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

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.

v1: 7+10 pages

References in corpus (18)

• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Constructing neural stationary states for open quantum many-body systems
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• The structure of preserved information in quantum processes
• Transformer variational wave functions for frustrated quantum spin systems
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Empowering deep neural quantum states through efficient optimization
• Transformer Quantum State: A Multi-Purpose Model for Quantum Many-Body Problems
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Exact solution of the infinite-range dissipative transverse-field Ising model
• Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems
• On the complexity of the steady-state of weakly symmetric open quantum lattices
• Liouville Space Neural Network Representation of Density Matrices