research

Band

4

Seiten

023161-1 - 023161-19

Anzahl der Seiten

19

ISSN

2643-1564

DOI

https://doi.org/10.1103/PhysRevResearch.4.023161

Publikationsdatum

05-2022

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik, 103036 Theoretische Physik, 102031 Theoretische Informatik, 101028 Mathematische Modellierung

Schlagwörter

ASJC Scopus Sachgebiete

Allgemeine Physik und Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/c276c522-0ad1-403d-bf6e-8b6a7f1bb44c