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IEEE International Conference on Quantum Computing and Engineering (QCE)

Experimentally Realizable Continuous-variable Quantum Neural Networks

Shikha Bangar, George Siopsis, Kübra Yeter Aydeniz

Published Sep 1, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qce53715.2022.00116

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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 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.
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-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.
A major challenge in quantum information is characterizing entanglement, for which entanglement witnesses offer effective means of detecting quantum correlations. We introduce a hybrid quantum-classical framework that learns a nonlinear entanglement witness directly from quantum data using continuous-variable quantum neural networks (CV-QNNs). Our architecture combines variational interferometers, squeezers and non-Gaussian Kerr gates with a small classical neural head to output a scalar witness value. Numerical simulations were conducted on two- and three-mode families, including Gaussian and non-Gaussian states in both pure and mixed forms. We observed over 99% classification accuracy and a robust performance gap compared to strong classical baselines, especially when scaling from two to three modes. Robustness to photon loss is further quantified under a finite number of measurement shots. On the theory side, we show that when the quantum measurement stage is informationally complete, the hybrid model can approximate any continuous witness-like functional on compact sets of states.Our findings highlight CV-QNNs as a promising framework for data-driven quantum state characterization and propose specific benchmarks where near-term photonic platforms offer tangible advantages.