Preparation and verification of tensor network states

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

Publications: Contribution to journalArticlePeer Reviewed

Abstract

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.

Original languageEnglish
Article number023161
Number of pages19
JournalPhysical Review Research
Volume4
Issue number2
DOIs
Publication statusPublished - 31 May 2022

Austrian Fields of Science 2012

  • 103025 Quantum mechanics
  • 103036 Theoretical physics
  • 102031 Theoretical computer science
  • 101028 Mathematical modelling

Keywords

  • SCHRODINGER CAT STATES
  • QUANTUM COMPUTATION
  • ENTANGLEMENT
  • GENERATION
  • COMPLEXITY
  • SUPREMACY
  • VERSION

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