Optical decoder learning for fiber communication at the quantum limit

Quantum information theory predicts that communication technology can be enhanced by using quantum signals to transfer classical bits. In order to fulfill this promise, the message-carrying signals must interact coherently at the decoding stage via a joint-detection receiver (JDR), whose realization with optical technologies remains an outstanding open problem to date. We introduce a supervised-learning framework for the systematic discovery of new JDR designs based on parametrized photonic integrated circuits. Our framework relies on the synthesis of a training set comprising quantum codewords and the corresponding classical message label; the codewords are processed by the JDR circuit and, after photo-detection, produce a guess for the label. The circuit parameters are then updated by minimizing a suitable loss function, reaching an optimal JDR design for that specific architecture. We showcase our method with coherent-state codes for the pure-loss bosonic channel, modelling optical-fiber and space communication, with a circuit architecture comprising linear optics, squeezing and threshold photo-detectors. We train JDR circuits for several code families, varying energy and code-size. We discover optical JDR circuit setups for maximum-size codes and small message-length that offer up to a $3$-fold enhancement in the bit decoding rate with respect to the optimal single-symbol receiver, and less than $7\%$-away from the theoretically optimal decoder, for which an explicit design is missing to date. Furthermore, the discovered receivers surpass previous JDR designs both in terms of bit decoding and bit transmission rate. Finally, we observe that the best-performing codes are those which can be mapped, via the JDR's optical processing, to modulations with different energy levels on different symbols, making the message symbols more distinguishabile via photo-detection.