Pauli Propagation for Imaginary Time Evolution

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.