Learning in quantum control: High-dimensional global optimization for noisy quantum dynamics

Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains

Entanglement propagation provides a key routine to understand quantum many-body dynamics in and out of equilibrium. Entanglement entropy (EE) usually approaches to a subsaturation known as the Page value S[over ˜]_{P}=S[over ˜]-dS (with S[over ˜] the maximum of EE and dS the Page correction) in, e.g., the random unitary evolutions. The ballistic spreading of EE usually appears in the early time and will be deviated far before the Page value is reached. In this work, we uncover that the magnetic field that maximizes the EE robustly induces persistent ballistic spreading of entanglement in quantum spin chains. The linear growth of EE is demonstrated to persist until the maximal S[over ˜] (along with a flat entanglement spectrum) is reached. The robustness of ballistic spreading and the enhancement of EE under such an optimal control are demonstrated, considering particularly perturbing the initial state by random pure states (RPSs). These are argued as the results from the endomorphism of the time evolution under such an entanglement-enhancing optimal control for the RPSs.

Hamiltonian Identification via Quantum Ensemble Classification

Identifying the Hamiltonian of an unknown quantum system is a critical task in the area of quantum information. In this article, we propose a systematic Hamiltonian identification approach via quantum ensemble multiclass classification (HI-QEMC). This approach is implemented by a three-step iterative refining process, i.e., parameter interval guess, verification, and judgment. In the parameter interval guess step, the parameter interval is divided into several sub-intervals and the true Hamiltonian parameter is guessed in one of them. In the parameter interval verification step, cross verification is applied to verify the accuracy of the guess. In the parameter interval judgment step, an adaptive interval judgment (AIJ) algorithm is designed to determine the sub-interval containing the true Hamiltonian parameter. Numerical results on two typical quantum systems, i.e., two-level quantum systems and three-level quantum systems, demonstrate the effectiveness and superior performance of the proposed approach for quantum Hamiltonian identification.

Generation of true quantum random numbers with on-demand probability distributions via single-photon quantum walks

Random numbers are at the heart of diverse fields, ranging from simulations of stochastic processes to classical and quantum cryptography. The requirement for true randomness in these applications has motivated various proposals for generating random numbers based on the inherent randomness of quantum systems. The generation of true random numbers with arbitrarily defined probability distributions is highly desirable for applications, but it is very challenging. Here we show that single-photon quantum walks can generate multi-bit random numbers with on-demand probability distributions, when the required "coin" parameters are found with the gradient descent (GD) algorithm. Our theoretical and experimental results exhibit high fidelity for various selected distributions. This GD-enhanced single-photon system provides a convenient way for building flexible and reliable quantum random number generators. Multi-bit random numbers are a necessary resource for high-dimensional quantum key distribution.

Quantum architecture search via truly proximal policy optimization

Quantum Architecture Search (QAS) is a process of voluntarily designing quantum circuit architectures using intelligent algorithms. Recently, Kuo et al. (Quantum architecture search via deep reinforcement learning. arXiv preprint arXiv:2104.07715, 2021) proposed a deep reinforcement learning-based QAS (QAS-PPO) method, which used the Proximal Policy Optimization (PPO) algorithm to automatically generate the quantum circuit without any expert knowledge in physics. However, QAS-PPO can neither strictly limit the probability ratio between old and new policies nor enforce well-defined trust domain constraints, resulting in poor performance. In this paper, we present a new deep reinforcement learning-based QAS method, called Trust Region-based PPO with Rollback for QAS (QAS-TR-PPO-RB), to automatically build the quantum gates sequence from the density matrix only. Specifically, inspired by the research work of Wang, we employ an improved clipping function to implement the rollback behavior to limit the probability ratio between the new strategy and the old strategy. In addition, we use the triggering condition of the clipping based on the trust domain to optimize the policy by restricting the policy within the trust domain, which leads to guaranteed monotone improvement. Experiments on several multi-qubit circuits demonstrate that our presented method achieves better policy performance and lower algorithm running time than the original deep reinforcement learning-based QAS method.

