Preparation and verification of tensor network states

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 semi-definite 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.

22 pages (12 + appendices), 4 figures

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Cited by in corpus (7)

• Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
• Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
• Efficient Verification of Ground States of Frustration-Free Hamiltonians
• Variational adiabatic transport of tensor networks
• Efficient Quantum Circuits based on the Quantum Natural Gradient
• Spectral Gap Optimization for Enhanced Adiabatic State Preparation
• A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems