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Physical Review A

Experimentally realizable continuous-variable quantum neural networks

Shikha Bangar, Leanto Sunny, Kübra Yeter Aydeniz, George Siopsis

Published Oct 16, 2023• 12 citations
Publisher

Abstract

The authors propose a continuous-variable quantum-classical neural network protocol that could be potentially realized in current photonic experiments. Their protocol only uses Gaussian operations, and a nonlinear operation is obtained through repeat-until-success measurements on ancillary qumodes. They applied their method to simulate quantum machine learning and computing problems.

DOI
10.1103/physreva.108.042414

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•Aug 1, 2018•338 citations
The authors propose a continuous-variable quantum-classical neural network protocol that could be potentially realized in current photonic experiments. Their protocol only uses Gaussian operations, and a nonlinear operation is obtained through repeat-until-success measurements on ancillary qumodes. They applied their method to simulate quantum machine learning and computing problems.
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-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.
The continuous-variable (CV) quantum computing has shown a 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. The previous work on CV neural network protocols requires the implementation of non-Gaussian operators in the network. These operators are used to introduce non-linearity which is an essential feature of neural networks. Due to these operators, the protocols become hard to execute experimentally. We built a CV hybrid quantum-classical neural network protocol that can be realized experimentally. Our protocol uses Gaussian gates only with the addition of ancillary qumodes. We achieve non-linearity through measurements on ancillary qumodes. Our gates can be implemented with squeezers and beam splitters; hence our protocol can be realized experimentally. We study two canonical machine learning problems in a supervised learning setting - curve fitting and binary classification to test our neural network. For the curve fitting problem, we used a fully quantum neural network which produced exceptional results as discussed in the paper. The second problem was more complicated in that we found the fraudulent transaction in the credit card data. After training, our model was able to identify genuine data with almost 92% accuracy. After studying both the problem, we can confidently conclude that our protocol gives good results with a great advantage that it can be implemented experimentally with current photonic quantum hardware.
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.
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.