Quantum state tomography (QST) is a crucial ingredient for almost all aspects of experimental quantum information processing. As an analog of the “imaging” technique in quantum settings, QST is born to be a data science problem, where machine learning techniques, noticeably neural networks, have been applied extensively. We build and demonstrate an optical neural network (ONN) for photonic polarization qubit QST. The ONN is equipped with built-in optical nonlinear activation functions based on electromagnetically induced transparency. The experimental results show that our ONN can determine the phase parameter of the qubit state accurately. As optics are highly desired for quantum interconnections, our ONN-QST may contribute to the realization of optical quantum networks and inspire the ideas combining artificial optical intelligence with quantum information studies.
Quantum state tomography (QST) is a crucial ingredient for almost all aspects of experimental quantum information processing. As an analog of the “imaging” technique in quantum settings, QST is born to be a data science problem, where machine learning techniques, noticeably neural networks, have been applied extensively. We build and demonstrate an optical neural network (ONN) for photonic polarization qubit QST. The ONN is equipped with built-in optical nonlinear activation functions based on electromagnetically induced transparency. The experimental results show that our ONN can determine the phase parameter of the qubit state accurately. As optics are highly desired for quantum interconnections, our ONN-QST may contribute to the realization of optical quantum networks and inspire the ideas combining artificial optical intelligence with quantum information studies.
Quantum state tomography (QST) is a crucial ingredient for almost all aspects of experimental quantum information processing. As an analog of the "imaging" technique in the quantum settings, QST is born to be a data science problem, where machine learning techniques, noticeably neural networks, have been applied extensively. In this work, we build an integrated all-optical setup for neural network QST, based on an all-optical neural network (AONN). Our AONN is equipped with built-in nonlinear activation function, which is based on electromagnetically induced transparency. Experiment results demonstrate the validity and efficiency of the all-optical setup, indicating that AONN can mitigate the state-preparation-and-measurement error and predict the phase parameter in the quantum state accurately. Given that optical setups are highly desired for future quantum networks, our all-optical setup of integrated AONN-QST may shed light on replenishing the all-optical quantum network with the last brick.
Quantum state tomography (QST) can be posed as an optimization problem, where the goal is to find the quantum state ρ that makes the observed data more likely. Obtaining the complete description of a quantum state is crucial for many quantum informational and computing tasks, and various approaches have been proposed to solve this fundamental problem. This thesis aims at presenting two models based on feedforward neural network architecture for QST. The first model is based on a multi-layer perceptron network, while the second one is based on autoregressive neural networks. We show that the perceptron model demonstrates less overfit compared to the standard iterative maximum likelihood model, however, the number of parameters in the network increases exponentially with respect to the system size. In contrast to the perceptron model, we show that the autoregressive model scales efficiently since the number of parameters grows polynomially instead of exponentially, making it suitable for QST of many-qubit systems. For the perceptron model, we presented a reconstruction of an engineered 4-qubit W state and an arbitrary optical superposition of up to 2 photons. On the other hand, using the autoregressive model, we performed QST of a 20-qubit engineered quantum state of trapped ions observed in an experiment. To the best of our knowledge, our results are the first of its kind in performing QST of complex and highly entangled out-of-equilibrium states produced by dynamics of an Ising-type Hamiltonian, engineered via laser fields on 1D trapped ion systems
Quantum state tomography (QST) is a fundamental technique in quantum information science, used to characterize the density matrix of an unknown quantum state. However, traditional QST methods are often computationally intensive, requiring a large number of measurements and sophisticated data analysis techniques. This paper proposes a novel approach utilizing self-organizing neural networks (SONNs) for direct quantum state reconstruction. The core idea is to train a SONN to learn the mapping between experimental measurement data and the corresponding density matrix, thereby bypassing the need for precise control over the quantum system and significantly reducing the computational burden. We detail the architecture of the SONN, the training process, and demonstrate the potential of this method to achieve accurate state reconstruction with fewer measurements. The proposed method offers a promising path towards more efficient and scalable QST, particularly for complex quantum systems.
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.
We apply deep-neural-network-based techniques to quantum state classification and reconstruction. Our methods demonstrate high classification accuracies and reconstruction fidelities, even in the presence of noise and with little data. Using optical quantum states as examples, we first demonstrate how convolutional neural networks (CNNs) can successfully classify several types of states distorted by, e.g., additive Gaussian noise or photon loss. We further show that a CNN trained on noisy inputs can learn to identify the most important regions in the data, which potentially can reduce the cost of tomography by guiding adaptive data collection. Secondly, we demonstrate reconstruction of quantum-state density matrices using neural networks that incorporate quantum-physics knowledge. The knowledge is implemented as custom neural-network layers that convert outputs from standard feed-forward neural networks to valid descriptions of quantum states. Any standard feed-forward neural-network architecture can be adapted for quantum state tomography (QST) with our method. We present further demonstrations of our proposed QST technique with conditional generative adversarial networks (QST-CGAN) [Ahmed et al., Phys. Rev. Lett. 127, 140502 (2021)]. We motivate our choice of a learnable loss function within an adversarial framework by demonstrating that the QST-CGAN outperforms, across a range of scenarios, generative networks trained with standard loss functions. For pure states with additive or convolutional Gaussian noise, the QST-CGAN is able to adapt to the noise and reconstruct the underlying state. The QST-CGAN reconstructs states using up to two orders of magnitude fewer iterative steps than iterative and accelerated projected-gradient-based maximum-likelihood estimation (MLE) methods. We also demonstrate that the QST-CGAN can reconstruct both pure and mixed states from two orders of magnitude fewer randomly chosen data points than these MLE methods. Our paper opens possibilities to use state-of-the-art deep-learning methods for quantum state classification and reconstruction under various types of noise.
Large machine learning models based on Convolutional Neural Networks (CNNs) with rapidly increasing numbers of parameters are being deployed in a wide array of computer vision tasks. However, the insatiable demand for computing resources required to train these models is fast outpacing the advancement of classical computing hardware, and new frameworks including Optical Neural Networks (ONNs) and quantum computing are being explored as future alternatives. In this work, we report a novel quantum computing based deep learning model, the Quantum Optical Convolutional Neural Network (QOCNN), to alleviate the computational bottleneck in future computer vision applications. Using the MNIST dataset, we have benchmarked this new architecture against a traditional CNN model based on the seminal LeNet architecture. We have also compared the performance against previously reported ONNs, the GridNet and ComplexNet, and a Quantum Optical Neural Network (QONN) that we built by combining the ComplexNet with quantum-inspired sinusoidal nonlinearities. Our work extends the prior research on QONN by adding quantum convolution and pooling layers. We have evaluated the models using the metrics of accuracies, confusion matrices, Receiver Operating Characteristic curves, and Matthews Correlation Coefficients. The performance of the models were similar, and the metrics indicated that the new QOCNN model is robust. Finally, we estimated the gains in computational efficiencies from executing this novel framework on a quantum computer, concluding that switching to a quantum computing based approach to deep learning may result in comparable accuracies to classical models while simultaneously achieving unprecedented boosts in computational performances and power allocation.