Programmable Open Quantum Systems

Area of Science:

• Quantum Information Science
• Quantum Control
• Open Quantum Systems

Background:

• Programmability is crucial in quantum computation and control, enabling diverse quantum transformations.
• Open quantum systems, previously viewed as error sources, are now recognized as computational resources.
• The programmability of open systems (Lindbladian semigroups) remains an underexplored area.

Purpose of the Study:

• To develop a framework for characterizing and quantifying the programmability of Lindbladian semigroups.
• To identify classes of quantum systems that are programmable.
• To establish a measure for the cost of programming these systems.

Main Methods:

• Combining physically implementable retrieval maps with time-varying program states.
• Analyzing symmetry and stochastic structures within Lindbladian dynamics.
• Defining an operational programming cost based on required samples.

Main Results:

• Identification of quantum programmable classes, including covariant semigroups and fully dissipative Pauli Lindbladians.
• A necessary condition for physical programmability was established, excluding certain generators.
• Construction of quasisampling protocols for nonphysically programmable cases.
• Introduction of an operational programming cost for Lindbladians.

Conclusions:

• The framework provides a quantitative measure of programmability for open quantum systems.
• Results bridge programmable channel theory with open system dynamics.
• Symmetry-driven compression schemes and resource estimates are offered for noisy quantum technologies.