The near-critical unitary dynamics of quantum Ising spin chains in transversal and longitudinal magnetic fields is studied using an artificial neural network representation of the wave function. A focus is set on strong spatial correlations which build up in the system following a quench into the vicinity of the quantum critical point. We compare correlations observed following reinforcement learning of the network states with analytical solutions in integrable cases and tDMRG simulations, as well as with predictions from a semi-classical discrete Truncated Wigner analysis. While the semi-classical approach excells mainly at short times and for small transverse fields, the neuralnetwork representation provides accurate results for a much wider range of parameters. Where long-range spin-spin correlations build up in the long-time dynamics we find qualitative agreement with exact results while quantitative deviations are of similar size as for the semi-classically predicted correlations, and slow convergence is observed when increasing the number of hidden neurons.

We study the performance of efficient quantum state tomography methods based on neural network quantum states using measured data from a two-photon experiment. Machine learning inspired variational methods provide a promising route towards scalable state characterization for quantum simulators. While the power of these methods has been demonstrated on synthetic data, applications to real experimental data remain scarce. We benchmark and compare several such approaches by applying them to measured data from an experiment producing two-qubit entangled states. We find that in the presence of experimental imperfections and noise, confining the variational manifold to physical states, i.e. to positive semi-definite density matrices, greatly improves the quality of the reconstructed states but renders the learning procedure more demanding. Including additional, possibly unjustified, constraints, such as assuming pure states, facilitates learning, but also biases the estimator.

The semi-classical discrete truncated Wigner approximation (dTWA) has recently been proposed as a simulation method for spin-1/2 systems. While it appears to provide a powerful approach which shows promising results in higher dimensions and for systems with long-range interactions, its performance is still not well understood in general. Here we perform a systematic benchmark on the one-dimensional transverse-field Ising model and point to limitations of the approximation arising after sudden quenches into the quantum critical regime. Our procedure allows to identify the limitations of the semi-classical simulations and with that to determine the regimes and questions where quantum simulators can provide information which is inaccessible to semi-classics.

A key challenge in scaling quantum computers is the calibration and control of multiple qubits. In solid-state quantum dots (QDs), the gate voltages required to stabilize quantized charges are unique for each individual qubit, resulting in a high-dimensional control parameter space that must be tuned automatically. Machine learning techniques are capable of processing high-dimensional data—provided that an appropriate training set is available—and have been successfully used for autotuning in the past. In this paper, we develop extremely small feed-forward neural networks that can be used to detect charge-state transitions in QD stability diagrams. We demonstrate that these neural networks can be trained on synthetic data produced by computer simulations, and robustly transferred to the task of tuning an experimental device into a desired charge state. The neural networks required for this task are sufficiently small as to enable an implementation in existing memristor crossbar arrays in the near future. This opens up the possibility of miniaturizing powerful control elements on low-power hardware, a significant step towards on-chip autotuning in future QD computers.

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