Scalable photonic reservoir computing for parallel machine learning tasks

Domain: physics
Published: 2025-12-31
Editorial outcome: minor_revision

Abstract
Neuromorphic photonics enables brain-inspired information processing with higher bandwidth and lower energy consumption than traditional electronics, addressing the growing computational demands of the Internet of Things, cloud services, and edge computing. However, even current state-of-the-art electronic and photonic platforms are incapable of delivering the scalable throughput, multitasking processing, and energy efficiency required by these applications. Here, we demonstrate a tunable photonic reservoir computing device based on a nonlinear amplifying loop mirror (NALM), leveraging a time-delayed, single-unit, all-optical architecture. By combining dense temporal encoding with wavelength-division multiplexing, the system supports concurrent multitasking across independent data channels, enabling scalable computational performance without additional hardware complexity. Experiments and theoretical validation on classification and prediction benchmarks demonstrate the device’s performance, achieving a throughput of 20 tera-operations-per-second and an energy efficiency of 4.4 fJ per operation. These results highlight a promising path towards reconfigurable, compact, and high-performance photonic processors for real-time intelligent applications.

Introduction
The rapid evolution of artificial intelligence (AI) and machine learning (ML) has revolutionized data processing, driving demand for computational platforms that are capable of handling vast amounts of data with high processing speed and minimal latency1,2. Neuromorphic photonics presents a promising solution to these challenges2–8 as it leverages optical systems to emulate neural networks, thus providing higher bandwidth, faster speeds, lower energy consumption, and smaller footprints compared to traditional electronic processors7,9–11. This solution can also lower carbon emissions, especially when training on large datasets. However, existing photonic architectures have critical limitations in computational throughput, energy efficiency, and latency, thus hindering their ability to meet the growing computational needs of AI, deep learning12, and other real-time-based applications13,14. Neuromorphic computing frameworks, such as extreme learning machines15, wave-based neural networks16, and reservoir computing (RC)17,18, have emerged as compelling approaches for the efficient implementation of photonic processing devices for ML.

Optical RC systems exploit physical dynamics to process input data, thus reducing training time and complexity while improving computational efficiency. To date, single-node optical RC architectures have been demonstrated using active components (such as semiconductor lasers19, amplifiers20,21, and electro-optic modulators22,23), as well as passive components24 (including saturable absorbers25,26 and photodiodes27). Despite significant progress, current RC implementations remain limited by their inherent architecture, in which nodes are created and interconnected through feedback mechanisms27,28. These mechanisms simplify the design by generating virtual nodes, but also introduce latency and limit processing speed, which is defined as system throughput (i.e., the total number of operations per second across all input data streams within a single reservoir unit). Recent efforts to increase computational throughput in RC have focused on faster electro-optical modulation and advanced data encoding schemes, such as pulse-amplitude modulation29–31 (PAM), often paired with wavelength-division multiplexing (WDM). However, these methods frequently rely on sequential sweeping across WDM channels32–34, or time-interleaving techniques35–39, which both introduce throughput latency and prevent the concurrent execution of independent tasks. Additional attempts at further scaling up performance have involved adding components or increasing the number and dimensionality of computational layers and readout components5,39. Typically, these result in decreased energy efficiency and processing speeds. Furthermore, existing WDM-based RC architectures21,38,39 also have limited tunability, when design constraints inherently fix both the reservoir memory and the activation function. At the same time, nonlinearity is introduced electronically at the input/output stage, resulting in optical-to-electrical-to-optical (OEO) latency and thus limiting the richness of reservoir dynamics. Such constraints significantly reduce system flexibility and adaptability for diverse ML tasks. Additionally, architectures employing spectral mixing approaches21 encounter nonlinear crosstalk40, which, in turn, limits the number of independently encoded channels and consequently degrades system accuracy and scalability.

To address these challenges, we demonstrate an RC device based on a nonlinear amplifying loop mirror (NALM) architecture. We leverage the NALM configuration for its proven ability to generate highly stable and nonlinear dynamics41–44, which are essential for optical reservoir computing. These dynamics enhance the reservoir’s computational capacity by enabling complex input mapping into a high-dimensional state space, thereby improving sensitivity to extremely small signal variations45,46. The intrinsic stability of the NALM ensures consistent classification performance, even under noisy or fluctuating input conditions.

Our device features an integrated nonlinear spiral waveguide (SW) and a semiconductor optical amplifier (SOA), both of which modulate the NALM overall nonlinear transfer function (i.e., the reservoir activation function). In contrast to previous RC implementations that rely on SOAs operating in saturation, whether in unidirectional configurations47–49 or through cross-gain modulation50,51, we set the SOA below saturation for all our experiments. Saturated SOAs exhibit plateaued gain, limiting the dynamic range and tunability of the nonlinear response. The unsaturated regime, on the other hand, allows for precise tunability of the gain and, therefore, of the reservoir activation function. Furthermore, by adjusting the intensity of the propagating field using a variable optical attenuator (VOA), we achieve additional control over the reservoir’s fading memory response, significantly enhancing both versatility and stability for diverse computational tasks.

In line with the standard single-node reservoir computing framework, we establish virtual nodes within the reservoir via time-multiplexing, with training restricted to the readout layer. However, by employing multiple synchronized continuous-wave (CW) laser sources, our device can support multi-task processing across wavelength channels. This enables true concurrency for parallel data injection, both for the same or different machine learning tasks. The latter significantly reduces hardware complexity and addresses scalability and performance bottlenecks in earlier architectures. As a result, we have achieved a throughput of up to 20 tera-operations per second (TOPS), consuming only a few femtojoules per operation, while maintaining high accuracy in both classification and regression tasks. The device setup, as depicted in Fig. 1, encompasses a figure-eight fiber cavity that enables efficient multi-processing and provides rich system tunability. Such figure-eight fiber shapes can produce a range of coherent nonlinear dynamics, both with41 and without42,43 CW injection. By leveraging dynamic regimes and higher dimensionality enabled by virtual nodes, we accurately separate and classify continuous-valued input signals, even when they are complex and highly nonlinear.

Results
We benchmarked our device to solve linearly inseparable problems using the m-bit delayed parity task, also known as the generalized exclusive OR (XOR)16. This nonlinear task performs the XOR operation between the current bit and the m prior bits stored in the reservoir memory and classifies the resulting sequences into two distinct classes. We injected a pseudorandom binary sequence (PRBS) of 4000 bits into a single-wavelength channel using a CW source (see the setup in Fig. 1) in the input device loop. Through the encoding procedure described in the Methods section entitled “Device architecture”, we generated 161 virtual processing nodes. Consistent with the RC paradigm, training was applied exclusively to the output weights, while the internal node connection weights remained fixed. These internal weights are inherently defined by the device configuration and the specific components that were employed, such as the SOA, the integrated SW, and the variable optical attenuator (VOA) (see Supplementary Note 1). We applied ridge regression27 to determine the optimal output weights required to reconstruct the target signal. The accuracy of the trained model was evaluated using standard performance metrics, such as the normalized root-mean-square error (NRMSE).

We investigated the classification performance when varying the SOA gain and the signal attenuation of the VOA by tuning their driving voltages, VSOA and VVOA, respectively (which correspond to a specific level of amplification gain g and attenuation level AVOA). Figure 2 shows the NRMSE maps (g and AVOA) for 2-bit, 3-bit, and 4-bit delayed sequences in (a), (b), and (c), respectively. For the 2-bit XOR, we achieved 100% classification accuracy for the validation dataset, as shown in the dark-blue shaded region of Fig. 2a, which is defined by g < 8.3 dB and AVOA < 4.9 dB (VSOA < 0.8 V and VVOA > 3 V). These values delimit operational regimes characterized by reduced nonlinear contributions from the SOA and by short fading memory controlled by the VOA.

For the 3- and 4-bit XOR sequences, a further nonlinear contribution to the overall response (i.e., the activation function) of the reservoir is required to enhance the output separability and reduce the NRMSE16. This is achieved when setting g > 6.1 dB and AVOA > 0.3 dB (VSOA > 0.5 V and VVOA > 1.5 V), respectively, for the 3- and 4-bit cases. This enables the device to achieve accuracies of 97% and 80% (with NRMSEs of 3% and 20%), as reported in Fig. 2b and c.

Reservoir tunability enables handling ML tasks with varying degrees of data separability and temporal correlations, as evident in the analysis of the effect on the propagating input signals as a function of the two tunable parameters. When an input signal, such as an optical field, enters the device reservoir loop through the 3 dB (50:50) input beamsplitter (Fig. 1), it separates into propagating and counter-propagating field components. Their phase difference, after they propagate in opposite directions and recombine at the beamsplitter, is affected by sequences of amplification and nonlinear interactions mediated by the intensity-dependent Kerr nonlinearity in the integrated SW52,53. During such an interaction, an increase in the amplification gain causes the SOA to contribute additional nonlinear responses, thereby enhancing classification performance when further nonlinear contributions are required54, without altering the physical reservoir topology. This unsaturated operational regime enables us to implement a controllable mechanism mediated by tunable parameters, allowing for the exploitation of nonlinearities arising from controlled optical feedback and intensity-dependent interference within the NALM. This approach allows for precise and reconfigurable reservoir functionality. In contrast to the cross-gain saturation-based nonlinearities demonstrated in earlier works50,51. Our architecture provides greater flexibility and control over reservoir dynamics.

Generally, in time-delayed RC, a higher reservoir nonlinearity can impair the fading memory, which is determined by the system’s round-trip time46,55. By fine-tuning the input intensity attenuation through VVOA, we can modify the strength of the interconnection among the reservoir virtual nodes. This adjustment regulates the amount of circulating intra-cavity power per round-trip, thereby compensating for the reservoir’s diminished capacity to store bits within its fading memory56.

Multi-processing and parallel operation
We established the multi-processing capabilities of our device by carrying out two well-known ML benchmarks in parallel: the Mackey-Glass (MG) and the 10th-order Nonlinear Auto Regressive Moving Average (NARMA10) time series prediction tasks. These two tasks address the nonlinearity and memory of the reservoir, challenging the trade-off that occurs between them. The chaotic nature of the MG system, with high sensitivity to initial conditions, requires a reservoir with high nonlinearity. On the other hand, NARMA10 requires a reservoir with a long fading memory to efficiently retain temporal dependencies among data points across various round-trips. Therefore, by performing both tasks simultaneously, we demonstrate the universal multi-processing potential of our device in tackling both of these diverse ML tasks.

We use two wavelength channels, one at 1549.2 nm for the MG task and the second at 1549.4 nm for NARMA10. Crosstalk effects were reduced by applying a 0.2 nm spectral separation between the channels. We generated 1200 data points for each time series and encoded them onto Nv = 161 virtual nodes in the reservoir through dense WDM. Based on the results of the m-bit XOR task (where the highest accuracies are achieved within the dark-blue-shaded regions shown in Fig. 2a), we found that the best performance can be reached with g = 10.3 dB (VSOA = 1.5 V) and AVOA ≈ 0 dB (VVOA = 0.5 V). We applied offline training and cross-validation57 independently on the two de-multiplexed outputs to obtain the weights that minimize the NRMSE between the targeted and predicted outputs. The results in Fig. 3 show misclassification rates of just 6% for MG and 1% for NARMA10, indicating high classification accuracy in both cases.