Algorithmic Primitives for Quantum-Assisted Quantum Control

We present two primitive algorithms to evaluate overlaps and transition matrix time series, which are then used to construct several quantum-assisted quantum control algorithms. Unlike previous approaches, our method bypasses tomographically complete measurements and instead relies solely on single qubit measurements. We analyze circuit complexity of composed algorithms and sources of noise arising from Trotterization and measurement errors.

Learning-Based Quantum Robust Control: Algorithm, Applications, and Experiments

Robust control design for quantum systems has been recognized as a key task in quantum information technology, molecular chemistry, and atomic physics. In this paper, an improved differential evolution algorithm, referred to as multiple-samples and mixed-strategy DE (msMS_DE), is proposed to search robust fields for various quantum control problems. In msMS_DE, multiple samples are used for fitness evaluation and a mixed strategy is employed for the mutation operation. In particular, the msMS_DE algorithm is applied to the control problems of: 1) open inhomogeneous quantum ensembles and 2) the consensus goal of a quantum network with uncertainties. Numerical results are presented to demonstrate the excellent performance of the improved machine learning algorithm for these two classes of quantum robust control problems. Furthermore, msMS_DE is experimentally implemented on femtosecond (fs) laser control applications to optimize two-photon absorption and control fragmentation of the molecule CH₂BrI. The experimental results demonstrate the excellent performance of msMS_DE in searching for effective fs laser pulses for various tasks.

Uncomputability and complexity of quantum control

In laboratory and numerical experiments, physical quantities are known with a finite precision and described by rational numbers. Based on this, we deduce that quantum control problems both for open and closed systems are in general not algorithmically solvable, i.e., there is no algorithm that can decide whether dynamics of an arbitrary quantum system can be manipulated by accessible external interactions (coherent or dissipative) such that a chosen target reaches a desired value. This conclusion holds even for the relaxed requirement of the target only approximately attaining the desired value. These findings do not preclude an algorithmic solvability for a particular class of quantum control problems. Moreover, any quantum control problem can be made algorithmically solvable if the set of accessible interactions (i.e., controls) is rich enough. To arrive at these results, we develop a technique based on establishing the equivalence between quantum control problems and Diophantine equations, which are polynomial equations with integer coefficients and integer unknowns. In addition to proving uncomputability, this technique allows to construct quantum control problems belonging to different complexity classes. In particular, an example of the control problem involving a two-mode coherent field is shown to be NP-hard, contradicting a widely held believe that two-body problems are easy.

Approaching the adiabatic timescale with machine learning

The control and manipulation of quantum systems without excitation are challenging, due to the complexities in fully modeling such systems accurately and the difficulties in controlling these inherently fragile systems experimentally. For example, while protocols to decompress Bose-Einstein condensates (BECs) faster than the adiabatic timescale (without excitation or loss) have been well developed theoretically, experimental implementations of these protocols have yet to reach speeds faster than the adiabatic timescale. In this work, we experimentally demonstrate an alternative approach based on a machine-learning algorithm which makes progress toward this goal. The algorithm is given control of the coupled decompression and transport of a metastable helium condensate, with its performance determined after each experimental iteration by measuring the excitations of the resultant BEC. After each iteration the algorithm adjusts its internal model of the system to create an improved control output for the next iteration. Given sufficient control over the decompression, the algorithm converges to a solution that sets the current speed record in relation to the adiabatic timescale, beating out other experimental realizations based on theoretical approaches. This method presents a feasible approach for implementing fast-state preparations or transformations in other quantum systems, without requiring a solution to a theoretical model of the system. Implications for fundamental physics and cooling are discussed.

