Quantum control aims to manipulate quantum systems toward specific quantum states or desired operations. Designing highly accurate and effective control steps is vitally important to various quantum applications, including energy minimization and circuit compilation. In this paper we focus on discrete binary quantum control problems and apply different optimization algorithms and techniques to improve computational efficiency and solution quality. Specifically, we develop a generic model and extend it in several ways. We introduce a squared L2 -penalty function to handle additional side constraints, to model requirements such as allowing at most one control to be active. We introduce a total variation (TV) regularizer to reduce the number of switches in the control. We modify the popular gradient ascent pulse engineering (GRAPE) algorithm, develop a new alternating direction method of multipliers (ADMM) algorithm to solve the continuous relaxation of the penalized model, and then apply rounding techniques to obtain binary control solutions. We propose a modified trust-region method to further improve the solutions. Our algorithms can obtain high-quality control results, as demonstrated by numerical studies on diverse quantum control examples.
Quantum control aims to manipulate quantum systems toward specific quantum states or desired operations. Designing highly accurate and effective control steps is vitally important to various quantum applications, including energy minimization and circuit compilation. In this paper we focus on discrete binary quantum control problems and apply different optimization algorithms and techniques to improve computational efficiency and solution quality. Specifically, we develop a generic model and extend it in several ways. We introduce a squared L2 -penalty function to handle additional side constraints, to model requirements such as allowing at most one control to be active. We introduce a total variation (TV) regularizer to reduce the number of switches in the control. We modify the popular gradient ascent pulse engineering (GRAPE) algorithm, develop a new alternating direction method of multipliers (ADMM) algorithm to solve the continuous relaxation of the penalized model, and then apply rounding techniques to obtain binary control solutions. We propose a modified trust-region method to further improve the solutions. Our algorithms can obtain high-quality control results, as demonstrated by numerical studies on diverse quantum control examples.
Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions are binary-valued and the problem is solved in diverse quantum algorithms. In this paper, we utilize classical optimization and computing techniques to develop an algorithmic framework that sequentially optimizes the number of control switches and the duration of each control interval on a continuous time horizon. Specifically, we first solve the continuous relaxation of the binary control problem based on time discretization and then use a heuristic to obtain a controller sequence with a penalty on the number of switches. Then, we formulate a switching time optimization model and apply sequential least-squares programming with accelerated time-evolution simulation to solve the model. We demonstrate that our computational framework can obtain binary controls with high-quality performance and also reduce computational time via solving a family of quantum control instances in various quantum physics applications.
Quantum optimal control, a powerful toolbox for engineering an optimal control field modulation that most precisely implements a desired quantum operation in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The gradient ascent pulse engineering (GRAPE) algorithm is a widely used method in quantum optimal control, which has achieved great success in different physical platforms. However, its computational complexity increases exponentially with the number of qubits, making it challenging to be implemented for large-scale quantum systems. To mitigate this issue, we present the iterative GRAPE algorithm (iGRAPE), which reduces the optimization problem into a series of lower-dimensional subproblems by incorporating disentanglement operations. Our numerical simulations on physical platforms such as nuclear magnetic resonance and superconducting quantum systems demonstrate that iGRAPE significantly enhances state preparation speed. Specifically, compared to GRAPE, iGRAPE achieves up to a five-fold acceleration in preparing Greenberger--Horne--Zeilinger states using a 12-qubit implementation, and up to a 13-fold acceleration for arbitrary state preparation with eight qubits. To further validate our findings, we conduct experimental validation of iGRAPE on a four-qubit nuclear magnetic resonance system. Overall, iGRAPE offers an efficient solution for implementing optimal control in large-scale quantum systems, holding great potential for advancing quantum technologies during the noisy intermediate-scale quantum era.
We present an iterative optimal control method of quantum systems, aimed at an implementation of a desired operation with optimal fidelity. The update step of the method is based on the linear response of the fidelity to the control operators, and its projection onto the mode functions of the corresponding operator. Our method extends methods such as gradient-ascent pulse engineering (GRAPE) and variational quantum algorithms, by determining the fidelity gradient in a hyperparameter-free manner, and using it for a multiparameter update, capitalizing on the multimode overlap of the perturbation and the mode functions. This directly reduces the number of dynamical trajectories that need to be evaluated in order to update a set of parameters. We demonstrate this approach, and compare it to the standard GRAPE algorithm, for the example of a quantum gate on two qubits, demonstrating a clear improvement in convergence and optimal fidelity of the generated protocol.
Applying sophisticated optimization methods to control problems in various systems offers a structured approach for achieving system efficiency and reliability, while ensuring the feasibility of physics-based constraints. This dissertation primarily focuses on developing optimization algorithms for control problems in complex systems with mixed-integer variables and parameter uncertainties. In Chapter 1, we provide a detailed introduction about the problem motivation and summarize our problems and contributions. Specifically, we develop new optimization models and algorithms for network-based traffic control and binary control in quantum systems, detailed as follows. Traffic signal control is an effective way of mitigating traffic congestion, where its complexity escalates in large cities due to numerous intersections and varying traffic conditions. Advancements in communication technologies within transportation infrastructures have made distributed traffic signal control at the network level possible and worth investigating. In Chapter 2, we build a stochastic optimization model for network-level traffic signal control under traffic demand uncertainty and solve it using decentralized algorithms. We compare the results with state-of-the-art traffic control methods via testing instances of real-world traffic networks and data. Quantum computing and quantum systems provide a novel way of significantly accelerating computation and their operations largely rely on quantum pulse control optimization to attain desired states or status. The optimization of binary quantum pulse control can potentially enhance the performance of classical quantum variational techniques and improve solution quality. In Chapter 3, we study a discrete-valued binary quantum control problem and propose an algorithmic framework to solve the problem with penalty on switches. In Chapter 4, we explore the binary quantum control problem in a continuous time horizon by optimizing both control functions and control time intervals. Moreover, the time-varying noise in quantum systems and the wide use of inhomogeneous quantum ensembles highlight the need for quantum controls considering uncertainties. In Chapter 5, we develop a stochastic optimization model for the binary quantum control problem with uncertain Hamiltonian controllers and solve it using gradient-based methods with rounding algorithms. We test the performance of our approaches and benchmark with state-of-the-art control methods in all three chapters. Lastly, in Chapter 6, we conclude the dissertation and state future research directions.
Gradient ascent pulse engineering algorithm (GRAPE) is a typical method to solve quantum optimal control problems. However, it suffers from an exponential resource in computing the time evolution of quantum systems with the increasing number of qubits, which is a barrier for its application in large-qubit systems. To mitigate this issue, we propose an iterative GRAPE algorithm (iGRAPE) for preparing a desired quantum state, where the large-scale, resource-consuming optimization problem is decomposed into a set of lower-dimensional optimization subproblems by disentanglement operations. Consequently these subproblems can be solved in parallel with less computing resources. For physical platforms such as nuclear magnetic resonance (NMR) and superconducting quantum systems, we show that iGRAPE can provide up to 13-fold speedup over GRAPE when preparing desired quantum states in systems within 12 qubits. Using a four-qubit NMR system, we also experimentally verify the feasibility of the iGRAPE algorithm.
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.