Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems

TL;DR

This paper introduces a transformer-based variational ansatz for efficiently computing steady states in dissipative quantum many-body systems, capturing long-range correlations with high accuracy.

Contribution

It proposes a novel transformer density operator ansatz that encodes steady states in a doubled Hilbert space, preserving translation invariance and capturing complex correlations.

Findings

Accurately predicts steady states of dissipative Ising and Heisenberg models.

Demonstrates the effectiveness of the transformer ansatz in quantum many-body systems.

Achieves high accuracy in modeling mixed steady states.

Abstract

The transformer architecture, known for capturing long-range dependencies and intricate patterns, has extended beyond natural language processing. Recently, it has attracted significant attention in quantum information and condensed matter physics. In this work, we propose the \textit{transformer density operator ansatz} for determining the steady states of dissipative quantum many-body systems. By vectorizing the density operator as a many-body state in a doubled Hilbert space, the transformer encodes the amplitude and phase of the state's coefficients, with its parameters serving as variational variables. Our design preserves translation invariance while leveraging attention mechanisms to capture diverse long-range correlations. We demonstrate the effectiveness of our approach by numerically calculating the steady states of dissipative Ising and Heisenberg spin chain models, showing that our method achieves excellent accuracy in predicting mixed steady states.