Parallel photonic information processing at gigabyte per second data rates using transient states

Abstract

The increasing demands on information processing require novel computational concepts and true parallelism. Nevertheless, hardware realizations of unconventional computing approaches never exceeded a marginal existence. While the application of optics in super-computing receives reawakened interest, new concepts, partly neuro-inspired, are being considered and developed. Here we experimentally demonstrate the potential of a simple photonic architecture to process information at unprecedented data rates, implementing a learning-based approach. A semiconductor laser subject to delayed self-feedback and optical data injection is employed to solve computationally hard tasks. We demonstrate simultaneous spoken digit and speaker recognition and chaotic time-series prediction at data rates beyond 1 Gbyte/s. We identify all digits with very low classification errors and perform chaotic time-series prediction with 10% error. Our approach bridges the areas of photonic information processing, cognitive and information science.

Figure 1. Reservoir computing concept and experimental scheme.

(a) Schematic representation of computation using nonlinear transient states generated by a single nonlinear element (NL) subject to delayed feedback. The N transient states x_m(t) used for computation are distributed along the delay line with spacing Θ. Here, u stands for the information input, y_k(t) for the value of the readout with index k. Panel (b) schematically shows the experimental realization of all-optical computation, utilizing a semiconductor laser diode as the nonlinear node. Information can be injected optically (electrically), given by u^(o) (u^(e)). The feedback delay is given by τ_D. The experimental setup comprises the laser diode, a tunable laser source to optically inject the information, a Mach–Zehnder modulator (MZM), a polarization controller, an attenuator, a circulator, splitters and a fast photo diode (PD) for signal detection.

Figure 2. Spoken digit classification with 5 GHz bandwidth.

Blue (red) data correspond to optical (electrical) information injection. The same reservoir responses for identifying the digit (a) and the speaker (b) demonstrate the potential of RC for true parallel computation. Best performance is found for a laser diode current I_b close to threshold (grey dotted line). A 20-fold cross-validation was repeated several times, with the s.d. given by the error bars.

Figure 3. Prediction error in a time-series prediction task.

(a) Dependence on laser diode current using 10 dB feedback attenuation. (b) Dependence on feedback attenuation using I_b=7.9 mA. The prediction error increases dramatically for I_b>8.9 mA, when the laser rest state becomes unstable. The importance of memory for time-series prediction can be seen in the lower panel, where the prediction error rapidly increases for a reduced feedback strength. Red error bars give the s.d. between three independent measurements. Blue error bars represent the s.d. for different training/testing partitions of the data.

Figure 4. Original and predicted trace and corresponding transients.

A sample of the target time series can be seen in (a). Data displayed in (b,c) were obtained by injecting data from the 180th to 240th time step from panel (a). (b) Shows experimental transient states for I_b=7.62, 9.2 and 10.78 mA, displayed in green, red and black, respectively. For high values of I_b, the transients lose the structure induced by the injected information, explaining the prediction error increase with I_b. (c) Shows an example of the target (black) and predicted (red) time series for I_b=7.6 mA. The top horizontal axis of panel (c) gives the times step number of the original target time trace, like given in (a). The lower horizontal axis represents the temporal duration for the prediction in the experiment, like given in (b).

Figure 5. Matrix multiplication to generate input to laser.

Cochleagram of digit six, uttered by speaker one is multiplied by matrix , creating the laser input.