Computational scalability of the device
We demonstrate system scalability through both increased bit density and parallel channel encoding, enabling the scaling up of computational throughput without requiring additional physical nodes. We next applied the device to solve a real-world task: recovering a nonlinearly perturbed telecom signal. Signal distortion, attenuation, dispersion, noise, and crosstalk originating from fiber propagation can all degrade or disrupt communications. Therefore, channel recovery techniques are essential for preserving signal integrity, minimizing downtime, and ensuring quality of service in networks29,58. This requires nonlinear, low-latency, high-speed processing capabilities. As shown by previous benchmarks, our device offers features that can meet these requirements, and its computational speed can be further enhanced by employing a dense information encoding scheme alongside multi-channel processing. The dense encoding scheme (see the Methods section entitled “Information encoding and readout”) enables us to inject multiple bits per wavelength channel into the reservoir, thereby increasing speed without adding extra computational units.

We generated a PRBS of 5×(215 − 1) bits and electro-optically encoded it onto a CW carrier signal. We then let the signal propagate through 60 km of standard single-mode fiber (SMF). Here, the once pristine signal experiences dispersion and nonlinear distortion, including cross-phase modulation and four-wave mixing, both of which are influenced by fiber length and signal intensity. Figure 4a and b show the time traces of the modulated field intensity using PAM30,31 before and after propagation, respectively, along with their corresponding eye diagrams. The distorted signal is then distributed and encoded across five independent channels, spaced at 0.2 nm intervals around 1550 nm (as shown in Fig. 4b), which we process concurrently via dense WDM. The number of encoding channels is limited only by the available CW sources and electro-optical intensity modulators (IMs). The representative bit sequences before and after recovery are shown in the Supplementary Fig. 5.

We trained and validated the output weights for each channel across four virtual nodes using the encoding technique and offline ridge regression. The bit error rate (BER, the metric that quantifies the percentage of misclassified bits in the recovered sequence) is shown in Fig. 5(a), illustrating the individual channels and different input power levels (Pin = 2.6 dBm, 3.8 dBm, 4.2 dBm, 4.6 dBm, 5.0 dBm, and 5.4 dBm), which are commonly used in telecommunications. We observed that the BER decreases as the input signal power increases, due to improved signal-to-noise ratio.

This change occurs regardless of the surge in distortion due to the intensity-dependent Kerr effect on transmission, which our approach can compensate for. The lowest BER value is 2×10−4 at 5.4 dBm of input power, representing a 145-fold improvement compared to the preprocessed distorted signal (see Fig. 5b). The inset of Fig. 5c displays a segment of the original bit sequence alongside the corresponding distorted optical signal, measured after propagation through the 60 km fiber link (prior to recovery processing). Figure 5d shows the recovered bit sequence at an input power of 5.4 dBm, with a zoomed-in segment highlighting the bit errors (marked with red squares).

The experimental results were validated using the model derived from the generalized nonlinear Schrodinger equation59 (GNLSE) (see Supplementary Note 1). We report the average BER over the five wavelength channels (red line) and the simulated BER values (black dots) in Fig. 5a. We observed excellent agreement between the numerical predictions and our experimental results, confirming the accuracy of our model.

We can quantify the throughput of our device in terms of MAC (multiply-and-accumulate) operations per second for parallel signal recovery. The device achieves a 2.7 Tera-MACs-1. From the MAC calculation, we estimate a speed of 20 Tera-operations per second (TOPS) for our device. In terms of energy efficiency, the overall power consumption of the processing unit is approximately 87 mW, leading to consumption of ~4.4 fJ OP-1 (see Supplementary Note 4 for detailed calculations), which outperforms both state-of-the-art fiber-based optical neural networks and photonic chips5,8,35,60–62. See Table 1 for a numerical comparison.

Methods
Device architecture
The device’s figure-eight cavity design (see Fig. 1) can be divided into input, processing (i.e., the reservoir or unit), and output stages, all of which contribute to the overall round-trip time and thereby cause the reservoir’s memory to fade. The input loop comprises a variable optical VOA (Thorlabs, V1550A) that controls the signal power, a 10:90 coupler that monitors the system, a 50:50 coupler that injects the modulated signal, and a second coupler that splits the signals into clockwise and counter clockwise directions in the NALM configuration. The NALM loop is composed of an SOA (Inphenix C-Band IPSAD1505) and an integrated 45 cm-long SW. This waveguide is fabricated from a CMOS-compatible, highly doped silica glass52,53,78–83. As such, the SW features high mode confinement due to the small waveguide profile (2×2µm2), with group velocity dispersion coefficients of β2 ∼ 10 ps2km−1 and β3 ~ 0.26 ps3km−1 at 1550 nm, as well as a large third-order nonlinear coefficient of γ = 220 W−1km−1. The SW, together with the phase shift mechanism between the two counter-propagating fields, performs the overall nonlinear activation function of the reservoir52,53. The SOA operates between the linear and nonlinear regimes, far from saturation, to avoid instabilities. These include self-oscillation and chaotic behaviors, as well as noise amplification and signal fluctuations, which would be detrimental to the current tasks. A polarization controller (PC) was used to select and optimize the transmission power of one field component, specifically either the transverse electromagnetic or magnetic field. Simultaneously, an optical bandpass filter (200 GHz) was used to limit the spectral bandwidth of the propagation fields, thereby improving the signal-to-noise ratio (SNR) and system stability by eliminating unwanted amplified spectral components. A 90:10 optical coupler is used to extract a fraction of the optical power from the loop to obtain a readout of the dynamic evolution of the node states, utilizing high-bandwidth photodiodes (PDs, Finisar XPDV21x0R series, 50 GHz bandwidth) and a digital oscilloscope (OS, Agilent DSO-x92804a, 28 GHz bandwidth). An additional OS is employed to perform the nonlinear recovery task. The overall length of the cavity is 14 m, corresponding to a round-trip time of approximately τr = 75 ns.

Information encoding and readout
We encode information (i.e., bits) into time-dependent vectors ui(n) by means of different arbitrary waveform generators (AWGs) (Keysight M8196A, 92 GSa s−1, 2 channels each), each driving an equal number of electro-optical Mach-Zehnder intensity modulators (IMs) (Optilab IML-1550-40-PM-V-HER, 40 GHz, polarization-maintaining, high extinction ratio, Vπ = 3 V). All modulators were synchronized using an external clock. The IMs were excited by the time-varying voltage signal containing the data, which in turn modulated the independent laser modes (i.e., the wavelength channels) produced by a narrowband continuous multi-wavelength (CW) source (ID Photonics CoBrite DXG, 4 outputs, linewidth <100 kHz). An additional CW source (Tunics T100S-HP, single output, linewidth <5 MHz) was employed to provide the fifth channel. The injected power per channel ranged from 1 mW to 5 mW, depending on the task. The applied voltage to the IMs varied between [-Vπ/2, Vπ/2], ensuring operation within their linear regime. When multi-processing is performed, the input channels are injected into the device via wavelength division multiplexing (WDM) using a waveshaper (WS).

The reservoir nodes are established by first sampling and holding the input signal containing data for a duration τ ≈ τr, then multiplying the signal by a uniformly distributed, multi-level random mask R(n), with values ranging between −1 and 1. The mask has a sampling period τ and duration θ per level, such that Ein(n) = u(n) * R(n), where Ein(n) is the resulting input signal to the device. This procedure maps the signal onto a higher-dimensional space by generating a number of ‘virtual’ node states (i.e., internal variables)84, the number of which is given by Nv = τ/θ. A slight desynchronization, δ ≈ θ, was applied to the sampling period τ on the AWG input sequence to ensure that all node states were dependent on neighboring nodes17.

For dense encoding, we input more than one bit of information (nb) in the reservoir per round-trip τr. We apply the sample and hold procedure over the asynchronous sampling rate (i.e., the inverse of the masking rate) of duration τ0 = τr/nb + δ0 to generate N' time-multiplexed transient states of duration θ0 = τ0/N0, for each τ0 time interval.

The small desynchronization δ0 ≈ θ0 between the sampling and injection rates causes a progressive shift in the input seen by adjacent virtual nodes and by nodes across round-trips, ensuring that neighboring nodes access distinct input segments over time and maintain the data correlation required for reservoir computing processing.

The output states, x(n), are measured from the virtual nodes at duration θ (or θ0) by using the PDs and OS. De-multiplexing using the WS is applied in cases of parallel computations. The average output power ranges from 100 μW to 300 μW per individual input channel.

M-bit delayed XOR task
To formally describe the m-bit delayed XOR task85, we define the operation within a logical framework. Given the input bit sequence {xn} with delay n and the number of bits m, the output sequence {yn} can be described by the following equation:
yn = xn ⊕ xn−1 ⊕ xn−2 ⊕ ... ⊕ xn−m if n ≥ m
yn = xn if n < m
where xn and yn are the current and output bits at time n, respectively.

Time series prediction tasks
The Mackey-Glass (MG) time series is defined by the following equation:
ẏMG(t) = β yMG(t−τ) / (1 + yMGp(t−τ)) − h yMG(t)
in which yMG(t) is the output at a time t, τ is the delay time, β is the growth rate, h is the decay rate, and p is the nonlinear parameter. Parameters were set as follows: τ = 17, β = 0.2, h = 0.1, p = 10. To simulate MG time series behavior, t was discretized using a time step Δt = 1 to produce values x(t) at discrete time points t = qΔt for q = 0, 1, 2, . . . .

The 10th-order Nonlinear Auto Regressive Moving Average (NARMA10) series follows the equation
y(t+1) = 0.3y(t) + 0.05y(t) * Σ(i=0 to 9) y(t−i) + 1.5u(t)x(t−9) + 0.1
in which y(t) is the output at time t, while u(t) is the input, chosen as a random sequence from a uniform distribution U[0, 1]. Similarly to the MG task, we applied a discretized time step Δt = 1 to the NARMA10 time series temporal variable t.

The time series were simultaneously and independently encoded onto two wavelength channels generated by the multi-output CW source. Two IMs and AWG channels drove this process. Following the previously described single-bit encoding technique, both signals were multiplexed using the WS and then injected simultaneously into the device. They were then de-multiplexed and read with the OS. Offline training (as detailed in the following sections) was performed on the two datasets collected.

