Optimal control and quantum computing

Tommaso Calarco

D.T. Muhamediyeva, Narzillo Mamatov, M. H. Raupova +2 more

The article considers the solution of the optimal control tasks in ecology and environmental protection based on quantum computing. Pollution dynamics are investigated, with natural decay, diffusion and controlled remediation treatments being considered. Optimal control is designed to minimize environmental impact while also minimizing the costs of cleaning up the environment. To solve the problem effectively, a quantum optimization algorithm is proposed. For this, the desired problem is transformed into a quadratic optimization problem. This enables the application of quantum computing to the formulation of optimal policies for environmental regulation. Experiments are performed, a comparison is made between quantum-classical approaches and conventional techniques, and the feasibility of quantum optimization in sustainability issues is debated.

Raphael Ehikhuemhen Asibor, Victor Osemudiamhen Asibor

This study optimizes qubit control protocols using optimal control theory, machine learning, and stochastic modeling to enhance quantum computing performance. Quantum computing represents a transformative leap in computational power, with qubits serving as the fundamental building blocks of quantum information processing. However, the efficient control and manipulation of qubits remain significant challenges due to decoherence, noise, and imperfect control pulses. This study focuses on optimizing qubit control protocols using advanced applied mathematical techniques, including optimal control theory, machine learning, and stochastic modeling, to enhance quantum computing performance. By leveraging these techniques, we develop robust control strategies that minimize errors, improve gate fidelity, and extend coherence times. Our methodology integrates numerical simulations with experimental validation, demonstrating significant improvements in qubit control accuracy and reliability. The results highlight the potential of these optimized protocols to enable scalable and fault-tolerant quantum computing. This work contributes to the ongoing efforts to realize practical quantum technologies, offering insights into the interplay between mathematical optimization and quantum system dynamics.

Hirmay Sandesara, Alok Shukla, Prakash Vedula

Jun Li, Xiaodong Yang, Xinhua Peng +1 more

A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.

V. P. Belavkin, Simon Edwards