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arXiv:2002.08376 · Machine Learning Science and Technology

A differentiable programming method for quantum control

Frank Schäfer, Michal Kloc, Christoph Bruder, Niels Lörch

Published May 29, 2020• 50 citations
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Abstract

Abstract Optimal control is highly desirable in many current quantum systems, especially to realize tasks in quantum information processing. We introduce a method based on differentiable programming to leverage explicit knowledge of the differential equations governing the dynamics of the system. In particular, a control agent is represented as a neural network that maps the state of the system at a given time to a control pulse. The parameters of this agent are optimized via gradient information obtained by direct differentiation through both the neural network and the differential equation of the system. This fully differentiable reinforcement learning approach ultimately yields time-dependent control parameters optimizing a desired figure of merit. We demonstrate the method’s viability and robustness to noise in eigenstate preparation tasks for three systems: a single qubit, a chain of qubits, and a quantum parametric oscillator.

DOI
10.1088/2632-2153/ab9802

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Abstract Optimal control is highly desirable in many current quantum systems, especially to realize tasks in quantum information processing. We introduce a method based on differentiable programming to leverage explicit knowledge of the differential equations governing the dynamics of the system. In particular, a control agent is represented as a neural network that maps the state of the system at a given time to a control pulse. The parameters of this agent are optimized via gradient information obtained by direct differentiation through both the neural network and the differential equation of the system. This fully differentiable reinforcement learning approach ultimately yields time-dependent control parameters optimizing a desired figure of merit. We demonstrate the method’s viability and robustness to noise in eigenstate preparation tasks for three systems: a single qubit, a chain of qubits, and a quantum parametric oscillator.
Abstract Control of the stochastic dynamics of a quantum system is indispensable in fields such as quantum information processing and metrology. However, there is no general ready-made approach to the design of efficient control strategies. Here, we propose a framework for the automated design of control schemes based on differentiable programming. We apply this approach to the state preparation and stabilization of a qubit subjected to homodyne detection. To this end, we formulate the control task as an optimization problem where the loss function quantifies the distance from the target state, and we employ neural networks (NNs) as controllers. The system’s time evolution is governed by a stochastic differential equation (SDE). To implement efficient training, we backpropagate the gradient information from the loss function through the SDE solver using adjoint sensitivity methods. As a first example, we feed the quantum state to the controller and focus on different methods of obtaining gradients. As a second example, we directly feed the homodyne detection signal to the controller. The instantaneous value of the homodyne current contains only very limited information on the actual state of the system, masked by unavoidable photon-number fluctuations. Despite the resulting poor signal-to-noise ratio, we can train our controller to prepare and stabilize the qubit to a target state with a mean fidelity of around 85%. We also compare the solutions found by the NN to a hand-crafted control strategy.
Abstract Quantum many-body control is a central milestone en route to harnessing quantum technologies. However, the exponential growth of the Hilbert space dimension with the number of qubits makes it challenging to classically simulate quantum many-body systems and, consequently, to devise reliable and robust optimal control protocols. Here we present a framework for efficiently controlling quantum many-body systems based on reinforcement learning (RL). We tackle the quantum-control problem by leveraging matrix product states (1) for representing the many-body state and (2) as part of the trainable machine learning architecture for our RL agent. The framework is applied to prepare ground states of the quantum Ising chain, including states in the critical region. It allows us to control systems far larger than neural-network-only architectures permit, while retaining the advantages of deep learning algorithms, such as generalizability and trainable robustness to noise. In particular, we demonstrate that RL agents are capable of finding universal controls, of learning how to optimally steer previously unseen many-body states and of adapting control protocols on the fly when the quantum dynamics is subject to stochastic perturbations. Furthermore, we map our RL framework to a hybrid quantum–classical algorithm that can be performed on noisy intermediate-scale quantum devices and test it under the presence of experimentally relevant sources of noise.
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.
This paper investigates the application of reinforcement learning (RL) for adaptive quantum control. Traditional quantum control methods often rely on pre-designed pulse shapes optimized for specific scenarios, lacking adaptability to variations in system parameters or environmental noise. This work proposes a novel framework where an RL agent learns to dynamically adjust quantum control pulses in real-time, maximizing the fidelity of quantum operations. The agent receives feedback from the quantum system, typically measured through state variables, and utilizes this information to optimize the control pulse sequence. This adaptive approach addresses the limitations of static control schemes and promises enhanced robustness and performance in complex quantum systems. The core claim centers on utilizing reinforcement learning to design optimal quantum control pulses. The central mechanism involves a trained controller dynamically adjusting pulses based on system feedback. The presented methodology offers a new approach to quantum control, particularly relevant in noisy environments and systems with parameter variations. The research demonstrates the potential of RL for achieving superior quantum control outcomes compared to conventional techniques. ---
The progress in machine learning during the last decade has had a considerable impact on many areas of science and technology, including quantum technology. This work explores the application of reinforcement learning (RL) methods to the quantum control problem of state transfer in a single qubit. The goal is to create an RL agent that learns an optimal policy and thus discovers optimal pulses to control the qubit. The most crucial step is to mathematically formulate the problem of interest as a Markov decision process (MDP). This enables the use of RL algorithms to solve the quantum control problem. Deep learning and the use of deep neural networks provide the freedom to employ continuous action and state spaces, offering the expressivity and generalization of the process. This flexibility helps to formulate the quantum state transfer problem as an MDP in several different ways. All the developed methodologies are applied to the fundamental problem of population inversion in a qubit. In most cases, the derived optimal pulses achieve fidelity equal to or higher than 0.9999, as required by quantum computing applications. The present methods can be easily extended to quantum systems with more energy levels and may be used for the efficient control of collections of qubits and to counteract the effect of noise, which are important topics for quantum sensing applications.
How to implement multi-qubit gates efficiently with high precision is essential for realizing universal fault-tolerant computing. For a physical system with some external controllable parameters, it is a great challenge to control the time dependence of these parameters to achieve a target multi-qubit gate efficiently and precisely. Here we construct a dueling double deep Q-learning neural network (DDDQN) to find out the optimized time dependence of controllable parameters to implement two typical quantum gates: a single-qubit Hadamard gate and a two-qubit CNOT gate. Compared with traditional optimal control methods, this deep reinforcement learning method can realize efficient and precise gate control without requiring any gradient information during the learning process. This work attempts to pave the way to investigate more quantum control problems with deep reinforcement learning techniques.