Classical Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics

Area of Science:

• Quantum Information Science
• Quantum Dynamics
• Open Quantum Systems

Background:

• Symmetries are crucial for understanding quantum system evolution and conserved quantities.
• System-environment interactions in open quantum systems can disrupt dynamical symmetries.
• Prior research on noisy quantum dynamics primarily addressed Markovian noise, overlooking non-Markovian effects prevalent in quantum technologies.

Purpose of the Study:

• To develop a framework for quantifying the impact of non-Markovian noise on symmetric quantum evolution.
• To analyze how different types of noise affect symmetry in quantum systems.
• To provide analytic insights into controlling and characterizing open quantum system dynamics.

Main Methods:

• Utilized root space decompositions and the filter function formalism.
• Developed an analytical approach to quantify noise effects on symmetry.
• Employed numerical simulations for verification.

Main Results:

• Demonstrated that symmetry-preserving noise maintains the symmetric subspace.
• Showed that nonsymmetric noise causes specific leakage errors, block diagonal in the symmetry representation.
• Validated findings using the transverse-field Ising model and a quantum error detecting code.

Conclusions:

• The framework provides analytic insights into non-Markovian noise effects on quantum symmetries.
• Distinguishes between symmetry-preserving and symmetry-breaking noise impacts.
• Offers tools for controlling and characterizing open quantum systems with non-Markovian noise.