Quantum Belief Propagation Algorithm versus Suzuki-Trotter approach in the one-dimensional Heisenberg chains

TL;DR

This paper compares a quantum belief propagation algorithm with the Suzuki-Trotter method for one-dimensional Heisenberg chains, highlighting a trade-off between speed and accuracy in quantum state approximation.

Contribution

It introduces a quantum belief propagation algorithm for quantum systems and evaluates its performance against the Suzuki-Trotter approach.

Findings

QBP is faster but less accurate than Suzuki-Trotter in 3-body Heisenberg example.

QBP can approximate local structures of quantum states efficiently.

Future work should focus on improving QBP accuracy.

Abstract

Quantum systems are the future candidates for computers and information processing devices. Information about quantum states and processes may be incomplete and scattered in these systems. We use a quantum version of Belief Propagation(BP) Algorithm to integrate the distributed information. In this algorithm the distributed information, which is in the form of density matrix, can be approximated to local structures. The validity of this algorithm is measured in comparison with Suzuki-Trotter(ST) method, using simulated information. ST in 3-body Heisenberg example gives a more accurate answer, however Quantum Belief Propagation (QBP) runs faster based on complexity. In order to develop it in the future, we should be looking for ways to increase the accuracy of QBP.