Finite-Depth Preparation of Tensor Network States from Measurement

TL;DR

This paper introduces a measurement-based protocol for preparing tensor network states with finite depth, enabling efficient realization of complex quantum states across various phases of matter.

Contribution

It develops criteria for deterministic state preparation via measurements, constructs families of preparable states in 1D and 2D, and provides verification diagnostics.

Findings

Constructed measurement-preparable states interpolating between key quantum states.

Engineered states with customizable correlation lengths and entanglement.

Provided diagnostics for verifying state preparability.

Abstract

Although tensor network states constitute a broad range of exotic quantum states, their realization is challenging and often requires resources whose depth scales with system size. In this work, we explore criteria on the local tensors for enabling deterministic state preparation via a single round of measurements and on-site unitary feedback. We use these criteria to construct families of measurement-preparable states in one and two dimensions, tuning between distinct symmetry-breaking, symmetry-protected, and intrinsic topological phases of matter. For instance, in one dimension we chart out a three-parameter family of preparable states which interpolate between the AKLT, cluster, GHZ and other states of interest. Our protocol even allows one to engineer preparable quantum states with a range of desired correlation lengths and entanglement properties. In addition to such constructive approaches, we present diagnostics for verifying whether a given tensor network state is preparable using measurements. We conclude by charting out generalizations, such as considering multiple rounds of measurements, implementing matrix product operators, and using incomplete basis measurements.