Phase transitions in the classical simulability of open quantum systems

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Computational Physics

Background:

• Understanding the dynamics of open quantum systems is crucial for quantum computing and condensed matter physics.
• Entanglement dynamics are key to characterizing quantum behavior but are challenging to simulate for large systems.
• Environmental coupling and temperature significantly influence quantum system evolution.

Purpose of the Study:

• To introduce a novel Langevin unravelling method for simulating open quantum systems using matrix product states.
• To investigate the impact of environmental coupling and temperature on entanglement dynamics.
• To identify conditions under which quantum systems can be classically simulated.

Main Methods:

• Developed the time-dependent variational principle-Langevin equation for density matrix evolution.
• Studied entanglement dynamics as a function of environmental temperature and coupling strength.
• Analyzed the transition to a classically simulable phase.

Main Results:

• Identified a transition where individual trajectory entanglement saturates with increasing temperature and coupling.
• Demonstrated that this saturation permits classical simulation of the system for all times.
• Established this as the Hamiltonian open system analog of entanglement saturation in random circuits.

Conclusions:

• Open quantum systems have a limit to quantum simulation advantage, even with quantum effects present.
• Quantum simulators operating in this saturated entanglement phase cannot achieve quantum advantage.
• The developed method provides a pathway to understand and potentially overcome simulation limitations.