Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian...

Area of Science:

• Quantum Physics
• Computational Physics
• Many-Body Systems

Background:

• Simulating open quantum many-body systems is computationally challenging.
• Existing methods often require expensive re-ordering protocols.
• Understanding system-reservoir interactions is crucial for quantum technologies.

Purpose of the Study:

• To develop an efficient algorithm for the time evolution of open quantum many-body systems.
• To propose a matrix-product state (MPS) architecture that exploits initial system and reservoir states.
• To adapt the algorithm for both Markovian and non-Markovian interactions.

Main Methods:

• Utilizing a convenient MPS-architecture structure that leverages initial system and reservoir states.
• Circumventing numerically expensive re-ordering protocols.
• Adapting the algorithm for non-Markovian interactions by including information backflow.
• Deriving the basis in the quantum stochastic Schrödinger picture.

Main Results:

• The algorithm efficiently simulates the time evolution of open quantum many-body systems.
• It is applicable to both Markovian and non-Markovian system-reservoir interactions.
• The Heisenberg spin chain model demonstrates the algorithm's ability to handle large system sizes (N=30).
• Highly unusual steady states were generated in a non-Markovian system with coherent feedback control.

Conclusions:

• The proposed MPS-based algorithm offers an efficient approach for simulating open quantum many-body systems.
• The method's adaptability to different interaction types (Markovian/non-Markovian) enhances its applicability.
• This work paves the way for studying complex quantum phenomena in larger systems and with advanced control techniques.