Efficient verification of Affleck-Kennedy-Lieb-Tasaki states

TL;DR

This paper introduces a highly efficient method for verifying AKLT states on various graphs, significantly reducing the resources needed compared to previous methods, with broad applicability in quantum information processing.

Contribution

The authors develop a general, graph-based verification protocol for AKLT states that achieves constant sample complexity regardless of system size, improving efficiency over prior approaches.

Findings

Verification protocols for AKLT states on 1D and 2D lattices

Constant sample cost independent of system size

Applicable to arbitrary graphs with up to five vertices

Abstract

Affleck-Kennedy-Lieb-Tasaki (AKLT) states are an important class of many-body quantum states that are useful in quantum information processing, including measurement-based quantum computation in particular. Here we propose a general approach for constructing efficient verification protocols for AKLT states on arbitrary graphs with local spin measurements. Our verification protocols build on bond verification protocols and matching covers (including edge coloring) of the underlying graphs, which have a simple geometric and graphic picture. We also provide rigorous performance guarantee that is required for practical applications. With our approach, most AKLT states of wide interest, including those defined on 1D and 2D lattices, can be verified with a constant sample cost, which is independent of the system size and is dramatically more efficient than all previous approaches. As an illustration, we construct concrete verification protocols for AKLT states on various lattices and on arbitrary graphs up to five vertices.