This paper deals with the progress made in applications of quantum computing in control and optimization. It concentrates on applying the geometric technique in order to investigate a finite control problem of a two-level quantum system, resonance control of a three-level system, simulation of bilinear quantum control systems, and optimal control using the Bellman principle. We show that a quantum object described by a Schroedinger equation can be controlled in an optimal way by electromagnetic modes. We also demonstrate an application of these techniques and an algebra-geometric approach to the study of dynamic processes in nonlinear systems. The information processing by means of controlled quantum lattices is discussed: we present new mathematical models of classical (CL) and quantum-mechanical lattices (QML) and their application to information processing. system-theoretical results on the observability, controllability and minimal realizability theorems are formulated for cl. The cellular dynamaton (CD) based on quantum oscillators is presented. Cellular's quantum computational search procedure can provide the basis for implementing adaptive global optimization algorithms. A brief overview of the procedure is given and a framework called lattice adaptive search is set up. A method of Yatsenko and one introduced by the authors fit into this framework and are compared.
This paper deals with the progress made in applications of quantum computing in control and optimization. It concentrates on applying the geometric technique in order to investigate a finite control problem of a two-level quantum system, resonance control of a three-level system, simulation of bilinear quantum control systems, and optimal control using the Bellman principle. We show that a quantum object described by a Schroedinger equation can be controlled in an optimal way by electromagnetic modes. We also demonstrate an application of these techniques and an algebra-geometric approach to the study of dynamic processes in nonlinear systems. The information processing by means of controlled quantum lattices is discussed: we present new mathematical models of classical (CL) and quantum-mechanical lattices (QML) and their application to information processing. system-theoretical results on the observability, controllability and minimal realizability theorems are formulated for cl. The cellular dynamaton (CD) based on quantum oscillators is presented. Cellular's quantum computational search procedure can provide the basis for implementing adaptive global optimization algorithms. A brief overview of the procedure is given and a framework called lattice adaptive search is set up. A method of Yatsenko and one introduced by the authors fit into this framework and are compared.
This paper presents a quantum optimization problem and solid-state quantum computing architectures. Quantum approach to global optimization and NP-complete problems are considered. Our approach to global optimization based on quantum mechanical entanglement, quantum resonant tunneling, cellular automaton and geometric control methods. A quantum optimization algorithm combines the properties of classical simulated annealing with the possibility of quantum tunneling between the minima. Quantum computation exploits the property of quantum states to implement quantum parallelism for global nonconvex optimization problem. This paper considers new mathematical models of classical (CL) and quantum-mechanical lattices (QML). System-theoretic results on the observability, controllability and minimal realizability theorems are formulated for CL. The cellular dynamaton (CD) based on quantum oscillators is presented. We investigate the conditions when stochastic resonance can occur through the interaction of dynamical neurons with intrinsic deterministic noise and an external periodic control.
The control of matter and energy at a fundamental level will be a cornerstone of new technologies for years to come. This idea is exemplified in a distilled form by controlling the dynamics of quantum mechanical systems via a time-dependent potential. The contributions detailed within this work focus on the computational aspects of formulating and solving quantum control problems efficiently.
The accurate numerical computation of optimal controls of infinite dimensional quantum control problems is a very difficult task that requires to take into account the features of the original infinite dimensional problem. An important issue is the choice of the functional space where the minimization process is defined. A systematic comparison of L2 versus H1 based minimization shows that the choice of the appropriate functional space matters and has many consequences in the implementation of some optimization techniques.
A matrix-free cascadic BFGS algorithm is introduced in the L 2 and H1 settings and it is demonstrated that the choice of H1 over L2 results in a substantial performance and robustness increase. A comparison between optimal control resulting from function space minimization and the control obtained by minimization over Chebyshev and POD basis function coefficients is presented.
A theoretical and computational framework is presented to obtain accurate controls for fast quantum state transitions that are needed in a host of applications such as nano electronic devices and quantum computing. This method is based on a reduced Hessian Krylov-Newton scheme applied to a norm-preserving discrete model of a dipole quantum control problem. The use of second-order numerical methods for solving the control problem is justified proving existence of optimal solutions and analyzing first- and second-order optimality conditions. Criteria for the discretization of the non-convex optimization problem and for the formulation of the Hessian are given to ensure accurate gradients and a symmetric Hessian. Robustness of the Newton approach is obtained using a globalization strategy with a robust linesearch procedure. Results of numerical experiments demonstrate that the Newton approach presented in this dissertation is able to provide fast and accurate controls for high-energy state transitions.
Control of bound-to-bound and bound-to-continuum transitions in open quantum systems and vector field control of two-dimensional systems is presented. An efficient space-time spectral discretization of the time-dependent Schrodinger equation and preconditioning strategy for a fast approximate solution with Krylov methods is outlined.
