Quantum

Symplectic Reck: In-Situ Learning of Gaussian Quantum Operations

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Briefings

A new symplectic Reck mesh architecture enables in-situ learning of unknown Gaussian quantum operations in photonic circuits. The system trains by nulling local response blocks sequentially using optical probes, identifying a local condition number to quantify required squeezing and measurement error sensitivity. Numerical results confirm finite-shot training and robustness against systematic gate-calibration errors, extending self-configuring optical networks from unitary to symplectic transformations.

Key points

• The symplectic Reck mesh physically realizes a factorization of a generic symplectic matrix S into a triangular array of two-mode and single-mode symplectic gates.
• Training proceeds by nulling local response blocks one at a time using optical probes, with a local condition number identifying the required squeezing for each nulling step.

Context

This research addresses physical learning in continuous-variable quantum systems using programmable photonic circuits. The symplectic Reck mesh generalizes the unitary Reck mesh used in optical neural networks, enabling hardware parameters to be trained directly from measured feedback for in-situ inversion of unknown Gaussian operations.

Limitations

The study relies on numerical demonstrations of finite-shot training and robustness to systematic errors. It does not provide experimental validation data, nor does it specify the physical platform's location or the specific measurement error sources observed during the training process.

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