Nonlinear telecom signal recovery task
The nonlinearly distorted signal, which also carries information, was obtained by propagating the corresponding pristine signal through 60 km of SMF-28, with a dispersion parameter D = 18 ps nm−1 km−1 and an attenuation constant α = 0.24 dB km−1. An additional 1 m of highly nonlinear optical fiber (with γ = 0.78 W−1 km−1) was added to account for the full extent of nonlinear effects over longer propagation distances, which is typical in telecommunications networks. The distorted signal, carrying 5×(215 – 1) bits, was sequentially split into five subsequences of 215 – 1 bits each and then independently encoded into the five wavelength channels using five IMs and AWG channels. Each AWG channel was operated at ~6.5 GHz. All five channels were amplified to 5 mW using an erbium-doped fiber amplifier (EDFA, Keopsys, PEFA-SP-C-PM−27-B202), then multiplexed into the reservoir. The additional IM and AWG channel were used to create the temporal node transients θ0 time intervals by using the PDs and OS via time multiplexing. These were implemented at a masking rate of approximately 24 GHz, creating 4 virtual nodes with a 20-level random mask, thereby enabling the encoding of 488 bits per round-trip. Offline training was performed on datasets built from the output node states of all five de-multiplexed wavelength channels, using the training procedure described in the following section.

Offline training
We employed a k-fold cross-validation approach, with k set to 5 for the MG and NARMA10 tasks and to 10 for the nonlinear channel equalization task. We then split the output datasets, consisting of xi values, into equally sized k subsets. The machine learning (ML) model was trained using ridge regression on k−1 folds and validated on the remaining fold. This process was repeated k times, with each fold used once as the validation set. For each fold, we determined the model’s accuracy by calculating the normalized root mean square error (NRMSE) as
NRMSE = sqrt( < (yi − y0i)^2 > / σ^2 )
in which σ2 is the sample variance, y0i is the targeted output, and yi is the weighted output: yi = Σ(j=1 to Nv) Wout,ij xj.
Finally, we calculated the average error across all iterations to obtain a more robust estimate of the model’s overall performance.

