High Resolution Image Download MS PowerPoint Slide Photonics has unlocked the potential for the energy-efficient acceleration of deep learning. Conventional platforms for photonic deep learning have implemented linear matrix calculations and nonlinear activations separately following traditional deep learning architectures. However, critical challenges remain in achieving and evaluating nonlinear expressivity─the ability of neural networks to approximate nonlinear functions─including the substantial cost of electro-optical conversion or optical nonlinearity and the absence of a metric to quantify the expressivity of photonic platforms. Here, we propose the concept of nonlinear unitary (NU) circuits for norm-preserving photonic learning, which achieve both linear and nonlinear expressivity within a building block. We examine two-dimensional NU operations─characterized by norm-preserving mappings and nonconservative inner products─using this building block, which can be employed to construct high-dimensional circuits. Using deep nonlinear unitary circuits, we demonstrate exponential growth in trajectory length and near-uniform coverage of the output space by developing platform-transparent metrices to quantify the nonlinear expressivity of the circuits. Along with neuroevolutionary learning examples, our results pave the way to highly expressive photonic neural networks with rigorous quantification.
High Resolution Image Download MS PowerPoint Slide Photonics has unlocked the potential for the energy-efficient acceleration of deep learning. Conventional platforms for photonic deep learning have implemented linear matrix calculations and nonlinear activations separately following traditional deep learning architectures. However, critical challenges remain in achieving and evaluating nonlinear expressivity─the ability of neural networks to approximate nonlinear functions─including the substantial cost of electro-optical conversion or optical nonlinearity and the absence of a metric to quantify the expressivity of photonic platforms. Here, we propose the concept of nonlinear unitary (NU) circuits for norm-preserving photonic learning, which achieve both linear and nonlinear expressivity within a building block. We examine two-dimensional NU operations─characterized by norm-preserving mappings and nonconservative inner products─using this building block, which can be employed to construct high-dimensional circuits. Using deep nonlinear unitary circuits, we demonstrate exponential growth in trajectory length and near-uniform coverage of the output space by developing platform-transparent metrices to quantify the nonlinear expressivity of the circuits. Along with neuroevolutionary learning examples, our results pave the way to highly expressive photonic neural networks with rigorous quantification.
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.
Quantum computing enables quantum neural networks (QNNs) to have great potential to surpass artificial neural networks. The powerful generalization of neural networks is attributed to nonlinear activation functions. Although various models related to QNNs have been developed, they are facing the challenge of merging the nonlinear, dissipative dynamics of neural computing into the linear, unitary quantum system. In this paper, we establish different quantum circuits to approximate nonlinear functions and then propose a generalizable framework to realize any nonlinear quantum neuron. We present two quantum neuron examples based on the proposed framework. The quantum resources required to construct a single quantum neuron are polynomial in function of the input size. Finally, both IBM Quantum Experience results and numerical simulations illustrate the effectiveness of the proposed framework.
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.
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.
In recent years, optical computing becomes a powerful task-specific platform, under the increasing demand for computing power (especially for neural networks). This doctoral thesis is devoted to the design, simulation, and testing of integrated silicon photonic circuits for optical neural networks and machine-learning-assisted quantum computing tasks. In Chapter 3, we demonstrate an optical neural chip that implements complex-valued neural networks and benchmark its performance under practical settings, proving strong learning capabilities. In Chapter 4, we demonstrate an efficient, physics-agnostic, and closed-loop protocol for training optical neural networks on chip. In Chapter 5, we demonstrate a silicon photonic chip that achieves chip-to-chip teleportation of high-dimensional quantum states, using the trainable quantum autoencoders. High fidelities are achieved between the input qutrit and the qutrit decoded from the teleported state. Our results present a promising avenue towards realizing deep optical neural networks and challenging quantum computing tasks with dedicated integrated silicon photonic circuits.
Developing hardware for high-dimensional unitary operators plays a vital role in implementing quantum computations and deep learning accelerations. Programmable photonic circuits are singularly promising candidates for universal unitaries owing to intrinsic unitarity, ultrafast tunability and energy efficiency of photonic platforms. Nonetheless, when the scale of a photonic circuit increases, the effects of noise on the fidelity of quantum operators and deep learning weight matrices become more severe. Here we demonstrate a nontrivial stochastic nature of large-scale programmable photonic circuits-heavy-tailed distributions of rotation operators-that enables the development of high-fidelity universal unitaries through designed pruning of superfluous rotations. The power law and the Pareto principle for the conventional architecture of programmable photonic circuits are revealed with the presence of hub phase shifters, allowing for the application of network pruning to the design of photonic hardware. For the Clements design of programmable photonic circuits, we extract a universal architecture for pruning random unitary matrices and prove that "the bad is sometimes better to be removed" to achieve high fidelity and energy efficiency. This result lowers the hurdle for high fidelity in large-scale quantum computing and photonic deep learning accelerators.