Quantum optical neural networks using atom-cavity interactions to provide all-optical nonlinearity

TL;DR

This work introduces a quantum optical neural network (QONN) that uses atom-cavity neurons to deliver all-optical nonlinear activation, eliminating electronic detectors and emitters in conventional ONNs. The network leverages cavity arrays for nonlinear activation and a spatial light modulator–based optical matrix-vector multiplier to realize inter-layer computations, with training performed via backpropagation. Demonstrations on MNIST and SAT-6 show high potential, including robustness to photon detuning and loss, and a convolutional variant that reduces parameter counts. The approach promises real-time, low-energy onboard learning for satellite sensing and secure communications, though a fully quantum treatment including entanglement remains a future direction.

Abstract

Optical neural networks (ONNs) have been developed to enhance processing speed and energy efficiency in machine learning by leveraging optical devices for nonlinear activation and establishing connections among neurons. In this work, we propose a quantum optical neural network (QONN) that utilizes atom-cavity neurons with controllable photon absorption and emission. These quantum neurons are designed to replace the electronic components in ONNs, which typically introduce delays and substantial energy consumption during nonlinear activation. To evaluate the performance of the QONN, we apply it to the MNIST digit classification task, considering the effects of photon absorption duration, random atom-cavity detuning, and stochastic photon loss. Additionally, we introduce a convolutional QONN to facilitate a real-world satellite image classification (SAT-6) task. Due to its compact hardware and low power consumption, the QONN offers a promising solution for real-time satellite sensing, reducing communication bandwidth with ground stations and thereby enhancing data security.

Figures (5)

• Figure 1: Quantum optical neural network for MNIST digit classification and DeepSat (SAT-6) airborne image classification tasks. a Schematic of the quantum optical neural network, consisting of optical matrix-vector multipliers (MVMs) and cavity arrays, where $z_{i}^{l}$ represents the incident photon amplitude entering each cavity neuron, and $a_{i}^{l}$ is the photon amplitude emitted by the atom inside the cavity neuron. The activation values $a_{i}^{l}$ from the cavity array of each layer are passed to the next layer through the optical MVM, with $z_{i}^{l+1}$ being the weighted sum of $a_{i}^{l}$. The optical MVM is implemented using a spatial light modulator (SLM). The weights $W_{ij}^{l}$, which are parameters optimized via backpropagation, are adjusted by controlling the transmission of each SLM pixel. The input images are encoded in $a_{i}^{\rm{in}}$. The final layer uses a photodetector (PD) array to obtain the output $a_{i}^{\rm{out}}$, which is used to compute the cost function. b Schematic of a cavity neuron that performs the quantum optical nonlinear activation as described by Eq. (\ref{['eq:activation']}). The neuron consists of a low-Q cavity with weaker atom-cavity coupling (in blue) and a high-Q cavity with stronger atom-cavity coupling (in red). In step 1, the incident photon is absorbed by the two-level atom, and the excitation is stored in the low-Q cavity while the high-Q cavity is turned off. In step 2, the high-Q cavity is turned on, and the excitation is transferred from the low-Q cavity to the high-Q cavity. In step 3, the high-Q cavity is re-opened, and the photon is emitted by the atom through a complete energy conversion from atomic excitation to photon emission.
• Figure 2: Performance of the quantum optical neural network with various photon absorption times for the MNIST task. a Test accuracy plotted against the photon absorption times in the first and second hidden layers, $t_{1}$ and $t_{2}$. b Test accuracy as a function of the absorption time $t$, with $t=t_{1}=t_{2}$, after 1 (green), 10 (red), and 20 (orange) training epochs. A training epoch is defined as a complete pass of the entire MNIST training dataset through the learning process. c Nonlinear activation function $a_{i}^{l}$ (identical for all neurons in the two layers since $t_{1}=t_{2}$), and the occurrence population distributions of the incident photon amplitudes $|z_{i}^{1}|$ and $|z_{i}^{2}|$, which serve as the arguments for the activation functions, The results shown in panel c correspond to three absorption times, $t=0.2$, $t=1$, and $t=4$, based on $10$ training epochs and the input image shown in the upper-left corner. The detuning is $\delta_{i}^{l}=0$, and the coupling strength is $g=1$ for every cavity neuron. The number of neurons is set to $N_{1} = N_{2} = 512$ in the two hidden layers.
• Figure 3: Performance of the quantum optical neural network with finite detuning for each cavity neuron on the MNIST task. The photon absorption times $t$ are identical in the first and second hidden layers. a Each cavity neuron is simulated with a random detuning $\delta_{i}^{l}$, where the probability is uniformly distributed within the range $[-2\delta_{0}, 2\delta_{0}]$, resulting in an average detuning magnitude of $\delta_{0}$. b All cavity neurons are identical and simulated with a fixed detuning $\delta_{i}^{l} = \delta_{0}$. The coupling strength is $g=1$, and the number of neurons is $N_{1} = N_{2} = 512$.
• Figure 4: Quantum optical neural network with stochastic photon loss. a Based on the schematic shown in Fig. \ref{['Fig1']}a, a stochastic layer (in magenta) is added before the activation $a_{i}^{1}$ entering the optical MVM to model photon loss during transmission. During the forward pass, each $a_{i}^{1}$ has a probability $P$ of remaining unchanged and a probability $1-P$ of being set to $0$. The photon passing rate $P$ is identical for all cavity neurons. b MNIST test accuracy plotted against the photon passing rate. The stochastic neural network consists of a single hidden layer with $512$ cavity neurons, each having a photon absorption time $t_{1} = 1$ and a detuning $\delta_{i}^{1} = 0$, and is trained for $10$ epochs.
• Figure 5: Quantum optical neural network performing DeepSat (SAT-6) airborne image classification task. a SAT-6 images with RGB channels representing six land cover classes. b Schematic of a convolutional layer embedded in the quantum optical neural network, where the convolution kernel is implemented using a set of SLMs, followed by average pooling realized through programmable photonic circuits. The photons are incident into the cavity neurons after the convolution and pooling operations. c Test accuracy of the quantum optical neural network on the SAT-6 task with varying numbers of cavity neurons in the first hidden layer. Two network structures are applied: one with a convolutional layer followed by a fully-connected layer (orange), and another with two fully-connected layers as shown in Fig. \ref{['Fig1']}a (blue). The number of parameters in the convolutional layer depends on the kernel size and the number of output channels. A $5 \times 5$ kernel with a stride of $1$ and $2 \times 2$ average pooling with a stride of $2$ are used. The number of output channels in the convolutional layer is set to $2$, $4$, $8$, and $16$, corresponding to the four orange dots in panel c, respectively. The second layer contains $512$ neurons in both structures. The network is trained for $10$ epochs.