The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous variable quantum systems. In this Letter, we develop a machine learning algorithm for comparing unknown continuous variable states using limited and noisy data. The algorithm works on non-Gaussian quantum states for which similarity testing could not be achieved with previous techniques. Our approach is based on a convolutional neural network that assesses the similarity of quantum states based on a lower-dimensional state representation built from measurement data. The network can be trained off-line with classically simulated data from a fiducial set of states sharing structural similarities with the states to be tested, with experimental data generated by measurements on the fiducial states, or with a combination of simulated and experimental data. We test the performance of the model on noisy cat states and states generated by arbitrary selective number-dependent phase gates. Our network can also be applied to the problem of comparing continuous variable states across different experimental platforms, with different sets of achievable measurements, and to the problem of experimentally testing whether two states are equivalent up to Gaussian unitary transformations.
The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous variable quantum systems. In this Letter, we develop a machine learning algorithm for comparing unknown continuous variable states using limited and noisy data. The algorithm works on non-Gaussian quantum states for which similarity testing could not be achieved with previous techniques. Our approach is based on a convolutional neural network that assesses the similarity of quantum states based on a lower-dimensional state representation built from measurement data. The network can be trained off-line with classically simulated data from a fiducial set of states sharing structural similarities with the states to be tested, with experimental data generated by measurements on the fiducial states, or with a combination of simulated and experimental data. We test the performance of the model on noisy cat states and states generated by arbitrary selective number-dependent phase gates. Our network can also be applied to the problem of comparing continuous variable states across different experimental platforms, with different sets of achievable measurements, and to the problem of experimentally testing whether two states are equivalent up to Gaussian unitary transformations.
Deep neural networks are a powerful tool for characterizing quantum states. Existing networks are typically trained with experimental data gathered from the quantum state that needs to be characterized. But is it possible to train a neural network offline, on a different set of states? Here we introduce a network that can be trained with classically simulated data from a fiducial set of states and measurements, and can later be used to characterize quantum states that share structural similarities with the fiducial states. With little guidance of quantum physics, the network builds its own data-driven representation of a quantum state, and then uses it to predict the outcome statistics of quantum measurements that have not been performed yet. The state representations produced by the network can also be used for tasks beyond the prediction of outcome statistics, including clustering of quantum states and identification of different phases of matter.
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.
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.
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.
Abstract Quantum machine learning is one of the most promising applications of quantum computing in the noisy intermediate-scale quantum (NISQ) era. We propose a quantum convolutional neural network(QCNN) inspired by convolutional neural networks (CNN), which greatly reduces the computing complexity compared with its classical counterparts, with O (( log 2 M ) 6 ) basic gates and O ( m 2 + e ) variational parameters, where M is the input data size, m is the filter mask size, and e is the number of parameters in a Hamiltonian. Our model is robust to certain noise for image recognition tasks and the parameters are independent on the input sizes, making it friendly to near-term quantum devices. We demonstrate QCNN with two explicit examples. First, QCNN is applied to image processing, and numerical simulation of three types of spatial filtering, image smoothing, sharpening, and edge detection is performed. Secondly, we demonstrate QCNN in recognizing image, namely, the recognition of handwritten numbers. Compared with previous work, this machine learning model can provide implementable quantum circuits that accurately corresponds to a specific classical convolutional kernel. It provides an efficient avenue to transform CNN to QCNN directly and opens up the prospect of exploiting quantum power to process information in the era of big data.
Quantum computing (QC) has opened the door to advancements in machine learning (ML) tasks that are currently implemented in the classical domain. Convolutional neural networks (CNNs) are classical ML architectures that exploit data locality and possess a simpler structure than a fully connected multi-layer perceptrons (MLPs) without compromising the accuracy of classification. However, the concept of preserving data locality is usually overlooked in the existing quantum counterparts of CNNs, particularly for extracting multifeatures in multidimensional data. In this paper, we present an multidimensional quantum convolutional classifier (MQCC) that performs multidimensional and multifeature quantum convolution with average and Euclidean pooling, thus adapting the CNN structure to a variational quantum algorithm (VQA). The experimental work was conducted using multidimensional data to validate the correctness and demonstrate the scalability of the proposed method utilizing both noisy and noise-free quantum simulations. We evaluated the MQCC model with reference to reported work on state-of-the-art quantum simulators from IBM Quantum and Xanadu using a variety of standard ML datasets. The experimental results show the favorable characteristics of our proposed techniques compared with existing work with respect to a number of quantitative metrics, such as the number of training parameters, cross-entropy loss, classification accuracy, circuit depth, and quantum gate count.