Partially unitary learning.

Area of Science:

• Quantum Information Science
• Quantum Computing
• Mathematical Physics

Background:

• Mapping quantum states between Hilbert spaces is crucial for quantum information processing.
• Existing methods often lack a systematic approach for optimizing this mapping, especially under realistic constraints.

Purpose of the Study:

• To formulate and solve the problem of optimal wavefunction mapping between input (IN) and output (OUT) Hilbert spaces.
• To develop a computational method for constructing the optimal quantum channel (U).

Main Methods:

• Formulation as an optimization problem maximizing total fidelity subject to partial unitarity constraints.
• Development of an iterative algorithm to find the global maximum of the fidelity function.
• Application of the algorithm to demonstrate its utility in various quantum scenarios.

Main Results:

• An operator U, representing a partially unitary quantum channel (isometry), is constructed for optimal IN-to-OUT Hilbert space mapping.
• An efficient iterative algorithm guarantees finding the global maximum fidelity.
• Demonstrated applicability across diverse quantum information tasks.

Conclusions:

• The developed iterative algorithm provides a robust method for optimal quantum channel construction.
• This work offers a practical tool for advancing quantum state manipulation and quantum information processing.
• A software implementation is available, facilitating broader research and application.