Augmenting Density Matrix Renormalization Group with Clifford Circuits

TL;DR

This paper introduces a novel method that combines Clifford circuits with DMRG to improve the simulation of highly entangled quantum states, especially in two-dimensional systems, with minimal additional computational cost.

Contribution

The work presents an integrated framework of Clifford circuits within DMRG, enhancing accuracy for quantum many-body simulations and adaptable to other numerical methods.

Findings

Significant accuracy improvement in quantum state simulations.

Minimal additional computational cost achieved.

Framework adaptable to various numerical approaches.

Abstract

Density Matrix Renormalization Group (DMRG) or Matrix Product States (MPS) are widely acknowledged as highly effective and accurate methods for solving one-dimensional quantum many-body systems. However, the direct application of DMRG to the study two-dimensional systems encounters challenges due to the limited entanglement encoded in the wave-function ansatz. Conversely, Clifford circuits offer a promising avenue for simulating states with substantial entanglement, albeit confined to stabilizer states. In this work, we present the seamless integration of Clifford circuits within the DMRG algorithm, leveraging the advantages of both Clifford circuits and DMRG. This integration leads to a significant enhancement in simulation accuracy with small additional computational cost. Moreover, this framework is useful not only for its current application but also for its potential to be easily adapted to various other numerical approaches