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arXiv:2202.10291 · Physical Review Applied

Machine-Learning-Assisted Quantum Control in a Random Environment

Tangyou Huang, Yue Ban, Eugene Ya. Sherman, Xi Chen

Published Feb 14, 2022• 19 citations
arXivHTMLPDF

Abstract

Disorder in condensed matter and atomic physics is responsible for a great variety of fascinating quantum phenomena, which are still challenging for understanding, not to mention the relevant dynamical control. Here we introduce proof of the concept and analyze a neural-network-based machine-learning algorithm for achieving feasible high-fidelity quantum control of a particle in random environment. To explicitly demonstrate its capabilities, we show that convolutional neural networks are able to solve this problem as they can recognize the disorder and, by supervised learning, further produce the policy for the efficient low-energy cost control of a quantum particle in a time-dependent random potential. We show that the accuracy of the proposed algorithm is enhanced by a higher-dimensional mapping of the disorder pattern and using two neural networks, each properly trained for the given task. The designed method, being computationally more efficient than the gradient-descent optimization, can be applicable to identify and control various noisy quantum systems on a heuristic basis.

DOI
10.1103/physrevapplied.17.024040

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Disorder in condensed matter and atomic physics is responsible for a great variety of fascinating quantum phenomena, which are still challenging for understanding, not to mention the relevant dynamical control. Here we introduce proof of the concept and analyze a neural-network-based machine-learning algorithm for achieving feasible high-fidelity quantum control of a particle in random environment. To explicitly demonstrate its capabilities, we show that convolutional neural networks are able to solve this problem as they can recognize the disorder and, by supervised learning, further produce the policy for the efficient low-energy cost control of a quantum particle in a time-dependent random potential. We show that the accuracy of the proposed algorithm is enhanced by a higher-dimensional mapping of the disorder pattern and using two neural networks, each properly trained for the given task. The designed method, being computationally more efficient than the gradient-descent optimization, can be applicable to identify and control various noisy quantum systems on a heuristic basis.
High-precision quantum control is essential for quantum computing and quantum information processing. However, its practical implementation is challenged by environmental noise, which affects the stability and accuracy of quantum systems. In this paper, using machine learning techniques we propose a quantum control approach that incorporates environmental factors into the design of control schemes, improving the control fidelity in noisy environments. Specifically, we investigate arbitrary quantum state preparation in a two-level system coupled to a bosonic bath. We use both Deep Reinforcement Learning (DRL) and Supervised Learning (SL) algorithms to design specific control pulses that mitigate the noise. These two neural network (NN) based algorithm both have the advantage that the well trained NN can output the optimal pulse sequence for any environmental parameters. Comparing the performance of these two algorithms, our results show that DRL is more effective in low-noise environments due to its strong optimization capabilities, while SL provides greater stability and performs better in high-noise conditions. These findings highlight the potential of machine learning techniques to enhance the quantum control fidelity in practical applications.
Robust and high-precision quantum control is extremely important but challenging for the functionalization of scalable quantum computation. In this paper, we show that this hard problem can be translated to a supervised machine learning task by thinking of the time-ordered quantum evolution as a layer-ordered neural network (NN). The seeking of robust quantum controls is then equivalent to training a highly generalizable NN, to which numerous tuning skills matured in machine learning can be transferred. This opens up a door through which a family of robust control algorithms can be developed. We exemplify such potential by introducing the commonly used trick of batch-based optimization, and the resulting batch-based gradient algorithm is numerically shown to be able to remarkably enhance the control robustness while maintaining high fidelity.
Abstract Emerging reinforcement learning techniques using deep neural networks have shown great promise in control optimization. They harness non-local regularities of noisy control trajectories and facilitate transfer learning between tasks. To leverage these powerful capabilities for quantum control optimization, we propose a new control framework to simultaneously optimize the speed and fidelity of quantum computation against both leakage and stochastic control errors. For a broad family of two-qubit unitary gates that are important for quantum simulation of many-electron systems, we improve the control robustness by adding control noise into training environments for reinforcement learning agents trained with trusted-region-policy-optimization. The agent control solutions demonstrate a two-order-of-magnitude reduction in average-gate-error over baseline stochastic-gradient-descent solutions and up to a one-order-of-magnitude reduction in gate time from optimal gate synthesis counterparts. These significant improvements in both fidelity and runtime are achieved by combining new physical understandings and state-of-the-art machine learning techniques. Our results open a venue for wider applications in quantum simulation, quantum chemistry and quantum supremacy tests using near-term quantum devices.
Supervised machine learning is emerging as a powerful computational tool to predict the properties of complex quantum systems at a limited computational cost. In this article, we quantify how accurately deep neural networks can learn the properties of disordered quantum systems as a function of the system size. We implement a scalable convolutional network that can address arbitrary system sizes. This network is compared with a recently introduced extensive convolutional architecture [Mills et al., Chem. Sci. 10, 4129 (2019)2041-652010.1039/C8SC04578J] and with conventional dense networks with all-to-all connectivity. The networks are trained to predict the exact ground-state energies of various disordered systems, namely, a continuous-space single-particle Hamiltonian for cold-atoms in speckle disorder, and different setups of a quantum Ising chain with random couplings, including one with only short-range interactions and one augmented with a long-range term. In all testbeds we consider, the scalable network retains high accuracy as the system size increases. Furthermore, we demonstrate that the network scalability enables a transfer-learning protocol, whereby a pretraining performed on small systems drastically accelerates the learning of large-system properties, allowing reaching high accuracy with small training sets. In fact, with the scalable network one can even extrapolate to sizes larger than those included in the training set, accurately reproducing the results of state-of-the-art quantum Monte Carlo simulations.
Entanglement, which quantifies nonlocal correlations in quantum mechanics, is the fascinating concept behind much of the aspiration towards quantum technologies. Nevertheless, directly measuring the entanglement of a many-particle system is very challenging. Here, we show that via supervised machine learning using a convolutional neural network, we can infer the entanglement from a measurable observable for a disordered interacting quantum many-particle system. Several structures of neural networks were tested and a convolutional neural network akin to structures used for image and speech recognition performed the best. After training on a set of 500 realizations of disorder, the network was applied to 200 new realizations and its results for the entanglement entropy were compared to a direct computation of the entanglement entropy. Excellent agreement was found, except for several rare regions which in a previous study were identified as belonging to an inclusion of a Griffiths-like quantum phase. Training the network on a test set with different parameters (in the same phase) also works quite well.
Accurate and precise quantum control is crucial for quantum information processing. Zero-area pulse control, originally developed for closed systems, has played a significant role in driving quantum systems toward desired states. However, its effectiveness is often compromised by environmental noise. Traditional methods can find optimal pulses for fixed environmental parameters, and they need to be recalculated again once the environmental parameters change. Here, we propose a supervised learning (SL)-based protocol to design optimal zero-area pulses in noisy environments. By including environmental parameters as input during training, the neural network (NN) learns to generate effective controls for various environmental parameters. We demonstrate the protocol using quantum state transmission through a spin chain governed by a non-Markovian master equation. The SL-optimized pulses significantly enhance transmission fidelity compared to ideal pulses, with greater improvements observed at higher system-bath coupling and temperature, where more optimization space exists. Interestingly, fidelity first increases and then decreases with stronger Markovianity, suggesting that highly Markovian environments limit control performance. We also compare the SL method with a genetic algorithm, and the similar results confirm the accuracy and generalization ability of the NN-based approach.