BACKGROUND

A communication system generally includes one or more sources, one or more receivers, and one or more channels. A source and a receiver communicate with each other via a respective channel. The source encodes a symbol onto a signal and transmitted the signal, after which the receiver decodes the transmitted signal to recover the symbol, subject to an error rate. The communication channel may, however, be affected by loss and noise that lead to degradation of encoded information. The receiver may incorporate error correction to at least partly mitigate this degradation. For example, error correction may be applied to the outputs of a homodyne detector to decode the signal with an acceptable error rate, as long as the signal-to-noise ratio of the transmitted signal is above a certain threshold determined by the employed error-correcting code. For very lossy communication channels, however, the signal-to-noise ratio of the transmitted signal may be further reduced by the fundamental quantum noise, in which case the signal cannot be decoded by a homodyne detector, and the symbol cannot be accurately determined.

SUMMARY

Quantum information theory has shown that the Holevo bound is below the error rate of a homodyne receiver. Accordingly, many techniques have been explored to improve upon the homodyne receiver's performance. For example, the Dolinar receiver asymptotically approaches the Helstrom bound by using information feed-forward. The Dolinar receiver separates the signal into infinitely small time segments, and displaces the signal based on the single-photon detection history. In practice, the time segment duration is limited by the fastest feed-forward processing time, and is therefore limited to a finite number of time modes. Nevertheless, it still surpasses the performance of the homodyne detector even with such experimental imperfections.

The Dolinar receiver and its variants minimize the posterior error rate with the assumption of equal time segmentation, and therefore can be thought of as a problem for mathematical optimization. However, when the received signal includes time-dependent noise or features, the number of coefficients needed to mathematical describe the error rate blows up quickly. Accordingly, the amount of time needed to compute the next displacement of the signal (i.e., latency) increases rapidly, thereby forcing the duration of each time segment to increase, in turn reducing the symbol rate (for a fixed error rate).

The present embodiments feature a quantum receiver that uses deep learning, and other machine-learning techniques, to rapidly provide feed-forward signals. The quantum receiver may be thought of as a generalized Dolinar receiver without restrictions such as equal time segmentation or Markovian feedforward. Three machine-learning architectures are explored: an artificial neural network (ANN), a probabilistic binary tree classifier (PBT), and runtime stochastic optimization with automatic differentiation (AD). These architectures handle the logic of hypothesis updating, displacement generation, measurements, feedforward parameters, and decisions simultaneously. For a particular architecture, the quantum receiver can be programmed to learn the history-dependent displacements to minimize the overall error rate.

In embodiments, a quantum receiver for decoding an optical signal includes a beamsplitter for interfering the optical signal with a local-oscillator field to generate a displaced field, and a single-photon detector for detecting the displaced field. The quantum receiver also includes a signal-processing circuit for determining, based on an electrical output of the single-photon detector, a measurement outcome. The signal-processing circuit also determines, based on the measurement outcome and a feed-forward machine-learning model, a next displacement. The quantum receiver also includes at least one modulator for modulating, based on the next displacement, one or both of the optical signal and the local-oscillator field.

In other embodiments, a method for decoding an optical signal includes interfering the optical signal with a local-oscillator field to generate a displaced field. The method also includes detecting the displaced field with a single-photon detector and determining, based on an electrical output of the single-photon detector, a measurement outcome. The method also includes determining, based on the measurement outcome and a feed-forward machine-learning model, a next displacement. The method also includes modulating, based on the next displacement, one or both of the optical signal and the local-oscillator field.

