Real-time operator evolution in two and three dimensions via sparse Pauli dynamics

TL;DR

This paper introduces an extension of sparse Pauli dynamics for real-time quantum operator evolution in 2D and 3D systems, demonstrating competitive accuracy and efficiency compared to tensor network methods, especially in high-dimensional challenging models.

Contribution

The paper develops an extended sparse Pauli dynamics method capable of simulating high-dimensional quantum dynamics with limited resources, including a truncation scheme for operator growth.

Findings

Competitive with tensor network methods in 1D and 2D

Successfully applied to 3D transverse-field Ising model

Capable of high-accuracy simulations with limited computational resources

Abstract

We study real-time operator evolution using sparse Pauli dynamics, a recently developed method for simulating expectation values of quantum circuits. On the examples of energy and charge diffusion in 1D spin chains and sudden quench dynamics in the 2D transverse-field Ising model, it is shown that this approach can compete with state-of-the-art tensor network methods. We further demonstrate the flexibility of the approach by studying quench dynamics in the 3D transverse-field Ising model which is highly challenging for tensor network methods. For the simulation of expectation value dynamics starting in a computational basis state, we introduce an extension of sparse Pauli dynamics that truncates the growing sum of Pauli operators by discarding terms with a large number of X and Y matrices. This is validated by our 2D and 3D simulations. Finally, we argue that sparse Pauli dynamics is not only capable of converging challenging observables to high accuracy, but can also serve as a reliable approximate approach even when given only limited computational resources.