In recent years, quantum simulators have been the focus of intense research due to their potential in unraveling the inner workings of complex quantum systems. The exponential scaling of the Hilbert space of quantum systems limits the capabilities of classical approaches. Quantum simulators, on the other hand, are suited to efficiently emulate these quantum systems for in-depth research. Out of the various platforms for quantum simulators, trapped-ions have been prized for their long coherence times, exceptional initialization and detection fidelities and their innate full-connectivity. In the development of the trapped-ion apparatus as a quantum simulator, numerous optimization problems emerge. In this thesis, we examine, develop and refine the strategies available to us for addressing such problems. A class of techniques of particular interest to us is the set of machine learning algorithms. This can be attributed to their capabilities at identifying correlations in massive data sets. \nSpecifically, we describe how artificial neural networks can be employed to assist in the programming of the trapped-ion system as an arbitrary spin model quantum simulator. In addition, we present an augmentation to the trapped-ion architecture, utilizing optical tweezers, that enables the programmable manipulation of phonon modes. We describe the protocols developed to effectively program the phonon modes and propose an application of the scheme for enhancing the performance of multi-species systems. Finally, we explore the use of machine learning algorithms to perform state readout of the trapped-ion system. The work in this thesis extends the utility of the trapped-ion system for performing quantum information processing experiments.
In recent years, quantum simulators have been the focus of intense research due to their potential in unraveling the inner workings of complex quantum systems. The exponential scaling of the Hilbert space of quantum systems limits the capabilities of classical approaches. Quantum simulators, on the other hand, are suited to efficiently emulate these quantum systems for in-depth research. Out of the various platforms for quantum simulators, trapped-ions have been prized for their long coherence times, exceptional initialization and detection fidelities and their innate full-connectivity. In the development of the trapped-ion apparatus as a quantum simulator, numerous optimization problems emerge. In this thesis, we examine, develop and refine the strategies available to us for addressing such problems. A class of techniques of particular interest to us is the set of machine learning algorithms. This can be attributed to their capabilities at identifying correlations in massive data sets. \nSpecifically, we describe how artificial neural networks can be employed to assist in the programming of the trapped-ion system as an arbitrary spin model quantum simulator. In addition, we present an augmentation to the trapped-ion architecture, utilizing optical tweezers, that enables the programmable manipulation of phonon modes. We describe the protocols developed to effectively program the phonon modes and propose an application of the scheme for enhancing the performance of multi-species systems. Finally, we explore the use of machine learning algorithms to perform state readout of the trapped-ion system. The work in this thesis extends the utility of the trapped-ion system for performing quantum information processing experiments.
Abstract Trapped ions have emerged as one of the highest quality platforms for the quantum simulation of interacting spin models of interest to various fields of physics. In such simulators, two effective spins can be made to interact with arbitrary strengths by coupling to the collective vibrational or phonon states of ions, controlled by precisely tuned laser beams. However, the task of determining laser control parameters required for a given spin–spin interaction graph is a type of inverse problem , which can be highly mathematically complex. In this paper, we adapt a modern machine learning technique developed for similar inverse problems to the task of finding the laser control parameters for a number of interaction graphs. We demonstrate that typical graphs, forming regular lattices of interest to physicists, can easily be produced for up to 50 ions using a single GPU workstation. The scaling of the machine learning method suggests that this can be expanded to hundreds of ions with moderate additional computational effort.
Trapped ions offer long coherence times and high-fidelity, programmable quantum operations, making them a promising platform for quantum simulation of condensed matter systems, quantum dynamics, and problems related to high-energy physics. We review selected developments in trapped-ion qubits and architectures and discuss quantum simulation applications that utilize these emerging capabilities. This review emphasizes developments in digital (gate-based) quantum simulations that exploit trapped-ion hardware capabilities, such as flexible qubit connectivity, selective midcircuit measurement, and classical feedback, to simulate models with long-range interactions, explore nonunitary dynamics, compress simulations of states with limited entanglement, and reduce the circuit depths required to prepare or simulate long-range entangled states.
