Quantum computation using optical modes has been well-established in its ability to construct deep neural networks. These networks have been shown to be flexible both architecturally as well as in terms of the type of data being processed. We leverage this property of the Continuous-Variable (CV) model to construct stacked single mode networks that are shown to learn structured classical information, while placing no restrictions on the size of the network, and at the same time maintaining its complexity. The hallmark of the CV model is its ability to forge non-linear functions using a set of gates that allows it to remain completely unitary. The proposed model exemplifies that the appropriate photonic hardware can be integrated with present day optical communication systems to meet our information processing requirements. In this paper, using the Strawberry Fields software library on the MNIST dataset of hand-written digits, we demonstrate the adaptability of the network to learn classical information in a multitude of machine learning tasks to very large fidelities.
Quantum computation using optical modes has been well-established in its ability to construct deep neural networks. These networks have been shown to be flexible both architecturally as well as in terms of the type of data being processed. We leverage this property of the Continuous-Variable (CV) model to construct stacked single mode networks that are shown to learn structured classical information, while placing no restrictions on the size of the network, and at the same time maintaining its complexity. The hallmark of the CV model is its ability to forge non-linear functions using a set of gates that allows it to remain completely unitary. The proposed model exemplifies that the appropriate photonic hardware can be integrated with present day optical communication systems to meet our information processing requirements. In this paper, using the Strawberry Fields software library on the MNIST dataset of hand-written digits, we demonstrate the adaptability of the network to learn classical information in a multitude of machine learning tasks to very large fidelities.
We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous degrees of freedom such as the amplitudes of the electromagnetic field. This circuit contains a layered structure of continuously parameterized gates which is universal for CV quantum computation. Affine transformations and nonlinear activation functions, two key elements in neural networks, are enacted in the quantum network using Gaussian and non-Gaussian gates, respectively. The non-Gaussian gates provide both the nonlinearity and the universality of the model. Due to the structure of the CV model, the CV quantum neural network can encode highly nonlinear transformations while remaining completely unitary. We show how a classical network can be embedded into the quantum formalism and propose quantum versions of various specialized models such as convolutional, recurrent, and residual networks. Finally, we present numerous modeling experiments built with the strawberry fields software library. These experiments, including a classifier for fraud detection, a network which generates tetris images, and a hybrid classical-quantum autoencoder, demonstrate the capability and adaptability of CV quantum neural networks.
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.
In this paper, classical and continuous variable (CV) quantum neural network hybrid multiclassifiers are presented using the MNIST dataset. The combination of cutoff dimension and probability measurement method in the CV model allows a quantum circuit to produce output vectors of size equal to n raised to the power of n where n represents cutoff dimension and m, the number of qumodes. They are then translated as one-hot encoded labels, padded with an appropriate number of zeros. The total of eight different classifiers are built using 2,3,...,8 qumodes, based on the binary classifier architecture proposed in Continuous variable quantum neural networks. The displacement gate and the Kerr gate in the CV model allow for the bias addition and nonlinear activation components of classical neural networks to quantum. The classifiers are composed of a classical feedforward neural network, a quantum data encoding circuit, and a CV quantum neural network circuit. On a truncated MNIST dataset of 600 samples, a 4 qumode hybrid classifier achieves 100% training accuracy.
Continuous-variable (CV) quantum computing has shown great potential for building neural network models. These neural networks can have different levels of quantum-classical hybridization depending on the complexity of the problem. Previous work on CV neural network protocols required the implementation of non-Gaussian operators in the network. These operators were used to introduce non-linearity, an essential feature of neural networks. However, these protocols are hard to execute experimentally. We built a CV hybrid quantum-classical neural network protocol that can be realized experimentally with current photonic quantum hardware. Our protocol uses Gaussian gates only with the addition of ancillary qumodes. We implemented non-linearity through repeat-until-success measurements on ancillary qumodes. To test our neural network, we studied canonical machine learning and quantum computer problems in a supervised learning setting -- state preparation, curve fitting, and classification problems. We achieved high fidelity in state preparation of single-photon (99.9%), cat (99.8%), and Gottesman-Kitaev-Preskill (93.9%) states, a well-fitted curve in the presence of noise at a cost of less than 1%, and more than 95% accuracy in classification problems. These results bode well for real-world applications of CV quantum neural networks.
Continuous-variable (CV) quantum computing offers a promising framework for scalable quantum machine learning, leveraging optical systems with infinite-dimensional Hilbert spaces. While discrete-variable (DV) quantum neural networks have shown remarkable progress in various computer vision tasks, CV quantum models remain comparatively underexplored. In this work, we present a feasibility study of continuous-variable quantum neural networks (CV-QCNNs) applied to biomedical image classification. Utilizing photonic circuit simulation frameworks, we construct CV quantum circuits composed of Gaussian gates, such as displacement, squeezing, rotation, and beamsplitters to emulate convolutional behavior. Our experiments are conducted on the MedMNIST dataset collection, a set of annotated medical image benchmarks for multiple diagnostic tasks. We evaluate CV-QCNN's performance in terms of classification accuracy, model expressiveness, and resilience to Gaussian noise, comparing against classical CNNs and equivalent DV quantum circuits. This study aims to identify trade-offs between DV and CV paradigms for quantum-enhanced medical imaging. Our results highlight the potential of continuous-variable models and their viability for future computer-aided diagnosis systems.
In this paper, classical and continuous variable (CV) quantum neural network hybrid multi-classifiers are presented using the MNIST dataset. Currently available classifiers can classify only up to two classes. The proposed architecture allows networks to classify classes up to nm classes, where n represents cutoff dimension and m the number of qumodes on photonic quantum computers. The combination of cutoff dimension and probability measurement method in the CV model allows a quantum circuit to produce output vectors of size nm. They are then interpreted as one-hot encoded labels, padded with nm - 10 zeros. The total of seven different classifiers is built using 2, 3, …, 6, and 8-qumodes on photonic quantum computing simulators, based on the binary classifier architecture proposed in “Continuous variable quantum neural networks” [1]. They are composed of a classical feed-forward neural network, a quantum data encoding circuit, and a CV quantum neural network circuit. On a truncated MNIST dataset of 600 samples, a 4-qumode hybrid classifier achieves 100% training accuracy.