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Geometrical versus time-series representation of data in learning quantum control

Mateusz Ostaszewski, Jarosław Adam Miszczak, Przemysław Sadowski

Published Mar 14, 2018• 0 citations
OpenAlex

Abstract

We study the application of machine learning methods based on a geometrical and time-series character of data in the application to quantum control. We demonstrate that recurrent neural networks posses the ability to generalize the correction pulses with respect to the level of noise present in the system. We also show that the utilisation of the geometrical structure of control pulses is sufficient for achieving high-fidelity in quantum control using machine learning procedures.

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We study the application of machine learning methods based on a geometrical and time-series character of data in the application to quantum control. We demonstrate that recurrent neural networks posses the ability to generalize the correction pulses with respect to the level of noise present in the system. We also show that the utilisation of the geometrical structure of control pulses is sufficient for achieving high-fidelity in quantum control using machine learning procedures.
Abstract Recently, machine learning techniques have become popular for analysing physical systems and solving problems occurring in quantum computing. In this paper we focus on using such techniques for finding the sequence of physical operations implementing the given quantum logical operation. In this context we analyse the flexibility of the data representation and compare the applicability of two machine learning approaches based on different representations of data. We demonstrate that the utilization of the geometrical structure of control pulses is sufficient for achieving high-fidelity of the implemented evolution. We also demonstrate that artificial neural networks, unlike geometrical methods, possess generalization abilities enabling them to generate control pulses for the systems with variable strength of the disturbance. The presented results suggest that in some quantum control scenarios, geometrical data representation and processing is competitive to more complex methods.
Quantum computing requires the optimization of control pulses to achieve high-fidelity quantum gates. We propose a machine learning-based protocol to address the challenges of evaluating gradients and modeling complex system dynamics. By training a recurrent neural network (RNN) to predict qubit behavior, our approach enables efficient gradient-based pulse optimization without the need for a detailed system model. First, we sample qubit dynamics using random control pulses with weak prior assumptions. We then train the RNN on the system's observed responses, and use the trained model to optimize high-fidelity control pulses. We demonstrate the effectiveness of this approach through simulations on a single ST0ST_0ST0​ qubit.
In this paper, machine learning and artificial neural network models are proposed for quantum noise classification in stochastic quantum dynamics. For this purpose, we train and then validate support vector machine, multi-layer perceptron and recurrent neural network, models with different complexity and accuracy, to solve supervised binary classification problems. By exploiting the quantum random walk formalism, we demonstrate the high efficacy of such tools in classifying noisy quantum dynamics using data sets collected in a single realisation of the quantum system evolution. In addition, we also show that for a successful classification one just needs to measure, in a sequence of discrete time instants, the probabilities that the analysed quantum system is in one of the allowed positions or energy configurations, without any external driving. Thus, neither measurements of quantum coherences nor sequences of control pulses are required. Since in principle the training of the machine learning models can be performed a-priori on synthetic data, our approach is expected to find direct application in a vast number of experimental schemes and also for the noise benchmarking of the already available noisy intermediate-scale quantum devices.
Recurrent neural networks play an important role in both research and industry. With the advent of quantum machine learning, the quantisation of recurrent neural networks has become recently relevant. We propose fully quantum recurrent neural networks, based on dissipative quantum neural networks, capable of learning general causal quantum automata. A quantum training algorithm is proposed and classical simulations for the case of product outputs with the fidelity as cost function are carried out. We thereby demonstrate the potential of these algorithms to learn complex quantum processes with memory in terms of the exemplary delay channel, the time evolution of quantum states governed by a time-dependent Hamiltonian, and high- and low-frequency noise mitigation. Numerical simulations indicate that our quantum recurrent neural networks exhibit a striking ability to generalise from small training sets.
Quantum control plays an irreplaceable role in practical use of quantum computers. However, some challenges have to be overcome to find more suitable and diverse control parameters. We propose a promising and generalizable average-fidelity-based machine-learning-inspired method to optimize the control parameters, in which a neural network with periodic feature enhancement is used as an ansatz. In the implementation of a single-qubit gate by cat-state nonadiabatic geometric quantum computation via reverse engineering, compared with the control parameters in the simple form of a trigonometric function, our approach can yield significantly higher-fidelity (>99.99(>99.99%)(>99.99 phase gates, such as the $\ensuremath{\pi}/8$ gate (t gate). Single-qubit gates are robust against systematic noise, additive white Gaussian noise, and decoherence. We numerically demonstrate that the neural network possesses the ability to expand the model space. With the help of our optimization, we provide a feasible way to implement cascaded multiqubit gates with high quality in a bosonic system. Therefore, the machine-learning-inspired method may be feasible in quantum optimal control of nonadiabatic geometric quantum computation.
In this work the application of machine learning methods for quantum control of trapped ion quantum computers is studied. This is done in the framework of a single quantum gate, the geometric phase gate. The fundamentals of trapping ions as well as machine learning are presented. The Hamiltoninan operator is derived for a system of two ions in a linear Paul trap. After presenting the consepts of open quantum systems and quantum computing in general, a master equation for two ions in a noisy environment that are driven by a laser is presented. The solution to the master equation is used to generate datasets that corresond to the application of a geometric phase gate. The datasets are then used to train a variety of machine learning models that emulate the mapping from the shape of the control laser all the way to the resulting fidelity of the gate operation. The output of the models is then optimised to acquire the optimal control parameters describing the laser pulse.