Noisy quantum cellular automata for quantum versus classical excitation transfer

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Computational Physics

Background:

• Classical Markov chains are widely used to model dynamical processes.
• Understanding quantum coherence is crucial for developing quantum technologies.
• Excitation transfer in 1D lattices is a fundamental problem in physics.

Purpose of the Study:

• To introduce a generalized framework for noisy quantum cellular automata.
• To compare the dynamics of classical and quantum systems in excitation transfer.
• To isolate and analyze the role of quantum coherence in these processes.

Main Methods:

• Developed a class of noisy quantum cellular automata on a qubit lattice.
• Included classical Markov chains and maps allowing quantum coherence.
• Applied the model to excitation transfer in 1D lattices with equal local transition probabilities.

Main Results:

• Demonstrated that the framework captures both classical and quantum dynamics.
• Showcased the ability to isolate coherent effects from classical ones.
• Enabled exact treatment of conditional dynamics in a discrete approach.

Conclusions:

• The proposed noisy quantum cellular automata provide a versatile tool for studying complex dynamics.
• This discrete approach simplifies open system dynamics while retaining rich behaviors.
• The framework facilitates a clear comparison of classical versus quantum effects in excitation transfer.