Quantum photonic circuits began growing in research interest due to the long coherence times of photonic qubits, allowing for potential long-range quantum communication. To miniaturize these photonic circuits, much research has been done into integrating these systems into a chip-architecture, commonly known as an integrated photonic circuit. Due to the collapse postulate of quantum mechanics, information encoded into photons must be extracted from measurement distributions, formally known as quantum state tomography. This thesis examines the use of neural networks in quantum state tomography, compared to the commonly used maximum likelihood estimation method in a two-qubit system, in the presence of errors typically found in integrated photonic circuits. It is shown in simulation, that by altering the training of a neural network to incorporate errors, the state reconstruction infidelity can be greatly decreased and far surpass the maximum likelihood estimation. Networks are also shown with low bit-precisions, allowing for the potential future use of ultra-fast optical processors to create the neural network. From this work, it can be concluded that neural networks are able to not only complete the task of quantum state tomography, but are able to withstand errors and create more faithful reconstructions for the outputs of integrated quantum photonic circuits.
Quantum photonic circuits began growing in research interest due to the long coherence times of photonic qubits, allowing for potential long-range quantum communication. To miniaturize these photonic circuits, much research has been done into integrating these systems into a chip-architecture, commonly known as an integrated photonic circuit. Due to the collapse postulate of quantum mechanics, information encoded into photons must be extracted from measurement distributions, formally known as quantum state tomography. This thesis examines the use of neural networks in quantum state tomography, compared to the commonly used maximum likelihood estimation method in a two-qubit system, in the presence of errors typically found in integrated photonic circuits. It is shown in simulation, that by altering the training of a neural network to incorporate errors, the state reconstruction infidelity can be greatly decreased and far surpass the maximum likelihood estimation. Networks are also shown with low bit-precisions, allowing for the potential future use of ultra-fast optical processors to create the neural network. From this work, it can be concluded that neural networks are able to not only complete the task of quantum state tomography, but are able to withstand errors and create more faithful reconstructions for the outputs of integrated quantum photonic circuits.
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
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.
The reliable characterization of quantum states is a fundamental task in quantum information science. For this purpose, quantum state tomography provides a standard framework for reconstructing quantum states from measurement data, yet it is often degraded by experimental noise. Mitigating such noise is therefore essential for the accurate estimation of the states in realistic settings. In this work, we propose a scalable tomography method based on multilayer perceptron networks that mitigate unknown noise through supervised learning. This approach is data-driven and thus does not rely on explicit assumptions about the noise model or measurement, making it readily extendable to general quantum systems. Numerical simulations, ranging from special pure states to random mixed states, demonstrate that the proposed method effectively mitigates noise across a broad range of scenarios, compared with the case without mitigation.
Multi-qubit state tomography is a key problem in quantum information technology, which has been studied extensively. In this work, we focus on multi-qubit state tomography based on neural network estimators and typical conventional estimation approaches. For multi-qubit pure states, fully connected neural networks and restricted Boltzmann machine networks are designed, respectively, to carry out state tomography of 2-qubit (low-dimensional) systems and 5-qubit (high-dimensional) systems. Comparisons are made with maximum likelihood estimation and least squares estimation, where performance indicators are selected as reconstruction accuracy, time cost and the number of parameters. Simulation results indicate that intelligent approaches have significant advantages over conventional approaches for state tomography of low-dimensional systems; for high-dimensional systems, however, the conventional approach is still dominant when the measurement is complete, while the restricted Boltzmann machine network can achieve higher reconstruction accuracy when the measurement is incomplete.
In recent years, optical computing becomes a powerful task-specific platform, under the increasing demand for computing power (especially for neural networks). This doctoral thesis is devoted to the design, simulation, and testing of integrated silicon photonic circuits for optical neural networks and machine-learning-assisted quantum computing tasks. In Chapter 3, we demonstrate an optical neural chip that implements complex-valued neural networks and benchmark its performance under practical settings, proving strong learning capabilities. In Chapter 4, we demonstrate an efficient, physics-agnostic, and closed-loop protocol for training optical neural networks on chip. In Chapter 5, we demonstrate a silicon photonic chip that achieves chip-to-chip teleportation of high-dimensional quantum states, using the trainable quantum autoencoders. High fidelities are achieved between the input qutrit and the qutrit decoded from the teleported state. Our results present a promising avenue towards realizing deep optical neural networks and challenging quantum computing tasks with dedicated integrated silicon photonic circuits.
This work proposes to carry out a study on integrated photonic circuits. Our goal is to develop a methodology for obtaining the parameters of a photonic circuit that allows us to perform a set of quantum operations necessary for the realization of a given task or quantum processing. More specifically, the quantum tasks involve the implementation of a POVM (Positive Operator Value Measure) through integrated photonic circuits. Thus, we seek to obtain optimized configurations for these devices so that the reduction of their structural complexity simplifies their manufacturing process. In addition, it is also our goal that such objects are robust against errors and losses and that the experimental applications that involve them present a minimization of the time necessary for their realization. We studied the symmetries of the proposed POVMs to, from them, configure the circuit in an optimized way. Initially, we studied the case of quantum state tomography for qubits and qutrits. We obtained planar circuits that had a smaller number of optical elements and an optical depth than those obtained by methods already known in the literature. In addition, these circuits implement all POVM elements at once, making it possible to obtain all their associated probabilities at once, minimizing the time spent on the experiment compared to experiments on an optical table or with reconfigurable circuits, where it is necessary to make changes to the configuration of the experimental apparatus from one POVM element to another. Looking for a way to generalize our protocol to larger systems, we developed a method to obtain three-dimensional photonic circuits that can be used in the experimental realization of quantum state tomography in qudits of any finite dimension. Our protocol generates circuits whose number of beam splitters and optical depth scale with functions less than in other protocols already known, showing a drastic reduction in their complexity. In addition, these circuits were highly robust in relation to the occurrence of losses. The same protocol used to obtain three-dimensional circuits for performing quantum tomography can be used to obtain circuits to implement quantum coherence measurements. The circuits obtained here also have the same advantages as the tomographic case.