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Physical Review Research

Deterministic optimal quantum cloning via a quantum-optical neural network

Denis Stanev, Nicolò Spagnolo, Fabio Sciarrino

Published Feb 23, 2023• 12 citations
Publisher

Abstract

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.

DOI
10.1103/physrevresearch.5.013139

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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.
Abstract Physically motivated quantum algorithms for specific near-term quantum hardware will likely be the next frontier in quantum information science. Here, we show how many of the features of neural networks for machine learning can naturally be mapped into the quantum optical domain by introducing the quantum optical neural network (QONN). Through numerical simulation and analysis we train the QONN to perform a range of quantum information processing tasks, including newly developed protocols for quantum optical state compression, reinforcement learning, black-box quantum simulation, and one-way quantum repeaters. We consistently demonstrate that our system can generalize from only a small set of training data onto inputs for which it has not been trained. Our results indicate that QONNs are a powerful design tool for quantum optical systems and, leveraging advances in integrated quantum photonics, a promising architecture for next-generation quantum processors.
Reconfigurable photonic integrated circuits (PICs) for quantum optical information processing are now routinely made in foundries with hundreds or thousands of components. Such PICs rely on linear optics, meaning that all photon-photon interactions are probabilistic, and hence that complex protocols that, for example, produce entanglement or graph states do so at low rates. Adding optical nonlinearities to the circuits provides an activation function analogous to that of classical neural networks, enabling deterministic photon-photon protocols in ideal circuits. Here, we discuss the next step: quantum photonic neural networks made from more realistic – i.e. imperfect – components. We show that these are capable of near-deterministic entanglement generation, when imperfections such as losses, imperfect routing and sub-optimal nonlinearities are balanced against network size. These results provide a design for real quantum photonic neural networks and demonstrate that they may play important roles in emerging quantum technologies.
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.
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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.
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.