Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution

TL;DR

This paper introduces a measurement-based imaginary time evolution method to efficiently prepare the AKLT ground state, achieving exponential speedup and compatibility with qubit-based simulators.

Contribution

It presents a novel deterministic approach for AKLT state preparation using MITE, significantly reducing resource requirements compared to traditional methods.

Findings

Constant scaling with the number of AKLT sites

Exponential improvement over naive convergence estimates

Compatible with qubit-based quantum simulators

Abstract

Quantum state preparation plays a crucial role in several areas of quantum information science, in applications such as quantum simulation, quantum metrology and quantum computing. However, typically state preparation requires resources that scale exponentially with the problem size, due to their probabilistic nature or otherwise, making studying such models challenging. In this article, we propose a method to prepare the ground state of the Affleck-Lieb-Kennedy-Tasaki (AKLT) model deterministically using a measurement-based imaginary time evolution (MITE) approach. By taking advantage of the special properties of the AKLT state, we show that it can be prepared efficiently using the MITE approach. Estimates based on the convergence of a sequence of local projections, as well as direct evolution of the MITE algorithm suggest a constant scaling with respect to the number of AKLT sites, which is an exponential improvement over the naive estimate for convergence. We show that the procedure is compatible with qubit-based simulators, and show that using a variational quantum algorithm for circuit recompilation, the measurement operator required for MITE can be well approximated by a circuit with a much shallower circuit depth compared with the one obtained using the default Qiskit method.