Theory Seminar: Preparation and verification of tensor network states

Esther Cruz (MPQ)
In this talk, I will present our recent work on the preparation and verification of a large family of tensor network states (TNs), which includes injective MPS and PEPS, and some TNs corresponding to classical spin models.

October 13, 2021

Esther Cruz (MPQ)
Group Seminar via Zoom
Wed, 13. October 2021,11:30 am (MEZ)

Abstract:

In this talk, I will present our recent work on the preparation and verification of a large family of tensor network states (TNs), which includes injective MPS and PEPS, and some TNs corresponding to classical spin models.

In the first part, I will talk about the proposed adiabatic algorithm and show how we can ensure its efficiency by finding uniform lower bounds to the gap of the parent Hamiltonian in an efficient manner, by computing a semi-definite program.

In the second part, I will talk about how one could devise a verification protocol that certifies the correct preparation of these states by a potentially untrusted quantum computer. To do so, we 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. If one has no access to the quantum state, we still conjecture the hardness of spoofing the verification test through some complexity-theoretic arguments.

Reference:

arXiv:2105.06866