Clifford Dressed Time-Dependent Variational Principle

TL;DR

This paper introduces a Clifford dressed TDVP algorithm that uses Clifford transformations to better control entanglement growth in matrix product state simulations, leading to improved efficiency and accuracy.

Contribution

The paper presents a novel Clifford dressed TDVP method that integrates Clifford transformations into MPS time evolution to enhance entanglement management and computational performance.

Findings

Significantly improves entanglement control in MPS simulations.

Achieves higher accuracy and longer simulation times.

Demonstrates effectiveness on various quantum many-body models.

Abstract

We propose an enhanced Time-Dependent Variational Principle (TDVP) algorithm for Matrix Product States (MPS) that integrates Clifford disentangling techniques to efficiently manage entanglement growth. By leveraging the Clifford group, which maps Pauli strings to other Pauli strings while maintaining low computational complexity, we introduce a Clifford dressed single-site 1-TDVP scheme. During the TDVP integration, we apply a global Clifford transformation as needed to reduce entanglement by iteratively sweeping over two-qubit Clifford unitaries that connect neighboring sites in a checkerboard pattern. We validate the new algorithm numerically using various quantum many-body models, including both integrable and non-integrable systems. Our results demonstrate that the Clifford dressed TDVP significantly improves entanglement management and computational efficiency, achieving higher accuracy, extended simulation times, and enhanced precision in computed observables compared to standard TDVP approaches. Additionally, we propose incorporating Clifford gates directly within the two-site 2-TDVP scheme.