Time-varying noises are one of the reasons that make it difficult for quantum systems to complete control tasks. How to quantify the influence of time-varying noises on control results and how to design a control law that can resist time-varying noises are two important problems. In this paper, the adversarial learning is introduced into quantum control and the loss function under the worst-case noise is used as a way to quantify the impact of time-varying noises on control performance. We utilize the Gradient Ascent Pulse Engineering (GRAPE) technique to search the worst-case noise and meanwhile offer a strategy to improve the robustness of the control law. Simulation experiments on a two-qubit system and a four-qubit system show that the found noises indeed can act as worst-case noises. Furthermore, the optimized control laws demonstrate good robustness to time-varying noises in state preparation tasks.
Time-varying noises are one of the reasons that make it difficult for quantum systems to complete control tasks. How to quantify the influence of time-varying noises on control results and how to design a control law that can resist time-varying noises are two important problems. In this paper, the adversarial learning is introduced into quantum control and the loss function under the worst-case noise is used as a way to quantify the impact of time-varying noises on control performance. We utilize the Gradient Ascent Pulse Engineering (GRAPE) technique to search the worst-case noise and meanwhile offer a strategy to improve the robustness of the control law. Simulation experiments on a two-qubit system and a four-qubit system show that the found noises indeed can act as worst-case noises. Furthermore, the optimized control laws demonstrate good robustness to time-varying noises in state preparation tasks.
Efficient approaches to quantum control and feedback are essential for quantum technologies, from sensing to quantum computation.Open-loop control tasks have been successfully solved using optimization techniques, including methods such as gradient-ascent pulse engineering (GRAPE) , relying on a differentiable model of the quantum dynamics.For feedback tasks, such methods are not directly applicable, since the aim is to discover strategies conditioned on measurement outcomes.In this work, we introduce feedback GRAPE, which borrows some concepts from model-free reinforcement learning to incorporate the response to strong stochastic (discrete or continuous) measurements, while still performing direct gradient ascent through the quantum dynamics.We illustrate its power considering various scenarios based on cavity-QED setups.Our method yields interpretable feedback strategies for state preparation and stabilization in the presence of noise.Our approach could be employed for discovering strategies in a wide range of feedback tasks, from calibration of multiqubit devices to linear-optics quantum computation strategies, quantum enhanced sensing with adaptive measurements, and quantum error correction.
Resisting diverse noise effects is crucial for the accurate manipulation of quantum systems. For static or slowly varying noises, many efficient noise mitigation strategies have been developed, such as composite pulses and dynamical decoupling. However, for fast fluctuating noise in the Markovian limit, whether and to what extent coherent quantum control can enhance quantum engineering tasks remains unclear and less explored. Here, we propose a robust quantum optimal control method to tackle Markovian noises. The basic idea is that, regarding the Markovian noise channel as perturbation, we quantitatively characterize the noise-induced error evolution by the perturbative expansion term, and then take them as the objective functions to be suppressed. During optimization, the optimal controls are obtained by maximizing the control target function and meanwhile minimizing the perturbative terms due to Markovian noise order by order. As demonstration examples, we first apply our method to quantum state transfer tasks on two-level and three-level $\mathrm{\ensuremath{\Lambda}}$ systems, then use it to design quantum gates in two-level and three-level ladder systems, all under Markovian noises. The simulation results illustrate that our method can notably enhance quantum state transfer fidelities and have very limited improvement on gate fidelities. The method presented here is versatile and can be extended to enhance the performance of various control tasks under Markovian noise in multilevel or multiqubit quantum systems.
High-precision operation of quantum computing systems must be robust to uncertainties and noises in the quantum hardware. We show that through a game played between the uncertainties (or noises) and the controls, adversarial uncertainty samples can be generated to find highly robust controls through the search for Nash equilibria. We propose a broad family of adversarial learning algorithms, namely a-GRAPE algorithms, which includes two effective learning schemes referred to as the best-response approach and the better-response approach within game-theoretic terminology, providing options for learning highly robust controls. Numerical experiments demonstrate that the balance between fidelity and robustness depends on the details of the chosen adversarial learning algorithm, which can effectively lead to a significant enhancement of control robustness while attaining high fidelity.
This research presents an ensemble Reinforcement Learning (RL) approach that combines Deep Q-Network (DQN) and Proximal Policy Optimization (PPO) algorithms to tackle quantum control problems. This research aims to use the complementary strengths of DQN and PPO algorithms to develop robust and adaptive control policies for noisy and uncertain quantum systems. We comprehensively analyse the proposed ensemble learning, including algorithmic details, implementation specifics, and experimental results. Through extensive experimentation and evaluation, we demonstrate the effectiveness of the ensemble approach in learning control strategies for manipulating quantum systems towards a random target state. The results highlight the potential of ensemble RL techniques in addressing the challenges of quantum control tasks, such as system noise and dynamics. By integrating multiple RL agents within an ensemble framework, We aim to advance current developments in quantum control and create a new path for the development of adaptive control systems for quantum systems. The performance of the ensemble model is assessed against Gradient Ascent Pulse Engineering (GRAPE) and robust Model Predictive Control (MPC) to demonstrate its efficiency in highly challenging and noisy environments.
Obtaining reliable state preparation protocols is a key step toward practical implementation of many quantum technologies, and one of the main tasks in quantum control. In this work, different reinforcement learning approaches are used to derive a feedback law for state preparation of a desired state in a target system. In particular, we focus on the robustness of the obtained strategies with respect to different types and amount of noise. Comparing the results indicates that the learned controls are more robust to unmodeled perturbations with respect to simple feedback strategy based on optimized population transfer, and that training on a simulated nominal model retains the same advantages displayed by controllers trained on real data. The possibility of effective off-line training of robust controllers promises significant advantages toward practical implementation.
Abstract The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. GRAPE is gradient search method based on exact expressions for gradient of the control objective. It has been applied to various coherently controlled closed and open quantum systems. In this work, we adopt the GRAPE method for optimizing objective functionals in open quantum systems driven by both coherent and incoherent controls. In our case, a tailored or engineered environment acts on the controlled system as control via time-dependent decoherence rates γ i ( t ) or, equivalently, via spectral density n ω ( t ) of the environment . To develop the GRAPE approach for this problem, we compute gradient of various objectives for general N -level open quantum systems for the piecewise constant class of control. The case of a single qubit is considered in details and solved analytically. For this case, an explicit analytical expression for evolution and objective gradient is obtained via diagonalization of a 3 × 3 matrix determining the system’s dynamics in the Bloch ball. The diagonalization is obtained by solving a cubic equation via Cardano’s method. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem and its complexity is estimated. Robustness of the optimal controls is also studied.