Integrating Neural Networks with a Quantum Simulator for State Reconstruction
Giacomo Torlai, Brian Timar, Evert van Nieuwenburg, Harry Levine, Ahmed Omran, Alexander Keesling, Hannes Bernien, Markus Greiner, Vladan Vuletić, Mikhail D. Lukin, Roger G. Melko, Manuel Endres
We demonstrate quantum many-body state reconstruction from experimental data generated by a programmable quantum simulator by means of a neural-network model incorporating known experimental errors. Specifically, we extract restricted Boltzmann machine wave functions from data produced by a Rydberg quantum simulator with eight and nine atoms in a single measurement basis and apply a novel regularization technique to mitigate the effects of measurement errors in the training data. Reconstructions of modest complexity are able to capture one- and two-body observables not accessible to experimentalists, as well as more sophisticated observables such as the Rényi mutual information. Our results open the door to integration of machine learning architectures with intermediate-scale quantum hardware.
We demonstrate quantum many-body state reconstruction from experimental data generated by a programmable quantum simulator by means of a neural-network model incorporating known experimental errors. Specifically, we extract restricted Boltzmann machine wave functions from data produced by a Rydberg quantum simulator with eight and nine atoms in a single measurement basis and apply a novel regularization technique to mitigate the effects of measurement errors in the training data. Reconstructions of modest complexity are able to capture one- and two-body observables not accessible to experimentalists, as well as more sophisticated observables such as the Rényi mutual information. Our results open the door to integration of machine learning architectures with intermediate-scale quantum hardware.
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.
Configurable arrays of optically trapped Rydberg atoms are a versatile platform for quantum computation and quantum simulation, also allowing controllable decoherence. We demonstrate theoretically that they also enable proof-of-principle demonstrations for a technique to build models for open quantum dynamics using machine learning with artificial neural networks, recently proposed by Mukherjee et al. [Quantum Sci. Technol. 10, 02LT01 (2025)]. Using the outcome of quantum transport through a network of sites that correspond to excited Rydberg atoms, the multistage neural-network algorithm successfully identifies the number of atoms (or nodes in the network) and, subsequently, their location. It further extracts an effective interaction Hamiltonian and decoherence operators induced by the environment. To probe the Rydberg array, one initiates dynamics repeatedly from the same initial state and then measures the transport probability to an output atom. Large datasets are generated by varying the position of the latter. Measurements are required in only one single basis, making the approach complementary to, e.g., quantum process tomography. Due to steeply increasing requirements for training data size, the present implementation appears best suited for networks of just a few sites. The cold-atom platform discussed in this article can be used to explore the performance of the proposed protocol when training the neural network with simulation data but then applying it to construct models based on experimental data.
A prerequisite to the successful development of quantum computers and simulators is precise understanding of the physical processes occurring therein, which can be achieved by measuring the quantum states that they produce.However, the resources required for traditional quantum state estimation scale exponentially with the system size, highlighting the need for alternative approaches.Here, we demonstrate an efficient method for reconstruction of significantly entangled multiqubit quantum states.Using a variational version of the matrix-product-state ansatz, we perform the tomography (in the pure-state approximation) of quantum states produced in a 20-qubit trapped-ion Ising-type quantum simulator, using the data acquired in only 27 bases, with 1000 measurements in each basis.We observe superior statereconstruction quality and faster convergence compared to the methods based on neural-network quantum state representations: restricted Boltzmann machines and feed-forward neural networks with autoregressive architecture.Our results pave the way toward efficient experimental characterization of complex states produced by the quench dynamics of many-body quantum systems.
Abstract Despite the complexity of quantum systems in the real world, models with just a few effective many-body states often suffice to describe their quantum dynamics, provided decoherence is accounted for. We show that a machine learning algorithm is able to construct such models, given a straightforward set of quantum dynamics measurements. The effective Hilbert space can be a black box, with variations of the coupling to just one accessible output state being sufficient to generate the required training data. We demonstrate through simulations of a Markovian open quantum system that a neural network can automatically detect the number N of effective states and the most relevant Hamiltonian terms and state-dephasing processes and rates. For systems with N ⩽ 5 we find typical mean relative errors of predictions in the 10 % range. With more advanced networks and larger training sets, it is conceivable that a future single software can provide the automated first stop solution to model building for an unknown device or system, complementing and validating the conventional approach based on physical insight into the system.
As the field of quantum technology continues to evolve, accurate quantum state preparation is becoming increasingly important for various applications in materials, matter, and devices. Computational methods allow the reconstruction of quantum states from experimental data, but the increasing complexity of quantum systems demands continuous algorithmic innovations. In this paper, we introduce QuCumber, an open-source software package designed to reconstruct quantum states using machine learning techniques. QuCumber leverages restricted Boltzmann machines (RBMs) to represent quantum wavefunctions based on projective measurements. By utilizing RBMs, QuCumber efficiently generates new measurements that facilitate the calculation of physical observables, some of which may not be directly accessible through experimental data alone. This paper demonstrates QuCumber’s capability to handle both real and complex wavefunctions, providing valuable tools for advancing quantum state analysis in line with the growing scale of quantum systems.
Abstract Quantum tomography is currently ubiquitous for testing any implementation of a quantum information processing device. Various sophisticated procedures for state and process reconstruction from measured data are well developed and benefit from precise knowledge of the model describing state-preparation-and-measurement (SPAM) apparatus. However, physical models suffer from intrinsic limitations as actual measurement operators and trial states cannot be known precisely. This scenario inevitably leads to SPAM errors degrading reconstruction performance. Here we develop a framework based on machine learning which generally applies to both the tomography and SPAM mitigation problem. We experimentally implement our method. We trained a supervised neural network to filter the experimental data and hence uncovered salient patterns that characterize the measurement probabilities for the original state and the ideal experimental apparatus free from SPAM errors. We compared the neural network state reconstruction protocol with a protocol treating SPAM errors by process tomography, as well as to an SPAM-agnostic protocol with idealized measurements. The average reconstruction fidelity is shown to be enhanced by 10% and 27%, respectively. The presented methods apply to the vast range of quantum experiments which rely on tomography.