We investigate the problem of control of quantum systems. Various notions of controllability of quantum systems are discussed and Lie algebraic techniques are employed to derive necessary and sufficient conditions for the resulting degrees of controllability. The results are employed to study the degree of controllability for various model systems. The problem of optimal control is formulated as a problem of maximisation of the expectation value of an observable of the system subject to dynamical constraints and costs. A class of iterative algorithms is discussed, and shown to converge to a solution of the Euler-Lagrange equations, which is a necessary condition for optimality of a solution. A numerical realisation of the algorithm is presented and potential implementation of the resulting control fields in the laboratory is discussed. The algorithm is applied to find optimal control fields for a variety of applications including selective and simultaneous excitation of individual quantum dots in a globally addressed ensemble, creation of superposition states, and selective excitation of certain vibrational modes of a simple molecule such as Hydrogen Fluoride. In each case we systematically explore the parameter space of the algorithm to select solutions with desirable physical features from the multitude of possible choices. As there are many possible optimal control fields which give similar yields the question of whether some are more robust than others is investigated. A number of optimal fields are analysed quantitatively in terms of robustness with regard to temporal and spectral noise affecting the fields, uncertainty in the model parameters and the effect of experimental limitations such as restrictions on the bandwidth of the fields. It is shown that whilst the solutions tend to be sensitive to uncertainty in the energy levels chosen for the model, they appear to be surprisingly tolerant to even severe bandwidth limitations.
This paper explores the integration of nonlinear control theory with quantum system modeling, presenting a novel approach to designing and optimizing control strategies for quantum systems. The core claim centers on leveraging the optimization techniques within nonlinear control theory to address the inherent complexities of quantum system dynamics. The mechanism involves formulating quantum systems' nonlinear dynamics into equivalent control problems, subsequently employing nonlinear control theory's optimization methods for solution. This combined approach promises enhanced precision and efficiency in quantum system control. The work demonstrates a theoretical framework for tackling this challenge, paving the way for future research and practical applications in areas such as quantum computing and quantum sensing. The key mathematical concepts utilized are presented, including Hamiltonian formalism, Liouville-Perron equation, and nonlinear control theory formulations. The final results offer a pathway to more effective manipulation of quantum states.
The increasing convergence of quantum computing (QC) and advanced robotic control is giving rise to a new class of intelligent automation systems. Utilizing quantum-inspired computational principles, contemporary robotic platforms demonstrate greater optimization efficiency, superior perceptual processing, and improved decision-making performance. This survey outlines the principal quantum-oriented control methodologies utilized in robotics, with particular emphasis on approaches that incorporate Quantum Neural Networks (QNN), Quantum Machine Learning (QML), and Quantum-behaved Particle Swarm Optimization (QPSO). The investigation systematically reviews recent advances in quantum-assisted adaptive control, trajectory planning, and optimization frameworks, spotlighting their contributions to improved robustness, precision, and energy efficiency. By analyzing research in quantum reinforcement learning, distributed Noisy Intermediate-Scale Quantum (NISQ) computing, and hybrid quantum-classical approaches, this review clarifies how quantum principles are transforming both theoretical and practical aspects of robotic control. Likewise, several real-world implementations ranging from industrial manipulators to autonomous and cognitive robotic systems demonstrate the growing feasibility of quantum-enhanced decision-making. The review concludes that while remarkable progress has been made in quantum-inspired control for robotics, most existing studies remain constrained to simulations with restricted experimental validation on physical platforms. Addressing this gap will be essential in future research to transition from theoretical and simulated models toward hardware-level implementations, enabling the realization of scalable, fault-tolerant quantum control architectures.
Quantum computing represents a fundamentally new paradigm in information processing, in which information is encoded and manipulated using two-level quantum systems known as qubits, whose evolution is governed by the principles of quantum mechanics. This chapter presents a structured introduction to the theoretical foundations of quantum computation, beginning with the limitations of classical computation and the physical constraints that motivate the need for a quantum model of computation. We develop the mathematical framework required to describe quantum information, introducing qubits as state vectors in Hilbert space and examining the roles of superposition, measurement, and unitary evolution. Single-qubit operations are presented through the Pauli and Hadamard gates, along with their geometric interpretation on the Bloch sphere. Building on this formalism, the discussion is extended to multi-qubit systems using tensor products, and quantum entanglement is introduced as a non-classical correlation fundamental to quantum information processing. The chapter then explores quantum algorithms, focusing on Grover’s unstructured search algorithm, to demonstrate how superposition, interference, and entanglement can be harnessed to achieve computational advantages over classical approaches. Finally, the chapter discusses applications of quantum computation, including quantum simulation, cryptography, search and optimization problems, and near-term hybrid quantum algorithms such as the Variational Quantum Eigensolver (VQE)and the Quantum Approximate Optimization (QAO) Algorithm, highlighting their relevance in the noisy intermediate-scale quantum (NISQ) era.