Variational approach to learning photonic unitary operators

Area of Science:

• Quantum optics and information processing.
• Harnessing structured light for computational tasks.

Background:

• Structured light, with tailored internal degrees of freedom, is crucial for quantum and classical information processing.
• Variational quantum computing principles offer a framework for optimization problems.

Purpose of the Study:

• To develop an adaptable scheme for learning unitary operations using high-dimensional structured light.
• To leverage optical matrix-vector multiplication for simulating computational processes.

Main Methods:

• Utilizing structured light modulated in the transverse spatial degree of freedom.
• Employing a pseudo-random walk over the unitary operation's parameter space.
• Implementing optical matrix-vector multiplication with Gaussian modes and cylindrical lenses.

Main Results:

• Theoretically outlined and experimentally demonstrated the learning scheme.
• Successfully learned optical unitary matrices for dimensions d = 2, 4, 8, and 16.
• Achieved average fidelities exceeding 90% for the learned operations.

Conclusions:

• The developed method advances high-dimensional information processing capabilities.
• The scheme is adaptable for quantum and classical state and channel tomography.
• Demonstrates a novel application of structured light in computational tasks.