Simulations for nonlinear channel equalization
We employed a 10,000-pseudorandom binary sequence (PRBS) extracted from the experimentally generated distorted signal. We then sampled the signal using ultra-dense encoding, mirroring the experimental procedure previously described. We injected 488 bits per cavity round-trip over four nodes into a single channel. The device response was numerically simulated using the generalized nonlinear Schrödinger equation (GNLSE) and then implemented in MATLAB (see Supplementary Note 1).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript introduces a photonic neural network architecture built using 4×4 multimode interferometers (MMIs) and a\nproposed multi-operand microring resonator (MMORR) for nonlinear operations. The primary goal is to provide a scalable\nand energy-efficient solution for deep learning acceleration by addressing limitations of Mach-Zehnder interferometer (MZI)\nand microring resonator (MRR) based networks. The authors present theoretical models, perform FDTD simulations, and\nevaluate the architecture on standard image classification datasets (MNIST, FMNIST, CIFAR-10). The work claims high\ncompute density and low power consumption. The proposal of MMIs combined with nonlinear MMORRs represents a\npotentially promising approach to optical computing and deep learning acceleration. The authors attempt to incorporate\nnonlinear optical activation functions directly into the architecture.\nHowever there are multiple critical weaknesses. It is not clear how the operation of the MMORR-based nonlinear unit is\nimplemented and the simulations fail to illustrate the computing mechanism convincingly. How is the nonlinearity generated\nin the MMORRs? Why is this approach is superior or even viable compared to known methods. The experimental\nvalidations are insufficient. In particular the experimental results on CIFAR-10 show only a 54.5% accuracy—significantly\nbelow state-of-the-art—and the authors do not explain this shortcoming or compare fairly with digital or hybrid solutions. The\ncompute density calculation ignores critical physical constraints like metal routing and electronic interface area, significantly\ninflating the reported performance. No evidence is provided for multi-mode utilization, even though final metrics are derived\nbased on it.\nThe paper claims power efficiency but does not rigorously detail the power consumption of each optical or electrical\ncomponent, nor does it benchmark against known designs or standards.\nThe paper does not discuss practical issues such as variability, fabrication tolerance, and bandwidth associated with optical\nnonlinearity.", "reviewer_2": "In the manuscript “Scalable Photonic Reservoir for Parallel Machine Learning Applications”, the authors design a figure-\neight shaped nonlinear amplifying loop mirror architecture for photonic reservoir computing, claiming that a 20-TOPS-level of\ncomputing power and a femto-joules-per-operation-level of efficiency are achieved. Even though the reported performances\nand capability seem to be superior, several questions need to be clarified to make the statements convincing.\n1. In figure 1, the authors proposed a double ring-resonator structure to implement an all-optical reservoir computing system.\nWhile the physical architecture is clearly depicted, the manuscript lacks detail regarding how the weights associated with the\nSOA and VOA are trained or simulated.\n2. The manuscript presents several results on machine learning tasks. However, the specific neural network architectures\nemployed to achieve these results are not described in sufficient detail. What is the exact configuration of the network that is\ndeployed and mapped onto the proposed photonic hardware? Providing a clear and comprehensive description of the\nnetwork structure is essential for ensuring the clarity of the presented results.\n3. The customized ring-resonating structure has a high risk for undesired self-exciting oscillations. How will you eliminate\nsuch noises to make the computing stable and the results repeatable?\n4. In Figure 4, the authors presented the original undistorted telecom signal and the distorted signal after propagation.\nHowever, such a figure only visualizes a common nonideal propagation phenomenon, and has little relation with the\nproposed research. The authors may need to provide the recovered signal shape after the proposed photonic reservoir\ncomputing.\n5. Figure 4 presents only a basic illustration of the time traces of the modulated field intensity before and after propagation.\nHowever, the manuscript lacks a detailed analysis or interpretation of these results, which may leave readers confused\nabout the significance and implications of the figure. More detailed numerical analysis for the performance is necessary to\nmake the research more convincing.\n6. The authors mentioned “scalable” in the title of the manuscript, however, there seems to be no discussions of computing\nscalability in the results section. More extra details, comparisons, figures, curves, and / or discussions that related to the\nnetwork scale and system scalability is necessary to support the claims in the title.\n7. In the system throughput analysis section, the manuscript does not clarify the clock frequency assumed in the numerical\ncalculations. Since throughput is inherently tied to the system’s operating frequency, the lack of this information hinders a\nproper assessment of the reported performance.\n8. In the energy efficiency analysis section, it remains unclear whether the authors have accounted for the energy\nconsumption and potential speed limitations introduced by peripheral components. These include, for example, the data\nfeeding mechanisms, data acquisition systems, and the voltage drivers required for modulating the weights. The authors are\nencouraged to clarify whether these peripheral factors were considered in the analysis, and if not, to discuss their possible\ninfluence on the practical implementation of the proposed system.\n9. While the manuscript introduces a new NALM-based architecture, it lacks a comprehensive comparison with other\nexisting photonic computing approaches in terms of key performance metrics such as throughput, energy efficiency, and\ncomputational accuracy. Including such comparisons would greatly strengthen the manuscript by highlighting the relative\nadvantages of the proposed design.\n10. In addition, it would be beneficial if the authors could provide baseline performance metrics for the demonstrated\ncomputing tasks using conventional methods (e.g., electronic computing method). Presenting such benchmarks would offer\nvaluable context for evaluating the practical benefits of the proposed photonic implementation.\nIn conclusion, the submitted manuscript reported a novel photonic reservoir computing architecture with claimed promising\nperformance and capability, but these mentioned questions need to be settled to further make the manuscript more\ncomprehensive and convincing.", "reviewer_3": "This paper proposes and implements a wavelength-division-multiplexed (WDM) reservoir computing (RC) system that\nenables parallel neuromorphic computation. As WDM-based RC has already been experimentally demonstrated in previous\nstudies (e.g., [1]), the main contribution of this paper lies in its implementation of a nonlinear delay system called the\nnonlinear amplifying loop mirror (NALM). Although this system utilizes gain saturation in a semiconductor optical amplifier\n(SOA), the principle itself has already been reported in prior works [2,3], and thus lacks sufficient novelty. While the\nexperimental demonstration is intriguing, the reported computational performance (20 tera operations per second) is lower\nthan that of previous studies ([1] 800 TOPS, [4] 200 TOPS), and therefore does not offer the level of impact typically\nexpected for a publication in Nature Communications. Accordingly, I do not recommend publication in Nature\nCommunications. I believe this work would be more suitably presented in journals such as Scientific Reports or\nCommunications Physics, once the following concerns are addressed.\nMajor comments:\n- The introduction should briefly review prior works on WDM-based approaches (e.g., [1,4,5]) and clearly delineate the\ndifferences between those studies and the present work. The authors should also cite earlier approaches that utilize SOA\ngain saturation (e.g., [2,3,6]) and clarify how their approach differs from them. In particular, [3,6] introduce nonlinearity via\ncross-gain saturation by injecting light into both ports of the SOA, and since the conceptual similarities are evident, the\ndistinctions must be made clear.\n- The relationship between the mathematical model in the Supplementary Information, and the experimental parameters\n(e.g., Gs and T_VOA shown in Fig. 2) is unclear. The correspondence between physical quantities such as Gs and T_VOA\nand the parameters in equations (S1–S15) should be explicitly stated.\n- Additionally, in Fig. 2, the units of T_VOA and Gs are given in volts (V), which are device-dependent parameters; as a\nresult, readers cannot determine what is actually being optimized. It would be preferable to express these quantities in terms\nof optical attenuation or gain, rather than voltage.\n- In reservoir computing, it is generally expected that the feedback gain (or spectral radius of a connection matrix within a\nreservoir) should be set to satisfy the echo state property (ESP) [7]. Can the authors discuss how to select the physical\nparameter to satisfy the ESP for the proposed configuration? In particular, it seems plausible that chaotic transitions could\noccur in this system if we set the strong feedback gain of the SOA. I guess that such region should be avoided.\n- Lastly, in the nonlinear equalization experiments, it was stated that four virtual nodes were used. In such a case, the delay\nlength would be significantly longer than a single symbol period (i.e., the inverse of the baud rate). Then, assuming the\nsimplified reservoir dynamics described by x(n) = f(Wx(n–p) + Mu(n)), the parameter p would be considerably larger than 1.\nWhy does the system still perform well under this condition? I apologize if I have misunderstood something, but clarification\nwould be appreciated.\n[1] https://www.nature.com/articles/s42005-021-00519-1\n[2] https://opg.optica.org/oe/fulltext.cfm?uri=oe-20-20-22783&id=242389\n[3] https://opg.optica.org/oe/fulltext.cfm?uri=oe-30-13-22871&id=476798\n[4] https://www.nature.com/articles/s41467-024-55172-3\n[5] https://opg.optica.org/optica/fulltext.cfm?uri=optica-10-11-1478&id=541462\n[6] https://ieeexplore.ieee.org/abstract/document/10368205\n[7] https://www.sciencedirect.com/science/article/abs/pii/S0893608012001852"}, "author_response": "We sincerely thank the reviewer for taking the time to assess our Manuscript. However, we respectfully note that\nseveral of the comments raised appear to pertain to a different topic or paper and do not reflect at all he content,\nmethodology, or scope of our work.\nTo clarify, our Manuscript focuses on a photonic reservoir computing architecture based on a nonlinear amplifying\nloop mirror (NALM), with emphasis on dense temporal encoding, wavelength-multiplexed multi-task processing,\nand experimental demonstrations across several machine learning benchmarks, including XOR tasks, time-series\npredictions, and nonlinear channel recovery. In contrast, the reviewer’s comments appear to refer to the use of\nmultimode interferometers and multi-operand microring resonators, which are not employed in this Manuscript, for\nimage classification on datasets such as MNIST and CIFAR-10, which are unrelated to the methodology and scope\nof our work.\n\nWe thank the reviewer for considering our work and for recognizing the promising performance and potential of our\napproach. To enhance the clarity and overall quality of the Manuscript, we have provided a detailed, point-by-point\nresponse to all the concerns raised.\n1. In figure 1, the authors proposed a double ring-resonator structure to implement an all-optical reservoir computing\nsystem. While the physical architecture is clearly depicted, the manuscript lacks detail regarding how the weights\nassociated with the SOA and VOA are trained or simulated.\nResponse\nOur approach is based on time-delay reservoir computing, as opposed to a spatial reservoir with trainable internal\nweights. In this architecture, computation is distributed across virtual nodes, which are time-multiplexed samples of\na single nonlinear dynamical system governed by a delayed feedback loop.\nImportantly, the internal reservoir weights are not trained. Instead, they are fixed and randomly defined through the\ninput masking procedure, as previously established (Appeltant et al., 2011). In our system, the random mask is\nimplemented via a sample-and-hold mechanism, and the values of the mask define the reservoir weights.\nThis was discussed in Section S1 of the Supplementary Information in the earlier submission on line 32 (now lines\n32-33).\nThe virtual nodes represent transient states of the nonlinear system, sampled at equally spaced time intervals over\nthe delay period.\nThe only trainable weights in the reservoir are the readout weights, for which a linear regression is performed on the\ncollected node states to produce the output (see Methods). Indeed, the reservoir approach eliminates the need for\ninternal weight optimization, which is a core advantage of this paradigm.\nTo further clarify: our system does not train internal weights via the SOA or VOA. Rather, there are fundamental\nfactors that shape the reservoir’s dynamic response, which we have demonstrated through a detailed theoretical\nanalysis using our model. Using our model, we explicitly show how modifying these physical parameters affects\nkey reservoir properties, such as memory and nonlinear transformation capabilities, as was detailed in the\nSupplementary Information (lines 115–120 in the earlier submission).\nMoreover, we would like to point out that our device doesn’t implement a ring-resonator structure, but rather a\nfigure-8 shaped cavity, which is fundamentally different in terms of field propagation and nonlinear interaction.\nACTION TAKEN\n Besides having been mathematically derived on lines 114–129 of the Supplementary Information, we have also\nrevised lines 32–33 of the Supplementary Information and lines 103–107 of the Manuscript. In the latter, we\nnow state: 'Consistent with the RC paradigm, training was applied exclusively to the output weights, while the\ninternal node connection weights remained fixed. These internal weights are inherently defined by the device\nconfiguration and the specific components employed, such as the SOA, the integrated SW, and the variable\noptical attenuator (VOA) (see also Supplementary Information).’ This clarifies that only the output weights are\ntrained in the reservoir computing framework and further explains the roles of the SOA and VOA in the\nreservoir dynamics.\n2. The manuscript presents several results on machine learning tasks. However, the specific neural network\narchitectures employed to achieve these results are not described in sufficient detail. What is the exact configuration\nof the network that is deployed and mapped onto the proposed photonic hardware? Providing a clear and\ncomprehensive description of the network structure is essential for ensuring the clarity of the presented results.\nResponse\nIt is indeed true that we didn’t sketch the corresponding network architecture. However, we consistently stated that\nour NALM configuration implements a reservoir computer (e.g., lines 58-68 in the earlier Manuscript version, now\nlines 73-96), which is a recurrent network architecture requiring the presence of a feedback loop in addition to an\noverall, tunable nonlinearity that our system can produce. Details on how the network configuration, i.e., the\nreservoir, is established on the device setup were presented in the Methods section (see paragraph beginning on line\n345, under ‘Information encoding and readout’, and paragraph beginning on line 319 under ‘Device Architecture’,\nrespectively, in the earlier Manuscript version).\nACTION TAKEN\n We have clarified the analogy between the RC structure and our NALM configuration, as outlined on lines 103-\n107.\n We have plotted the reservoir structure in the new Figure S.1, added to the Supplementary Information, where\nEqs. S1-S3 describe its behavior.\n3. The customized ring-resonating structure poses a high risk of undesired self-excited oscillations. How will you\neliminate such noises to make the computing stable and the results repeatable?\nResponse\nWe thank the reviewer for bringing this important point to our attention. Self-excited oscillations are a known\ndynamic in ring resonator-based structures; however, our architecture, based on a figure-eight configuration rather\nthan a resonant cavity, with an integrated spiral waveguide as the nonlinear element, inherently mitigates this issue.\nThis is in line with the findings in our previous work (Aadhi et al., 2019). We maintain the SOA bias below the\nonset of nonlinear gain regimes, where Ikeda-type instabilities emerge. By operating safely within this threshold, the\nsystem remains in a stable regime. As was detailed in the Methods section (lines 280-281 in the earlier Manuscript\nversion, now on lines 332-334), we operate the SOA below saturation, far from the region in which gain instabilities\nand spontaneous oscillations typically emerge. Furthermore, our implementation of the NALM architecture includes\na narrow (~200 GHz) bandpass filter (see Fig. 1). This element limits the spectral bandwidth and effectively\nsuppresses chaotic oscillatory behavior, such as square-wave and fast oscillations. In addition, this element limits\nmodulation instability gain, therefore, ensuring the stability of computing results.\nExperimentally, we identify in Fig. 2(a–c) the specific regions of parameter space, defined by the SOA bias voltage\nand VOA attenuation, where the device achieves high accuracy and low NRMSE. These regions are characterized\nby stable operating regimes that are free from oscillatory noise, which was validated across benchmark tasks.\nFinally, the experimental results presented in Figs. 3 and 5, demonstrated across multiple independent wavelength\nchannels and diverse benchmark tasks, proving the high repeatability and computational stability of our system. The\nconsistent performance across XOR, Mackey-Glass, NARMA10, and nonlinear channel recovery tasks further\nreinforces the robustness of our architecture against noise-induced instabilities.\nTherefore, we confirm that we have not observed any self-excited oscillations that would introduce parasitic effects\nin our system.\nACTION TAKEN\n We have revised lines 332-334 of the Manuscript to clarify this matter further. We now state: ‘The SOA\noperates between the linear and nonlinear regimes, far from saturation, to avoid instabilities. These include\nself-oscillation and chaotic behaviors, as well as noise amplification and signal fluctuations, which would be\ndetrimental to the current tasks.’\n4. In Figure 4, the authors presented the original undistorted telecom signal and the distorted signal after\npropagation. However, such a figure only visualizes a common non-ideal propagation phenomenon and has little\nrelation to the proposed research. The authors may need to provide the recovered signal shape after the proposed\nphotonic reservoir computing.\n5. Figure 4 presents only a basic illustration of the time traces of the modulated field intensity before and after\npropagation. However, the manuscript lacks a detailed analysis or interpretation of these results, which may leave\nreaders confused about the significance and implications of the figure. More detailed numerical analysis for the\nperformance is necessary to make the research more convincing.\nResponse\nWe want to clarify that the distorted signal shown in Figure 4(b) is not a generic or idealized example of signal\ndegradation, but the result of actual experimental measurements acquired after propagation through a 60 km\nstandard single-mode fiber link, which introduces both dispersion and nonlinear impairments, including cross-phase\nmodulation and four-wave mixing (as was described on lines 180–188 in the earlier Manuscript version, now on\nlines 213-221). Such a distorted telecom signal serves as the actual input to our device, which recovers the original\nsignal upon machine learning training.\nWhile the system’s performance is already quantified in Figure 5 via the bit error rate (BER), as a standard metric in\ntelecom applications, we agree that showing qualitative examples of the recovered waveforms would strengthen the\nManuscript.\nWe want to clarify the following points regarding the analysis and interpretation of these results: The performance\nof our device in recovering these distorted signals is quantitatively presented in Figure 5(a), where we report the\nBER as a function of input power across five wavelength channels. This BER analysis compares the signal quality\nbefore and after processing. It is discussed in detail in the Manuscript on lines 222–223, where we state: ‘The bit\nerror rate (BER, the metric that quantifies the percentage of misclassified bits in the recovered sequence).’ Fig. 5(b)\nfurther emphasizes this comparison by plotting both the pre-processed (green markers) and post-processed (purple\nmarkers) BER, clearly showing the benefit of using the device.\nThis experimental analysis is supported by numerical simulations, performed using our custom model based on the\ngeneralized nonlinear Schrödinger equation, as described in the Methods section and derived in Supplementary\nInformation (Section S.1). The simulation results, shown as black dots in Figure 5(a), closely match the\nexperimental BER trends, thus validating the model and our overall approach.\nThe signal to be recovered was a digital sequence of bits (0 and 1) encoded onto the modulated amplitude of a\ncontinuous-wave laser. As a result, the recovered signal consists of discrete digital levels, not a continuous\nwaveform. Thus, the concept of a 'shape' is not well-defined in this context, as it applies specifically to analog\nsignals.\nACTION TAKEN (in response to points 4 and 5)\n Accordingly, we have added new plots in Fig. 5, showing in (c) the original bit sequence alongside its distorted\ncarrier signal after nonlinear propagation through the 60 km fiber at 5.2 power; in (d) the corresponding\nrecovered sequence after processing by our device, as also detailed on lines 241-245. We have also added an\nExtended Data figure, which shows all traces before and after recovery, for each power level used.\n6. The authors mentioned “scalable” in the title of the manuscript, however, there seems to be no discussions of\ncomputing scalability in the results section. More extra details, comparisons, figures, curves, and / or discussions\nthat related to the network scale and system scalability is necessary to support the claims in the title.\nResponse\nWe thank the reviewers for bringing this to our attention.\nWe demonstrate the scalability of our network in terms of computational throughput (TOPs/s), as defined in Eq. (5)\nof the Manuscript. This throughput scales directly with both the encoding speed and the number of wavelength\nchannels. Unlike traditional time-multiplexed optical RC devices, where encoding speed is fundamentally limited by\nthe cavity round-trip time, our dense encoding technique significantly increases the information throughput per\ntemporal frame (quantified by the parameter 𝑛 in Eq. (5), enabling higher data rates without requiring additional\nb\ncomputational units.\nThis scalability is further enhanced through multi-level encoding, as illustrated in Section S.4 of the Supplementary\nInformation, where we employ a PAM-4 scheme. Additionally, we demonstrate the potential for broadband\nfrequency conversion using four-wave mixing, which could scale system performance to the peta-operations-per-\nsecond range (see lines 310-314 of the Manuscript). In parallel, scalability is also achieved by increasing the number\nof wavelength channels and enabling multi-processing. This was experimentally validated using nine parallel\nwavelength channels for simultaneous data encoding, as described in the same section.\nACTION TAKEN\n We have clarified, throughout the Manuscript, that scalability refers specifically to computational throughput.\nTo further emphasize this, we have added the following sentence on lines 202-203 of the Manuscript: ‘We\ndemonstrate system scalability through both increased bit density and parallel channel encoding, enabling\nscaling of computational throughput without requiring additional physical nodes.’\n We have also revised section S.4 of the Supplementary Information on lines 213-216: ‘This approach highlights\nthe scalability of our platform, where both dense temporal encoding and parallel wavelength multiplexing\ncontribute independently to increased processing throughput without additional hardware complexity.’\n We have revised the Abstract to better reflect the key novelties, including the scalable aspect.\n7. In the system throughput analysis section, the manuscript does not clarify the clock frequency assumed in the\nnumerical calculations. Since throughput is inherently tied to the system’s operating frequency, the lack of this\ninformation hinders a proper assessment of the reported performance.\nResponse\nIn the domain of reservoir computing, the fundamental clock frequency is commonly associated with the inverse of\nthe round-trip time of the feedback loop, i.e., the inverse of the system latency (Hülser et al., 2022). In other papers,\nhowever, the clock frequency is defined in relation to the desynchronization factor, also referred to as the\nasynchronous clock frequency (Tang et al., 2023). In this context, what we refer to as latency has also been referred\nto as the round-trip time, defining the clock cycle.\nAlthough the clock frequency was not explicitly defined in the earlier version of the Manuscript, we did discuss the\nsystem throughput in relation to latency, which was quantified as 75 ns, on lines 242–246 in the earlier Manuscript\nversion, now on lines 289-291. Furthermore, in Eqs. (6) and (7), the throughput is accounted for in terms of system\nspeed and supports the performance claims of our device.\nACTION TAKEN\n To ensure clarity and remove any ambiguity, we have reorganized the text on lines 289-296 and explicitly\nmentioned the fundamental clock frequency of our reservoir, clarifying its physical origin. We also discuss its\nrelation to system latency and how it defines the reservoir’s throughput and, consequently, the overall device\nperformance. We report an extract of the edited text here: ‘The reservoir’s throughput is directly linked to its\nfundamental clock frequency, defined as the inverse of the round-trip time. In our system, this corresponds to\n13.3 MHz (75 ns round-trip), setting the device’s intrinsic operational speed and hence its inherent\nthroughput...’\n8. In the energy efficiency analysis section, it remains unclear whether the authors have accounted for the energy\nconsumption and potential speed limitations introduced by peripheral components. These include, for example, the\ndata feeding mechanisms, data acquisition systems, and the voltage drivers required for modulating the weights. The\nauthors are encouraged to clarify whether these peripheral factors were considered in the analysis, and if not, to\ndiscuss their possible influence on the practical implementation of the proposed system.\nResponse\nWe appreciate the reviewer’s insightful comment. We estimated the energy efficiency of our system using\ncommonly adopted methods reported in previous studies, which we cite in our Manuscript. In some of these studies,\nfor example, in Gu et al (Gu et al., 2024), the energy analysis primarily considers the consumption of the processing\nunit itself, treating peripheral components (e.g., data encoding and readout equipment) separately. This distinction is\njustified, as peripheral equipment can often be replaced with more energy-efficient alternatives in future\nimplementations.\nIn our case, we report the energy consumption of the processing unit of the device, which includes the entire figure-\nof-eight cavity configuration and all its components (see Fig. 1). Since our reservoir is predominantly composed of\nintegrated and passive elements, the main energy contribution comes from these components, with low power drawn\nby the integrated active elements, such as the SOA used in the processing unit.\nWe acknowledge that the power consumption of the VOA was not included in our previous calculation. However,\nwe confirm that the energy consumption associated with the processing unit remains of the same order of magnitude\nas previously calculated and reported in our work.\nACTION TAKEN\n We have recalculated the power consumption of the processing unit in Eq. 7, adding the VOA power draw on\nlines 474-475, where we state: ‘𝑃 =25 𝑚𝑊 is the maximal power consumption associated with the VOA in\n𝑉𝑂𝐴\nthe operating conditions of our experiments.’