Flavio Beccari (Max Planck Institute of Quantum Optics)

Preparation and verification of tensor network states

In this talk I will introduce a family of tensor network states defined on regular lattices that can be efficiently prepared with a quantum computer by adiabatic evolution. This family comprises relevant classes of states, such as injective Matrix Product and Projected Entangled-Pair States, and some corresponding to classical spin models. I will show how uniform lower bounds to the gap of the parent Hamiltonian along the adiabatic trajectory can be efficiently computed using semi-definite programming. I will also present 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. I will 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.