Parametrized quantum circuits are essential components of variational quantum algorithms. Until now, optical implementations of these circuits have relied solely on adjustable linear optical units. In this study, we demonstrate that using programmable nonlinearities, rather than linear optics, offers a more efficient method for constructing quantum optical circuits -- especially quantum neural networks. This approach significantly reduces the number of adjustable parameters and the circuit depth needed to achieve high-fidelity operation. Specifically, we explored a quantum optical neural network (QONN) architecture composed of meshes of two-mode interferometers programmable by adjustable Kerr-like nonlinearities. We assessed the capabilities of our quantum optical neural network architecture and compared its performance to previously studied architectures that use multimode linear optics units. Additionally, we suggest future research directions for improving programmable quantum optical circuits.
Parametrized quantum circuits are essential components of variational quantum algorithms. Until now, optical implementations of these circuits have relied solely on adjustable linear optical units. In this study, we demonstrate that using programmable nonlinearities, rather than linear optics, offers a more efficient method for constructing quantum optical circuits -- especially quantum neural networks. This approach significantly reduces the number of adjustable parameters and the circuit depth needed to achieve high-fidelity operation. Specifically, we explored a quantum optical neural network (QONN) architecture composed of meshes of two-mode interferometers programmable by adjustable Kerr-like nonlinearities. We assessed the capabilities of our quantum optical neural network architecture and compared its performance to previously studied architectures that use multimode linear optics units. Additionally, we suggest future research directions for improving programmable quantum optical circuits.
Recent photonic quantum machine learning proposals combined linear optics with adaptivity to enhance expressivity and improve algorithm performance and scalability. The particle-number-preserving property of linear optical platforms was recently employed to design a quantum convolutional neural network architecture with advantages in terms of resource complexity and the number of parameters needed. Here, we design and experimentally implement a photonic quantum convolutional neural network (PQCNN) based on linear optics equipped with adaptive state injection, a tool that increases the linear optical circuits controllability. We validate the PQCNN for a binary image classification on a photonic platform utilizing a semiconductor quantum dot-based single-photon source and programmable integrated photonic interferometers comprising 8 and 12 modes. To investigate the scalability of the PQCNN design, we performed numerical simulations on datasets of different sizes. These findings demonstrate potential utilities of a simple adaptive technique for a nonlinear boson sampling task, compatible with near-term quantum devices.
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.
The growing computational demands of classical neural networks have intensified the search for energy-efficient and powerful computational alternatives. Quantum neural networks (QNNs) implemented on integrated photonic platforms offer a compelling avenue, offering exceptional computational power enhancements, with inherent programmability and scalability of integrated architectures. A critical challenge, however, is implementing the fundamental non-unitary and nonlinear activation function of QNNs within a linear quantum photonic system. Existing strategies, such as the adding ancillary qubits and measurement-based feedback or forward are constrained by high qubit resource costs, overhead devices, and poor cascadability. Here, we propose a novel deep photonic QNN with an expanded computational Hilbert space via input replication and mode expansion, which enables the realization of effective non-unitary and nonlinear activation on a linear programmable quantum photonic chip. This approach eliminates the need for physical ancillary qubits, measurement-induced qubit consumption and the measurement device burden, thereby significantly reduce resource costs. The fabricated chip integrates four high-quality entanglement sources and a programmable high-dimensional interferometric network, enabling a two-hidden-layer QNN that exhibits dimension-enhanced expressivity over the existing QNN architectures. We demonstrate its capabilities across diverse tasks, including nonlinear classification, image generation, and quantum Gibbs state preparation. This work establishes a scalable and efficient architecture toward practical quantum deep learning systems capable of tackling problems beyond the reach of classical computation.
Continuous-variables (CV) quantum optics is a natural formalism for neural networks (NNs) due to its ability to reproduce the information processing of such trainable interconnected systems. In quantum optics, Gaussian operators induce affine mappings on the quadratures of optical modes while non-Gaussian resources (the challenging piece for physical implementation) originate the nonlinear effects, unlocking quantum analogs of an artificial neuron. This work presents a novel experimentally-feasible framework for continuous-variable quantum optical neural networks (QONNs) developed with available photonic components: coherent states as input encoding, a general Gaussian transformation followed by multi-mode photon subtractions as the processing layer, and homodyne detection as outputs readout. The closed-form expressions of such architecture are derived demonstrating the family of adaptive activations and the quantum-optical neurons that emerge from the amount of photon-subtracted modes, proving that the proposed design satisfies the Universal Approximation Theorem within a single layer. To classically simulate the QONN training, the high-performance QuaNNTO library has been developed based on Wick-Isserlis expansion and Bogoliubov transformations, allowing multi-layer exact expectation values of non-Gaussian states without truncating the infinite-dimensional Hilbert space. Experiments on supervised learning and state-preparation tasks show balanced-resource efficiency with strong expressivity and generalization capabilities, illustrating the potential of the architecture for scalable photonic quantum machine learning and for quantum applications such as complex non-Gaussian gate synthesis.
Quantum machine learning represents a promising approach to disclose novel possibilities for quantum information protocols. Thus, recent efforts have been dedicated to determine how to merge, or extend, machine learning approaches in the quantum domain. A relevant example is provided by a quantum-optical neural network (QONN), a class of physical systems that aim to represent the quantum-optical version of classical neural networks. This architecture was first introduced to identify the structure of optical circuits in analogy to their classical counterpart, showing the possibility of tackling different quantum tasks. However, the full potential of such an approach still needs to be explored. In this work, we provide a step forward in this direction by employing it to tackle the fundamental task of optical quantum cloning. The employed architecture has been successfully trained to perform deterministic universal quantum cloning on a photonic platform, achieving results that are very close to that of an optimal universal quantum cloner. Furthermore, we have verified numerically the robustness of this approach with respect to experimental imperfections relevant for future implementations. This work thus shows the capabilities and flexibility of QONNs, which might prove important for designing even more complex optical circuits.
The lack of interactions between single photons prohibits direct nonlinear operations in quantum optical circuits, representing a central obstacle in photonic quantum technologies. Here, we demonstrate multi-mode nonlinear photonic circuits where both linear and direct nonlinear operations can be programmed with high precision at the single-photon level. Nonlinear interaction is realised with a tunable quantum dot embedded in a nanophotonic waveguide mediating interactions between individual photons within a temporal linear optical interferometer. We demonstrate the capability to reprogramme the nonlinear photonic circuits and implement protocols where strong nonlinearities are required, in particular for quantum simulation of anharmonic molecular dynamics, thereby showcasing the new key functionalities enabled by our technology. Adding tunable photon-photon nonlinearities to programmable photonic circuits would greatly extend their capabilities. Here, the authors demonstrate this by embedding a photonic-crystal waveguide nanostructure hosting an InAs quantum dot within a programmable linear optical circuit, and using it to realise a proof-of-concept quantum simulation of anharmonic molecular vibrational dynamics.