\n In response to the reviewer’s recommendation, on lines 478-487 in the Methods section, we now provide a clear\ndistinction between the energy consumption of (i) the processing unit alone and (ii) the processing unit\nincluding peripheral components. Here, we state that ‘Peripheral components used for data encoding, readout,\nand acquisition operate alongside the processing unit but do not contribute directly to computation. Therefore,\nfollowing the methodology adopted in previous studies 60, we exclude their power consumption from the\nevaluation of the device’s computational efficiency. Moreover, these components can be replaced with more\nenergy-efficient hardware in future implementations. For completeness, however, we report their power usage\nin our current setup. The multi-output CW laser used to generate the input channels consumes a total of 18 W.\nThe IMs, one for the processing unit (masking) and five for channel encoding, consume approximately 400 mW\noverall. The AWGs, comprising 2 channels each (three AWGs employed, five channels for data encoding, and\none for masking), draw approximately 150 W in total. Photodetectors and other encoding and readout\ncomponents contribute negligibly to power consumption, typically at a level below the milliwatt range.’\n We corrected the value of energy efficiency reported in the Manuscript, which is now estimated at 4.4 fJ/OP.\n We have also specified throughout the Manuscript that we refer to energy efficiency related to the processing\nunit exclusively, including adding a note in Table 1.\n9. While the manuscript introduces a new NALM-based architecture, it lacks a comprehensive comparison with\nother existing photonic computing approaches in terms of key performance metrics such as throughput, energy\nefficiency, and computational accuracy. Including such comparisons would greatly strengthen the manuscript by\nhighlighting the relative advantages of the proposed design.\nResponse\nWe thank the reviewer for this valuable suggestion.\nWhile the current version of the Manuscript already introduces performance metrics that allow for a quantitative\nevaluation of our device in terms of computational throughput, energy efficiency, and accuracy, we agree with the\nreviewer that further details are beneficial.\nConsistent with our previous replies, Eqs. (5–7) define the throughput and energy efficiency metrics used to assess\nour system. Additionally, Table 1 in the Manuscript provides a comparative overview of key performance\nindicators, including the computational throughput (as defined by the maximum number of MAC operations per\nsecond, as seen in (Bernstein et al., 2023)), energy efficiency, and the type of machine learning task, for a range of\nstate-of-the-art photonic computing platforms.\nRegarding accuracy, this is quantified using the normalized root mean square error (NRMSE), as introduced in Eq.\n(4) and explicitly referenced on lines 108-109 of the Manuscript, or in terms of BER, as reported on lines 222-225 of\nthe Manuscript.\nACTION TAKEN\n To further strengthen this comparison as requested, we have added a new column to Table 1 that summarizes\nthe reported computational accuracy for each listed architecture per specified ML task.\n10. In addition, it would be beneficial if the authors could provide baseline performance metrics for the\ndemonstrated computing tasks using conventional methods (e.g., electronic computing method). Presenting such\nbenchmarks would offer valuable context for evaluating the practical benefits of the proposed photonic\nimplementation.\nResponse\nWe appreciate the suggestion and recommendation, which enable us to further expand on the benefits of our\nproposed implementation. The latency and power efficiency of DSPs are highly dependent on the design of the\nASICs that support the algorithm. Nonetheless, the energy consumption of electronics for multiplication and\nadditions can be found to be 208.5 fJ/bit and 26 fJ/bit, respectively, in (Pillai et al., 2014), and a standard Feed-\nForward Equalizer algorithm for an NRZ 25 GBaud requires 33 operations (17 multiplications, 16 additions). Thus,\na DSP alternative to our method would require ~ 3 pJ/bit/ per channel. The latency of the DSP algorithm is often\nhighly dependent on the ASIC architecture, but conventionally ranges from 100 ns to the ms timescale.\nACTION TAKEN\n For comparison, we have included, on lines 293-304, the general performance of DSP algorithms and the range\nof performances observed in published research on optical signal processing in peer-reviewed journals. In\nparticular, we state: ‘As quantitatively derived in Eqs. (6) and (7), the device achieves a maximum throughput of\ndigital signal processing-based equalization methods (DSP), which are less effective at mitigating nonlinear\ndistortions over long distances and consume significantly more power. In this regard, our architecture offers\ngreater energy efficiency per operation than other photonic counterparts, whose processing unit consumes only\n4.4 fJ/OP. This is because the device’s reservoir consists of integrated and passive elements; therefore, the\nmain energy consumption arises from these components, with negligible power drawn by the active elements,\nsuch as the SOA and IM. For comparison, DSP algorithms average energy consumption of approximately three\npJ/bit per channel for our communication protocol, with latency between 100 ns and 1 us depending on the\nsystem clock speed64, while reported optical signal processing methods' performances range from 20 to 200 ps\nlatency and 0.1 to 1 pJ/bit channel.’\n We have included two new articles as references for this comparison: (Liu et al., 2024) (112 Gbps/lane, 0.1\npj/bit, ~ ps range) and (Staffoli et al., 2024) (20 Gbps/lane, latency ~ 200 ps, 1.25 pJ/bit). We used these as the\nperformance range anticipated for the current telecom signal processing implementations, as stated on lines\n300-304.\nIn conclusion, the submitted manuscript reported a novel photonic reservoir computing architecture with claimed\npromising performance and capability, but these mentioned questions need to be settled to further make the manuscript more\ncomprehensive and convincing.\nWe sincerely thank the reviewer again for the very constructive and insightful feedback, as well as for recognizing\nthe potential of our work. We have carefully considered all the suggestions and believe that we have addressed them\nthoroughly in the revised Manuscript.\nReviewer #3 (Remarks to the Author):\nThis paper proposes and implements a wavelength-division-multiplexed (WDM) reservoir computing (RC) system\nthat enables parallel neuromorphic computation. As WDM-based RC has already been experimentally demonstrated\nin previous studies (e.g., [1]), the main contribution of this paper lies in its implementation of a nonlinear delay\nsystem called the nonlinear amplifying loop mirror (NALM).\nWe thank the reviewer for bringing this aspect to our attention. We were indeed aware of [1] work that had already\ncited it in our Manuscript. However, we would like to take this opportunity to clarify further the key differences\nbetween our work and references [1], [4], and [5], particularly regarding WDM-related aspects, which were also\nraised in a later comment (Reviewer Comment #1).\nA major distinction between our system and that of [1,4,5] lies in the scalability of the architecture, in terms of both\nreservoir structure and detection overhead, which directly impacts processing capability, adaptability, and overall\nhardware efficiency.\nWhile these prior works differ in implementation, they share several common limitations:\n1. The systems lack tunability, with the activation function, fading memory inherently constrained by the design,\nlimiting flexibility and adaptability to tackle different machine learning tasks.\n2. The reservoir dynamics remain linear, with nonlinearity applied only at the input/output stages via electronics,\nintroducing Optical-to-Electrical-to-Optical (OEO) latency.\n3. These systems do not support true task-level parallelism (or concurrency, defined in the Manuscript), as multiple\nwavelength or spatial channels are typically used to decompose and distribute a single task across parallel streams,\nrather than enabling independent execution of multiple distinct tasks.\nIn [1], the system employs spatio-temporal multiplexing, where each bit is delayed using fixed delay lines and\nprocessed in separate reservoir units that act as masking nodes. This enables interleaved processing (i.e., not real\nconcurrency), hence adding throughput latency in input/readout. Moreover, operation is constrained to specific input\nlaser conditions (e.g., θ = T/N), and each reservoir unit requires a separate pulsed laser source, further limiting\nflexibility and scalability. The system also requires 32 photodiodes per channel, resulting in significant detection\noverhead.\nIn [4], a similar interleaving strategy replaces recurrent feedback with a linear structure where delayed bit streams\nemulate memory. However, identical to [1], this fixes the node dimensionality and limits scalability. While\nfrequency channels can parallelize a task by mimicking the identical input (as we also demonstrate in Figure 3 in the\nManuscript), this system does not support task differentiation across channels. Importantly, the use of interleaving\nfor parallelization compromises true concurrency, as it introduces preprocessing latency that ultimately limits the\ncomputational throughput, the actual processing speed of the device.\nIn [5], multiple wavelength channels are only used to increase reservoir complexity by mixing frequency-domain\nnodes through a cascaded architecture. However, the system does not support independent reservoir tasks. Instead, it\nincreases the effective dimensionality of a single task through spectral coupling, without enabling per-channel\nflexibility or parallel execution of tasks with varying complexity.\nAcross all three systems, nonlinearity is confined to the input and output layers and implemented electronically,\nmaking the reservoir dynamics effectively linear. This reliance on electronic activation introduces OEO latency and\nlimits the exploitation of ultrafast, nonlinear effects intrinsic to the optical approach.\nIn contrast, besides computational scalability, our system is designed to allow a tunable control of the reservoir\nproperties. We use CW lasers with amplitude modulation to encode information, and reservoir properties are\nreconfigurable via the configuration tunable parameters, such as the SAO and VAO driving voltages. This enables\nus to process data with varying levels of complexity across multiple wavelength channels, all within a single shared\nreservoir. Our architecture supports any signal speed, limited only by the upper limit of input/readout electronics\nbandwidth, enabling a universal, fully reconfigurable optical computing platform. This flexibility is demonstrated\nthrough our applications in XOR logic, time-series classification, and nonlinear channel equalization, all of which\nutilize a unified reservoir.\nRegarding the reviewer’s comment: ‘the main contribution of this paper lies in its implementation of a nonlinear\ndelay system called the nonlinear amplifying loop mirror (NALM).’\nOur choice to employ a NALM configuration to realize our processing device is guided by its proven efficacy in\ngenerating highly stable and controllable nonlinear interactions, essential for optical reservoir computing (Kues et\nal., 2017; Aadhi et al., 2019; Xiong et al., 2023). Previous approaches, such as those based on unidirectional cavities\nor cross-gain modulation, have limitations including fixed nonlinear dynamics and reduced task versatility (Duport\net al., 2012, 2016; Vandoorne et al., 2008).\nIn contrast, the NALM architecture inherently supports robust and controllable nonlinear response, relying\npromising results demonstrated our previous studies (Aadhi et al. 2019, Optics Express, 27, 25251-25259), where\nthe figure-eight cavity configuration demonstrated high tunability and a very rich nonlinear dynamics response,\nbeneficial for advanced optical computing and reservoir computing tasks, in terms of fine classification of inputs.\nAdditionally, earlier studies, such as those by Adams et al. (1994) and Kues et al. (2017), underline the NALM’s\nintrinsic advantages in stable nonlinear dynamics, making it particularly attractive for reliable optical reservoir\ncomputing applications.\nBesides the novel configuration we implemented, our work introduces several key architectural and operational\nnovelties not only in terms of speed. This may have been misinterpreted in the earlier Manuscript version due to a\nlack of clarity. We want to summarize the novelty aspects of our work here as follows.\ni. True concurrent multi-task processing, with each wavelength channel independently masked and processed in\nparallel within the same reservoir units (stated on lines 83–90, demonstrated in the parallel execution of the MG\ntime-series and NARMA10 prediction tasks, along with the multi-channel recovery task).\nii. Computational throughput scalability is achieved by combining dense temporal encoding (each channel carries\nmultiple bits per round-trip, thereby enhancing information density and computational speed) with parallel\nwavelength channels, allowing each channel to carry multiple bits per round-trip. This significantly enhances\ninformation density and computational efficiency without requiring additional components or modifications to\nthe device architecture (see lines 208-212).\niii. Tunable nonlinearity embedded directly in the reservoir, enabled by the NALM mechanism and the presence of\nan SOA operating in an unsaturated regime, allowing precise control over the nonlinear response and avoiding\nthe limitations associated with cross-gain saturation.\niv. High energy-efficiency compared to previous demonstrations, even those chip-based (see Table 1 in the\nManuscript).\nTaken together, our work presents a qualitatively different approach to optical neuromorphic computing, focusing\non scalable, reconfigurable, and energy-efficient parallel processing, with experimentally demonstrated performance\nfrom our device.\nACTION TAKEN\n To address the reviewer’s comments regarding other WDM-based approaches, we have substantially revised the\nManuscript introduction (lines 50-64) to discuss better the differences of our approach with respect to earlier\nworks. We now state: ‘Recent efforts to increase computational throughput in reservoir computing have\nfocused on faster electro-optical modulation and advanced data encoding schemes, such as pulse-amplitude\nmodulation27–29 (PAM), often paired with wavelength-division multiplexing (WDM). However, these methods\nfrequently rely on sequential sweeping across WDM channels30–32, or time-interleaving techniques33–37, which\nboth introduce throughput latency and prevent the concurrent execution of independent tasks. Further attempts\nto scale performance further, by adding components or increasing the number and dimensionality of\ncomputational layers and readout components5,37. Typically, this results in decreased energy efficiency and\nprocessing speeds.