Convex Optimization for Nonequilibrium Steady States on a Hybrid Quantum Processor

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Dynamics

Background:

• Characterizing open quantum systems is crucial for quantum technologies.
• Determining steady states of quantum dynamics presents significant computational challenges.
• Existing variational quantum approaches face limitations in solving for steady states.

Purpose of the Study:

• To develop a quantum-assisted algorithm for efficiently determining steady states of open quantum systems.
• To address limitations associated with variational quantum methods in solving Lindblad dynamics.
• To enable the estimation of steady states for higher-dimensional quantum systems.

Main Methods:

• Reformulation of finding fixed points in Lindblad dynamics as a feasibility semidefinite program.
• Development of a hybrid quantum-classical algorithm.
• Demonstration on higher-dimensional open quantum systems.

Main Results:

• The proposed algorithm successfully estimates steady states of open quantum systems.
• The method bypasses known issues encountered with variational quantum approaches.
• The algorithm demonstrates capability in handling higher-dimensional systems.
• The approach can identify multiple steady states in systems exhibiting symmetries.

Conclusions:

• The quantum-assisted semidefinite programming approach offers a robust method for finding steady states in open quantum systems.
• This hybrid algorithm enhances the scalability and applicability of quantum methods in studying complex quantum dynamics.
• The ability to find multiple steady states opens new avenues for exploring quantum system symmetries.