Neural-Network Approach to Dissipative Quantum Many-Body Dynamics

Abstract

In experimentally realistic situations, quantum systems are never perfectly isolated and the coupling to their environment needs to be taken into account. Often, the effect of the environment can be well approximated by a Markovian master equation. However, solving this master equation for quantum many-body systems, becomes exceedingly hard due to the high dimension of the Hilbert space. Here we present an approach to the effective simulation of the dynamics of open quantum many-body systems based on machine learning techniques. We represent the mixed many-body quantum states with neural networks in the form of restricted Boltzmann machines and derive a variational Monte-Carlo algorithm for their time evolution and stationary states. We document the accuracy of the approach with numerical examples for a dissipative spin lattice system.

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• Constructing neural stationary states for open quantum many-body systems
• Creating and concentrating quantum resource states in noisy environments using a quantum neural network
• Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems
• Nonuniform phases in the geometrically frustrated dissipative XYZ model
• Steady-state phases of dissipative spin-1/2 XYZ model with frustrated interaction
• Steady-state susceptibility in continuous phase transitions of dissipative systems
• Investigating Network Parameters in Neural-Network Quantum States
• Transport in Conductors and Rectifiers: Mean-Field Redfield Equations and Non-Equilibrium Green's Functions
• Bidirectional information flow quantum state tomography
• Stochastic Simulation of Emission Spectra and Classical Photon Statistics of Quantum Dot Superluminescent Diodes
• A Tensor Network Approach to Finite Markov Decision Processes