\nMoreover, existing WDM-based RC architectures36–38 exhibit limited tunability. For instance, both the reservoir\nmemory and activation function are inherently fixed by design constraints. At the same time, nonlinearity is\nintroduced electronically at the input/output stage, resulting in optical-to-electrical-to-optical (OEO) latency\nand limiting the richness of reservoir dynamics. Such constraints significantly reduce system flexibility and\nadaptability for diverse ML tasks. Additionally, architectures employing spectral mixing approaches38\nencounter nonlinear crosstalk39, restricting the number of independently encoded channels and consequently\ndegrading system accuracy and scalability.’\n We have revised the abstract to clearly present the key novelties upfront, ensuring a prompt understanding of\nthe main contributions of the work.\n We have further clarified the motivation and advantages that led us to exploit the NALM configuration for\nreservoir computing (lines 67-71). We state ‘We leverage the NALM configuration for its proven ability to\ngenerate highly stable and nonlinear dynamics40–43, essential for optical reservoir computing. These dynamics\nenhance the reservoir’s computational capacity by enabling complex input mapping into a high-dimensional\nstate space, thereby improving sensitivity to extremely small signal variations44,45. The intrinsic stability of the\nNALM ensures consistent classification performance, even under noisy or fluctuating input conditions.’\n-Although this system utilizes gain saturation in a semiconductor optical amplifier (SOA), the principle itself has\nalready been reported in prior works [2,3], and thus lacks sufficient novelty.\nResponse\nWe thank the reviewer for their valuable and insightful comments, which allow us to clarify in more detail why our\ndevice avoids SOA gain saturation and how this significantly enhances our system's tunability and control, thus\nunderpinning the novelty and impact of our work.\nWe fully agree with the reviewer that SOAs are already widely used for processing units in optical reservoir\ncomputing. Indeed, seminal works by Vandoorne et al. (2008) and Duport et al. (2012, 2016) operate their reservoir\ndevices in a unidirectional configuration with SOAs in the saturation gain regime, resulting in a fixed nonlinear\nresponse resembling a tanh function. Similarly, Refs. [2,6] showcase cross-gain modulation (XGM) approaches,\nwhere nonlinear processing explicitly relies on operation within the saturation region, as also emphasized in Ref. [3].\nIn contrast, our approach leverages fundamentally different dynamics by intentionally avoiding SOA gain saturation.\nAs mentioned earlier and noted in the earlier Manuscript version as well (lines 280-281), our device does not operate\nin the gain saturation regime: “The SOA is operated between the linear and nonlinear regimes, far from saturation.”\nTherefore, we believe that these conceptual and operational differences position the novelty of our work relative to\nprior studies, thereby reinforcing its significance.\nSpecifically, gain saturation restricts the dynamic range of the nonlinear response, as the SOA gain plateaus at\nsaturation, substantially limiting the ability to finely tune the reservoir nonlinearity and thus its optimal\nconfiguration for ML tasks. By operating the SOA primarily below the saturation regime, we can precisely control\nthe gain via driving voltage adjustments, enhancing the tunability and performance of our device.\nQuantitatively, this tunability is clearly demonstrated in our parameter maps (Fig. 2), where the joint optimization of\nthe SOA gain and VOA settings leads to high accuracy in machine learning tasks. Specifically, we used the n-bit\ndelayed XOR task, which requires precise control over both the memory and nonlinearity of the reservoir, to\nbenchmark this capability. We achieved 100% classification accuracy for the 2-bit XOR task, 97% for the 3-bit\nXOR task, and 80% for the 4-bit XOR task. Notably, such task-specific optimizations would not be possible if the\nSOA gain was fixed at saturation levels.\nAdditionally, operating the SOA away from saturation significantly enhances system stability by mitigating intensity\nfluctuations and self-oscillation effects commonly observed in saturated gain regimes, particularly in NALM\nconfigurations(Aadhi et al., 2019). As previously noted in our response to Reviewer #2’s question, these instabilities\nare detrimental to the reservoir’s ability to classify input signals reliably(Appeltant et al., 2011), thereby impairing\noverall computational performance.\nACTION TAKEN\n To address comments regarding the operational regimes of the SOA used in this work, and to emphasize the key\ndifferences between our approach and earlier methods based on saturated gain operation, we have clarified the\ntext by adding the following text on lines 73–79 ‘Our device features an integrated nonlinear spiral waveguide\n(SW) and a semiconductor optical amplifier (SOA), which both modulate the NALM overall nonlinear transfer\nfunction (i.e., the reservoir activation function). In contrast to previous RC implementations that rely on SOAs\noperating in saturation, whether in unidirectional configurations46–48 or through cross-gain modulation49,50, we\nset the SOA below saturation for all our experiments. Saturated SOAs exhibit plateaued gain, limiting the\ndynamic range and tunability of the nonlinear response. The unsaturated regime, instead, allows precise\ntunability of the gain, and therefore of the reservoir activation function.’\n We provided further explanation on lines 154-162 regarding the nonlinearity arising from our device, which is\ndistinguished from previous gain-saturation reservoir computing-based devices reported. Here we state ‘During\nsuch an interaction, an increase in the amplification gain causes the SOA to contribute additional nonlinear\nresponse, thereby enhancing classification performance when further nonlinear contributions are required53\nwithout altering the physical reservoir topology. This unsaturated operational regime enables us to implement a\ncontrollable mechanism mediated by tunable parameters, allowing for the exploitation of nonlinearities arising\nfrom controlled optical feedback and intensity-dependent interference within the NALM. This approach allows\nfor precise and reconfigurable reservoir functionality. In contrast to the cross-gain saturation-based\nnonlinearities demonstrated in earlier works 49,50. Our architecture provides greater flexibility and control over\nreservoir dynamics.’\n-While the experimental demonstration is intriguing, the reported computational performance (20 tera operations per\nsecond) is lower than that of previous studies ([1] 800 TOPS, [4] 200 TOPS), and therefore does not offer the level\nof impact typically expected for a publication in Nature Communications. Accordingly, I do not recommend\npublication in Nature Communications. I believe this work would be more suitably presented in journals such as\nScientific Reports or Communications Physics, once the following concerns are addressed.\nResponse\nWe respectfully disagree with the reviewer’s comment and appreciate the opportunity to clarify both the\ncomputational performance in relation to the studies cited ([1], [4]) and the novelty of our work.\nRegarding the processing speed in [1], a careful review shows that the experimentally demonstrated throughput is\nexplicitly stated as approximately 20 to 44 TMAC/s per wavelength channel, not 800 TOPS. The mentioned"}, {"round": 2, "reviewer_comments": {"reviewer_2": "The revision offers more details regarding figure-eight shaped nonlinear amplifying loop mirror architecture for photonic\nreservoir computing and has addressed some of my concerns. There still remain some issues that should be addressed to\nsupport this paper's claims.\n1.In the revised manuscript, the authors have clarified the factors contributing to the system’s scalability, such as\nencoding speed and the number of wavelength channels. However, it remains unclear whether the gains in computational\nthroughput from these factors are fundamentally bounded. I recommend adding relevant analyses to help readers understand the\npotential upper limits of the system’s capability. Furthermore, while the authors state that the improvement in computational\nthroughput requires no additional computational units, it would be valuable to discuss whether there are other hardware\ncosts involved-for example, increased demands on lasers and AWGs, and the associated higher power consumption.\n2.The revised manuscript compares the proposed system with DSP only in terms of latency and energy consumption,\nwithout detailing the performance of the two hardware platforms on the same tasks, e.g., NRMSE in the time-series\nprediction task and BER in the nonlinear telecom signal recovery task. Since latency and energy consumption comparisons are\nonly meaningful under comparable task performance, adding this information would better demonstrate the advantages\nof the proposed method.\n3.The nonlinear telecom signal recovery task, the manuscript states that the proposed hardware can recover distorted\nsignals and effectively reduce BER. However, the presented results lack a baseline comparison, making it difficult to assess\nwhether the method’s performance is truly competitive. Including relevant baselines would help readers better appreciate the\nmethod’s effectiveness.\n4.In Table 1, the authors compare their work with existing photonic computing approaches, but omit prior implementations of\nphotonic reservoirs, which are highly relevant to the proposed system. Including comparisons with such works is necessary\nto provide a more comprehensive evaluation.\nIn conclusion, the current version still contains several issues and a second-round revision that addresses these major\nconcerns is recommended.", "reviewer_3": "I appreciate the authors' thorough and thoughtful responses to our previous comments. The revised manuscript addresses\nall of my concerns. I recommend the acceptance of the manuscript."}, "author_response": "REVIEWER COMMENTS\nReviewer #2 (Remarks to the Author):\nThe revision offers more details regarding figure-eight shaped nonlinear amplifying loop mirror\narchitecture for photonic reservoir computing and has addressed some of my concerns. There still remain\nsome issues that should be addressed to support this paper's claims.\n1.In the revised manuscript, the authors have clarified the factors contributing to the system’s scalability, such as\nencoding speed and the number of wavelength channels. However, it remains unclear whether the gains in computational\nthroughput from these factors are fundamentally bounded. I recommend adding relevant analyses to help readers understand the\npotential upper limits of the system’s capability. \nWe thank the reviewer for this insightful question on the fundamental throughput limits of our system.\nThe fiber loop latency sets the initial speed limit, since each round-trip corresponds to a single\ncomputational step. In practice, this constraint is mitigated in our approach through dense encoding and\nconcurrent multi-channel processing, which enables many operations to occur within each loop cycle and\nthereby pushes the effective throughput well beyond the single-loop latency bound.\nThe next bottleneck to consider arises from the limited bandwidth of the encoding hardware. Specifically,\nour AWGs and modulators operate up to about 6.5 GHz, and we use 24 GHz modulation to generate four\nvirtual nodes per channel. With faster encoding hardware, the dominant limitation would shift to the\nsemiconductor optical amplifier (SOA) dynamics, which impose the fundamental bounds on device\noperation.\nTwo intrinsic SOA properties are responsible: the carrier recovery time (𝜏 ), which sets the maximum\n(cid:3045)(cid:3032)(cid:3030)\nupdate frequency, and the saturation energy (E ), which fixes the maximum tolerable energy per\n(cid:2929)(cid:2911)(cid:2930)\nmasking cycle.\n(cid:2869)\nThe total masking rate, defined as 𝑓 = 𝑁 𝑓 , must satisfy 𝑓 ≤ , where here 𝑁 is the\n(cid:3040)(cid:3028)(cid:3046)(cid:3038) (cid:3049) (cid:3032)(cid:3041)(cid:3030) (cid:3040)(cid:3028)(cid:3046)(cid:3038) (cid:3049)\n(cid:3099)(cid:3293)(cid:3280)(cid:3278)\nnumber of virtual nodes per channel and 𝑓 is the encoding rate per channel. If this limit is exceeded,\n(cid:3032)(cid:3041)(cid:3030)\nthe SOA cannot recover its gain between pulses, resulting in dynamic gain compression and signal\ndistortion. At the same time, the input energy per cycle, defined as 𝐸 =\n(cid:3017)(cid:3269)\n, where 𝑃 is the total\n(cid:3021) (cid:3021)\n(cid:3033)(cid:3288)(cid:3276)(cid:3294)(cid:3286)\ncirculating power must remain below 𝐸 , otherwise, nonlinear distortions such as self-phase modulation\n(cid:3046)(cid:3028)(cid:3047)\nand spectral broadening appear. Additionally, exceeding this threshold would also impact the nonlinear\ntunability of the reservoir transfer function, which we demonstrate in this work. These two constraints act\nin opposite directions: raising the encoding frequency lowers the energy per symbol, which helps to\nsatisfy the saturation condition, but it pushes closer to the recovery-time limit, while reducing the\nfrequency relaxes the recovery requirement but increases the energy per symbol, risking saturation.\nThe balance between these limits determines the maximum distortion-free throughput, and combining\nthem with the reservoir operation count leads to the expression now included in the revised\nSupplementary Information (Eq. S21):\nN\nS(cid:2923)(cid:2911)(cid:2934) = 2⋅ (cid:2932) ⋅ (cid:3435)O ⋅ N ⋅ C + R ⋅C(cid:4593)(cid:4593) (cid:3439),\n(cid:2904)(cid:2899)(cid:2900)(cid:2903) τ (cid:2924) (cid:2926) (cid:2916) (cid:2923) (cid:2916)\n(cid:2928)(cid:2915)(cid:2913)\nwhere 𝑆(cid:3040)(cid:3028)(cid:3051) the maximum sustainable throughput, expressed in tera-operations per second (TOPS); 𝑛 is\n(cid:3021)(cid:3016)(cid:3017)(cid:3020) (cid:3030)\nthe number of wavelength channels used for parallel processing; 𝑁 is the number of virtual nodes per\n(cid:3049)\nchannel; 𝜏 is the SOA carrier recovery time; 𝑂 is the total number of reservoir operations per round-\n(cid:3045)(cid:3032)(cid:3030) (cid:3041)\n1\ntrip (equal to 10 in our case, counting both linear and nonlinear contributions, see footnote now included\nin the revised Supplementary Information); 𝑁 is the number of physical nodes in the reservoir (equal to 1\n(cid:3043)\nhere); 𝐶 and 𝐶′ is a factor that accounts for arithmetic involving complex-valued variables (node states,\n(cid:3033) (cid:3033)\nweights, inputs). In our device, S(cid:2923)(cid:2911)(cid:2934) = 24 TOPS per channel.