Clifford-Dressed Variational Principles for Precise Loschmidt Echoes

TL;DR

This paper introduces a Clifford-dressed variational approach that improves the calculation of Loschmidt echoes in many-body quantum systems by controlling entanglement growth and simplifying amplitude computations.

Contribution

It extends the Clifford dressed TDVP to efficiently compute wavefunction overlaps, enabling accurate Loschmidt echo analysis in complex many-body models.

Findings

Effective control of entanglement growth during evolution

Feasible overlap computation between MPS and stabilizer states

Successful benchmarking on 1D and 2D Ising models

Abstract

We extend the recently introduced Clifford dressed Time-Dependent Variational Principle (TDVP) to efficiently compute many-body wavefunction amplitudes in the computational basis. This advancement enhances the study of Loschmidt echoes, which generally require accurate calculations of the overlap between the evolved state and the initial wavefunction. By incorporating Clifford disentangling gates during TDVP evolution, our method effectively controls entanglement growth while keeping the computation of these amplitudes accessible. Specifically, it reduces the problem to evaluating the overlap between a Matrix Product State (MPS) and a stabilizer state, a task that remains computationally feasible within the proposed framework. To demonstrate the effectiveness of this approach, we first benchmark it on the one-dimensional transverse-field Ising model. We then apply it to more challenging scenarios, including a non-integrable next-to-nearest-neighbor Ising chain and a two-dimensional Ising model. Our results highlight the versatility and efficiency of the Clifford-augmented MPS, showcasing its capability to go beyond the evaluation of simple expectation values. This makes it a powerful tool for exploring various aspects of many-body quantum dynamics.