Pauli Propagation for Imaginary-Time Evolution

TL;DR

This paper introduces the Imaginary-Time Pauli Propagation (ITPP) algorithm, extending the Pauli Propagation framework to simulate imaginary-time evolution for computing thermal and ground-state properties efficiently.

Contribution

The paper derives explicit update rules for imaginary-time evolution of Pauli operators and demonstrates an algorithm that balances accuracy and computational cost through operator truncation.

Findings

Benchmarking on the transverse-field Ising model shows controlled accuracy-cost trade-offs.

Operator growth under imaginary-time evolution presents challenges.

Combining imaginary and real-time propagation suggests a unified approach for open quantum systems.

Abstract

We extend the Pauli Propagation framework to simulate imaginary-time evolution. By deriving explicit update rules for the propagation of Pauli operators under imaginary-time evolution generated by Pauli strings, we introduce an imaginary-time Pauli Propagation (ITPP) algorithm for approximating imaginary-time dynamics directly in the Pauli basis. This approach enables the computation of thermal and ground-state properties while retaining the key computational advantages of Pauli Propagation. Benchmarking ITPP on the one-dimensional transverse-field Ising model demonstrates that truncation provides a controlled trade-off between accuracy and computational cost, while also revealing challenges associated with operator growth under imaginary-time evolution. Finally, combining imaginary-time and real-time Pauli Propagation naturally suggests a pathway toward simulating open quantum system dynamics within a unified framework.