Variational Neural-Network Ansatz for Steady States in Open Quantum Systems

Area of Science:

• Quantum physics
• Computational physics
• Machine learning

Background:

• Open quantum systems are crucial for understanding quantum phenomena.
• Determining the steady state of these systems is computationally challenging.
• Existing methods often struggle with large or complex lattice systems.

Purpose of the Study:

• To introduce a novel variational approach for calculating the steady state of open quantum lattice systems.
• To demonstrate the efficacy of neural networks in solving complex quantum problems.
• To provide a scalable method applicable to various dissipative quantum models.

Main Methods:

• A purified neural network Ansatz is employed to represent the steady-state density matrix.
• The approach utilizes an extended Hilbert space incorporating ancillary degrees of freedom.
• Variational minimization is achieved through Markov chain Monte Carlo sampling of cost functions derived from the master equation.

Main Results:

• The proposed method successfully determines the steady state of open quantum lattice systems.
• The neural network approach offers a powerful alternative to traditional computational techniques.
• Proof-of-principle application to the dissipative quantum transverse Ising model validates the method's capability.

Conclusions:

• The developed variational neural network approach provides an efficient and general tool for studying open quantum lattice systems.
• This method opens new avenues for simulating complex quantum dynamics and exploring novel quantum phenomena.
• The technique is adaptable and holds promise for broader applications in quantum information and condensed matter physics.