\n(cid:2904)(cid:2899)(cid:2900)(cid:2903)\nWe scale by adding more parallel wavelength channels, beyond the current 5 channels. The device\noperates effectively with dense wavelength division multiplexing (DWDM). In standard systems, this\nmeans up to about 80 channels. We demonstrated this scalability by generating nine distinct wavelength\nchannels through the modulation and amplification of the sidebands of a single continuous-wave (CW)\nlaser (see Fig. S5 in the Supplementary Information). This proves that the device can support more than 5\nchannels simultaneously, thereby achieving higher throughput.\nImportantly, our concurrent processing approach reduces latency and allows the system to operate near\nthe fundamental limits set by SOA recovery and saturation dynamics. This represents one of the main\nfoundations of our work.\nACTIONS TAKEN\n We moved the earlier formulation of the processing speed from the Methods section of the original\nManuscript to the new Section 4.1 of the revised Supplementary Information. The discussion on\nspeed, fundamental throughput limits, and computational scalability has been expanded, with full\ndetails (lines 211–260, Supplementary Information), to explicitly address the impact of the SOA on\ncomputational throughput. This addition clarifies the physical origin of the upper bound and its\nconnection to both SOA dynamics and device parameters.\n We have also added a paragraph from lines 311 to 323 of the Discussion Section of the Manuscript\nreferring to the upper bound on throughput scalability.\n To avoid ambiguity in the definition of processing speed and throughput, and following the\nreviewer’s concern, we have added the sentence in the Manuscript from line 46 to line 50: “Despite\nsignificant progress, RC implementations remain limited by their inherent architecture, where nodes\nare created and interconnected through feedback mechanisms. These mechanisms simplify the design\nby generating virtual nodes, but also introduce latency and restrict processing speed, defined as\nsystem throughput, i.e., the total number of operations per second across all input data streams\nwithin a single reservoir unit.”\n We have now included a footnote below line 226 of the Supplementary Information clarifying how\nthe definition of processing speed accounts for the nonlinear steps: “ The contribution to the\nnonlinear computational steps arises from the application of the nonlinear operators acting on the\nelectric field, as defined in Eqs. (S10)–(S12). Specifically, Eq. (S10) involves two nonlinear\noperations, Eq. (S11) adds two more, and Eq. (S12) introduces one additional operation, for a total\nof five nonlinear operations. Because the electric field is complex, this number is then multiplied by a\nfactor of 2, resulting in 10 nonlinear operations overall.”\nadditional computational units, it would be valuable to discuss whether there are other hardware\ncosts involved-for example, increased demands on lasers and AWGs, and the associated higher power\nconsumption.\nResponse\nWe acknowledge the reviewer’s point regarding peripheral hardware costs and quantify the power\nconsumption of peripheral hardware, discussing ways to reduce it.\nIn the former manuscript, we had previously quantified the consumption of the input hardware,\nconsidering ~150 W for the three AWGs employed (five data channels plus one masking channel), ~0.4\nW for the five IMs, and ~18 W for the CW lasers. Importantly, our current scheme employs dense\nencoding, where multiple bits are injected per cavity round-trip per channel, thereby increasing\nthroughput without requiring an increase in the number of physical AWGs, IMs, or lasers. In this work,\nwe operate with binary intensity modulation, where each symbol carries a single bit (b = 1).\nIn the former Manuscript, we have already reported that the computational throughput can be further\nincreased by using additional laser sources or more advanced encoding techniques, such as quadrature-\namplitude modulation (QAM). More generally, the total aggregate rate (the overall number of bits\nprocessed per second across all channels) can be expressed as\n𝑅 = 𝑛 × 𝑅 × 𝑏,\n(cid:3047)(cid:3042)(cid:3047)(cid:3028)(cid:3039) (cid:3030) (cid:3046)(cid:3052)(cid:3040)\nwhere 𝑅 is the symbol rate per channel, and b is the number of bits per symbol.\n(cid:3046)(cid:3052)(cid:3040)\nTo increase computational throughput without impacting or even reducing the power consumption of the\nperipheral, one could use higher-order modulation formats such as 64-QAM (b = 6). This is sufficient to\nreplace our current five data channels with just one at the same symbol rate. In practice, this would lower\nAWG usage from ~150 W to ~25 W (an ~83% reduction), reduce IM consumption from ~0.4 W to ~70\nmW (also ~83% reduction), and cut the number of active laser channel from five to one (an 80%\nreduction), which reduces laser wall power by about 40 to 55 percent, based on vendor data and fixed\noverhead assumption.\nWith polarization-dependent multiplexing techniques, the effective modulation order would further\nincrease, providing additional margin for throughput and reducing the need for modulation equipment\neven further.\nBeyond modulation, another way to reduce laser overhead is to replace multiple discrete CW sources with\nan integrated multi-wavelength source, such as distributed-feedback laser arrays, thereby allowing a\nsingle chip to feed all channels. This eliminates per-line idle losses and, based on typical device\nspecifications, is expected to save several watts when using one integrated source at the same optical\nsignal-to-noise ratio and linewidth performance.\nThese alternatives were not implemented in the present work due to the lack of access to coherent\ndetection equipment (e.g., high-Q photodetectors), advanced high-order AWG drivers, and integrated\nmulti-wavelength sources in our laboratory. Nonetheless, in combination with our already employed\ndense encoding scheme, they represent clear future directions to mitigate peripheral overhead while\nleaving the reservoir core scaling unaffected.\n Together with Section S.4.1 on throughput, we moved the section on power consumption estimation\n(lines 301–312) to the Supplementary Information as the new Section S.4.2. Following the reviewer’s\nrecommendation, this section now provides a more detailed discussion of the encoding hardware\ncosts and how these can be mitigated through alternative encoding strategies.\n We have also revised the text in the Discussion (lines 319–323) to highlight the role of advanced\nencoding techniques and dense multiplexing in both reducing hardware consumption and increasing\nthroughput: “For instance, with 80 channels, as typically achieved in standard DWDM, the\narchitecture can reach a combined throughput of nearly two peta-operations per second (POPS) \nunder binary modulation. By employing phase-sensitive processing and higher-order modulation\nformats, such as 64-quadrature-amplitude modulation (6 bits per symbol), the effective throughput\ncan increase to several tens of POPS.”\n2.The revised manuscript compares the proposed system with DSP only in terms of latency and energy consumption,\nwithout detailing the performance of the two hardware platforms on the same tasks, e.g., NRMSE in the time-series\nprediction task and BER in the nonlinear telecom signal recovery task. Since latency and energy consumption comparisons are\nonly meaningful under comparable task performance, adding this information would better demonstrate the advantages\nof the proposed method.\nResponse\nWe thank the reviewer for their comment. Since our device implements optical reservoir computing, we\nevaluated its performance by comparing its speed and energy consumption in detail with other optical\nneural network implementations, as previously reported in Table 1 of the Manuscript. In the same Table,\nwe also report and compare classification accuracy in terms of a percentage calculated as (1- NRMSE) %,\na common metric for tasks such as Mackey–Glass and NARMA .\ndata signals and recover them from transmission distortions in telecommunication channels, with\nperformance quantified by the BER. In the previous version of the Manuscript, we briefly compared our\ndevice’s performance with DSP-based approaches for nonlinear channel recovery as a specific case study.\nRecent advanced DSP methods for channel equalization, such as the deep-unfolded digital\nbackpropagation demonstrated by Tang et al. (Optics Express 29, 36242, 2021), have achieved a BER\nthreshold of 2 × 10⁻². Song et al. (Optics Express 30, 26774, 2022) reported a real-time FPGA-based\ncoherent receiver using optimal interpolation clock recovery, reaching a BER of 2.4×10⁻⁴ at 15 Gbaud\nwith 16-QAM. These DSP schemes rely on thousands of multipliers and operate with energy\nconsumption in the picojoule-per-bit range. In contrast, our device achieves a BER of 2×10⁻⁴ while\nexhibiting orders of magnitude improvement in energy efficiency, operating in the few-femtojoule-per-\noperation range.\nACTIONS TAKEN\n We expanded and refined the discussion on DSP techniques for nonlinear channel equalization on\nlines 289–295. The updated text now includes quantitative examples and a detailed comparison\nbetween the performance of our approach and such DSP-based methods applied to nonlinear channel\nequalization: “Advanced DSP methods, including digital backpropagation, typically report BER\nvalues near 2×10⁻². Real-time field-programmable gate array-based coherent receivers have\nachieved 2.4 × 10⁻⁴ at 15 Gbaud with 16-quadrature amplitude modulation (16-QAM)64. These\n4\napproaches require thousands of multipliers and significantly higher power consumption, typically\naround 3 pJ per bit per channel, with latency between 100 ns and 1 μs, depending on the system\nclock. In contrast, optical signal processing methods offer a latency of 20 to 200 ps and energy\nconsumption ranging from 0.1 to 1 pJ per bit per channel.”\n We added further accuracy comparison for bit recovery tasks performed by other approaches in Table\n1.\n3.In the nonlinear telecom signal recovery task, the manuscript states that the proposed hardware can\nrecover distorted signals and effectively reduce BER. However, the presented results lack a baseline\ncomparison, making it difficult to assess whether the method’s performance is truly competitive.\nIncluding relevant baselines would help readers better appreciate the method’s effectiveness.\nResponse\nWe thank the reviewer for this important comment. Following our previous response to point #2 and our\nAction Taken, we have now reiterated some performance comparisons of our system relative to standard\nDSP methods used in nonlinear signal recovery (lines 289-295)\nTo provide further detail, we can introduce additional baseline comparisons in terms of Q-factor\nimprovement, a performance metric used to assess the quality of a telecom (optical) signal after recovery.\nFor instance, digital backpropagation (DBP), which numerically inverts fiber propagation, has been\nshown to improve the Q-factor by up to ~2 dB (Opt. Express 19, 9453–9460, 2011). This corresponds to a\nBER reduction from ~1 × 10⁻³ to the low 10⁻⁴ range, although DBP remains computationally expensive\nand scales poorly with algorithmic depth. Recent electronic neural networks have demonstrated ~1 dB Q-\nfactor improvements (Nat. Commun. 10, 3033, 2019), reducing BER from ~2×10⁻³ to ~1.1×10⁻³,\nwhile\nphotonic–electronic hybrid neural networks have reported ~0.8 dB gains (Nat. Electron. 4, 837–844,\n2021), corresponding to a BER reduction by about a factor of 1.7.\nBy contrast, the recovered optical signal with our device shows a minimum BER of 2×10⁻⁴ after 60 km of\nnonlinear propagation, which corresponds to a Q-factor improvement of ~4.6 dB. This surpasses the BER\nand Q-factor improvements of DSP, as well as electronics-based neural network processing, while\nsustaining a total throughput of 20 TOPS and operating in the few-femtojoule-per-operation regime.\nThese results demonstrate that our approach delivers comparable or superior performance, with latency\nand energy consumption orders of magnitude lower than those of DSP- or hybrid-based methods.\nACTIONS TAKEN\n We further expand the paragraph from line 296 to 302, including baseline comparison in terms of the\nQ-factor improvement of the recovered signal of our device vs some reported electronics-based and\nDSP techniques: “In terms of signal quality enhancement achieved after compensation, electronic\nneural networks can reach a Q-factor improvement of roughly 2 dB with a BER of about 1.1×10⁻³,\nwhile photonic–electronic hybrid networks can achieve an improvement of about 0.8 dB with a BER\naround 10⁻4. Our device achieves a BER of 2×10⁻⁴ after 60 km of transmission at 5.4 dBm input\npower, corresponding to a Q-factor improvement of approximately 4.6 dB (see Fig. 5 (b)). It operates\nat 4.4 fJ per operation, outperforming DSP and electronic neural-network processing as well as\npreviously reported photonic neural-network implementations, as summarized in Table 1.”\n5\n4.In Table 1, the authors compare their work with existing photonic computing approaches, but omit prior\nimplementations of photonic reservoirs, which are highly relevant to the proposed system. Including\ncomparisons with such works is necessary to provide a more comprehensive evaluation.\nACTIONS TAKEN\n We have updated Table 1 to include representative examples of photonic reservoir implementations,\ndisplaying their key metrics alongside other photonic computing approaches\nIn conclusion, the current version still contains several issues and a second-round revision that addresses\nthese major concerns is recommended.\nWe thank Reviewer #2 for their thorough assessment and constructive feedback. We appreciate the\nrecommendation for further revisions and are confident that the updated manuscript now addresses all\nmajor concerns, strengthening the clarity and significance of our results.\nReviewer #3 (Remarks to the Author):\nI appreciate the authors' thorough and thoughtful responses to our previous comments. The revised\nmanuscript addresses all of my concerns. I recommend the acceptance of the manuscript.\nWe sincerely thank Reviewer #3 for their supportive evaluation and recommendation for acceptance. We\nare grateful for the feedback provided throughout the review process, which has helped us improve the\nclarity and completeness of the Manuscript\nI appreciate the authors’ thorough and constructive responses to the reviewers’ comments. The revised manuscript\nsatisfactorily addresses all previous concerns, and I recommend it for publication in Nature Communications.\nWe thank the reviewer for their insightful comments and suggestions, which helped us improve the quality and impact\nof our work."}]

Decision letter