Thermal State Simulation with Pauli and Majorana Propagation

TL;DR

This paper presents a novel propagation-based method for simulating thermal states in quantum systems by leveraging the sparsity of high-temperature states in Pauli and Majorana bases, enabling efficient imaginary-time evolution.

Contribution

It introduces a new approach to simulate thermal states using operator basis propagation, with analytic error guarantees and validation on large-scale models.

Findings

Efficient high-temperature state simulation demonstrated on 1D J1-J2 model.

Validated approach on triangular-lattice Hubbard model for static correlations.

Analytic bounds established for truncation errors during evolution.

Abstract

We introduce a propagation-based approach to thermal state simulation by adapting Pauli and Majorana propagation to imaginary-time evolution in the Schr\"odinger picture. Our key observation is that high-temperature states can be sparse in the Pauli or Majorana bases, approaching the identity at infinite temperature. By formulating imaginary-time evolution directly in these operator bases and evolving from the maximally mixed state, we access a continuum of temperatures where the state remains efficiently representable. We provide analytic guarantees for small-coefficient truncation and Pauli-weight (Majorana-length) truncation strategies by quantifying the error growth and the impact of backflow. Large-scale numerics on the 1D J1-J2 model (energies) and the triangular-lattice Hubbard model (static correlations) validate efficiency at high temperatures.