Trapped ions offer long coherence times and high fidelity, programmable quantum operations, making them a promising platform for quantum simulation of condensed matter systems, quantum dynamics, and problems related to high-energy physics. We review selected developments in trapped-ion qubits and architectures and discuss quantum simulation applications that utilize these emerging capabilities. This review emphasizes developments in digital (gate-based) quantum simulations that exploit trapped-ion hardware capabilities, such as flexible qubit connectivity, selective mid-circuit measurement, and classical feedback, to simulate models with long-range interactions, explore non-unitary dynamics, compress simulations of states with limited entanglement, and reduce the circuit depths required to prepare or simulate long-range entangled states.
The simulation of quantum matter with classical hardware plays a central role in the discovery and development of quantum many-body systems, with far-reaching implications in condensed matter physics and quantum technologies. In general, efficient and sophisticated algorithms are required to overcome the severe challenge posed by the exponential scaling of the Hilbert space of quantum systems. In contrast, hardware built with quantum bits of information are inherently capable of efficiently finding solutions of quantum many-body problems. While a universal and scalable quantum computer is still beyond the horizon, recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediate scale quantum hardware. \n \nThe complexity underlying quantum many-body systems closely resembles the one encountered in many problems in the world of information and technology. In both contexts, the complexity stems from a large number of interacting degrees of freedom. A powerful strategy in the latter scenario is machine learning, a subfield of artificial intelligence where large amounts of data are used to extract relevant features and patterns. In particular, artificial neural networks have been demonstrated to be capable of discovering low-dimensional representations of complex objects from high-dimensional dataset, leading to the profound technological revolution we all witness in our daily life. \n \nIn this Thesis, we envision a new paradigm for scientific discovery in quantum physics. On the one hand, we have the essentially unlimited data generated with the increasing amount of highly controllable quantum hardware. On the other hand, we have a set of powerful algorithms that efficiently capture non-trivial correlations from high-dimensional data. Therefore, we fully embrace this data-driven approach to quantum mechanics, and anticipate new exciting possibilities in the field of quantum many-body physics and quantum information science. We revive a powerful stochastic neural network called a restricted Boltzmann machine, which slowly moved out of fashion after playing a central role in the machine learning revolution of the early 2010s. We introduce a neural-network representation of quantum states based on this generative model. We propose a set of algorithms to reconstruct unknown quantum states from measurement data and numerically demonstrate their potential, with important implications for current experiments. These include the reconstruction of experimentally inaccessible properties, such as entanglement, and diagnostics to determine sources of noise. Furthermore, we introduce a machine learning framework for quantum error correction, where a neural network learns the best decoding strategy directly from data. We expect that the full integration between quantum hardware and artificial intelligence will become the gold standard, and will drive the world into the era of fault-tolerant quantum computing and large-scale quantum simulations.
Abstract We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms.
Developments in Artificial Intelligence (AI) are helping to solve complex physical problems that otherwise may be too computationally demanding to solve using traditional approaches. Universal Approximation Theorems tell us that we can model any physical system if we can approximate the system with some continuous function (i.e., compact convergence topology and algorithmically generated sets of functions, such as the convolutional neural network), whether for an arbitrary depth or arbitrary width neural network. We consider the problem of solving a set ofNcoupled algebraic equations asNbecomes very large and apply machine learning (ML) to solve this problem for any value ofN. The physical problem we are focusing on is to model the equilibrium positions of ions in an ion trap. A storage ring quantum computer could contain well over tens of thousands of ions. Quickly determining the equilibrium positions will be important to minimize the time to target and observe each ion. As each ion serves as a single qubit, this is important for setting and measuring the individual qubit states. The phonon modes from a collection of ions acts as another qubit, useful for gate operations. Measuring the phonon modes, where ions are oscillating around their respective equilibrium positions also means understanding the equilibrium positions very well. Turning all of this into a virtual diagnostic allows real time prediction and comparison to ensure unique definition of each ion.