Remote optimization of an ultracold atoms experiment by experts and citizen scientists

The emerging field of gamified citizen science continually probes the fault line between human and artificial intelligence. A better understanding of citizen scientists’ search strategies may lead to cognitive insights and provide inspiration for algorithmic improvements. Our project remotely engages both the general public and experts in the real-time optimization of an experimental laboratory setting. In this citizen science project the game and data acquisition are designed as a social science experiment aimed at extracting the collective search behavior of the players. A further understanding of these human skills will be a crucial challenge in the coming years, as hybrid intelligence solutions are pursued in corporate and research environments.

We introduce a remote interface to control and optimize the experimental production of Bose–Einstein condensates (BECs) and find improved solutions using two distinct implementations. First, a team of theoreticians used a remote version of their dressed chopped random basis optimization algorithm (RedCRAB), and second, a gamified interface allowed 600 citizen scientists from around the world to participate in real-time optimization. Quantitative studies of player search behavior demonstrated that they collectively engage in a combination of local and global searches. This form of multiagent adaptive search prevents premature convergence by the explorative behavior of low-performing players while high-performing players locally refine their solutions. In addition, many successful citizen science games have relied on a problem representation that directly engaged the visual or experiential intuition of the players. Here we demonstrate that citizen scientists can also be successful in an entirely abstract problem visualization. This is encouraging because a much wider range of challenges could potentially be opened to gamification in the future.

Multiparameter optimisation of a magneto-optical trap using deep learning

Machine learning based on artificial neural networks has emerged as an efficient means to develop empirical models of complex systems. Cold atomic ensembles have become commonplace in laboratories around the world, however, many-body interactions give rise to complex dynamics that preclude precise analytic optimisation of the cooling and trapping process. Here, we implement a deep artificial neural network to optimise the magneto-optic cooling and trapping of neutral atomic ensembles. The solution identified by machine learning is radically different to the smoothly varying adiabatic solutions currently used. Despite this, the solutions outperform best known solutions producing higher optical densities.

Machine learning & artificial intelligence in the quantum domain: a review of recent progress

Quantum information technologies, on the one hand, and intelligent learning systems, on the other, are both emergent technologies that are likely to have a transformative impact on our society in the future. The respective underlying fields of basic research-quantum information versus machine learning (ML) and artificial intelligence (AI)-have their own specific questions and challenges, which have hitherto been investigated largely independently. However, in a growing body of recent work, researchers have been probing the question of the extent to which these fields can indeed learn and benefit from each other. Quantum ML explores the interaction between quantum computing and ML, investigating how results and techniques from one field can be used to solve the problems of the other. Recently we have witnessed significant breakthroughs in both directions of influence. For instance, quantum computing is finding a vital application in providing speed-ups for ML problems, critical in our 'big data' world. Conversely, ML already permeates many cutting-edge technologies and may become instrumental in advanced quantum technologies. Aside from quantum speed-up in data analysis, or classical ML optimization used in quantum experiments, quantum enhancements have also been (theoretically) demonstrated for interactive learning tasks, highlighting the potential of quantum-enhanced learning agents. Finally, works exploring the use of AI for the very design of quantum experiments and for performing parts of genuine research autonomously, have reported their first successes. Beyond the topics of mutual enhancement-exploring what ML/AI can do for quantum physics and vice versa-researchers have also broached the fundamental issue of quantum generalizations of learning and AI concepts. This deals with questions of the very meaning of learning and intelligence in a world that is fully described by quantum mechanics. In this review, we describe the main ideas, recent developments and progress in a broad spectrum of research investigating ML and AI in the quantum domain.

Machine Learning Topological Invariants with Neural Networks

In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with nearly 100% accuracy, even for Hamiltonians with larger winding numbers that are not included in the training data. These results show a remarkable success that the neural network can capture the global and nonlinear topological features of quantum phases from local inputs. By opening up the neural network, we confirm that the network does learn the discrete version of the winding number formula. We also make a couple of remarks regarding the role of the symmetry and the opposite effect of regularization techniques when applying machine learning to physical systems.