This paper introduces a novel theoretical framework that reformulates optimal control as a quantum search problem using Grover’s algorithm, leveraging its quadratic speedup. Specifically, the method encodes all possible control inputs into a quantum superposition state and uses a reference value interpreted as a candidate minimum to evaluate which inputs yield a lower control cost. To guide the search, we integrate a quantum comparator circuit to identify the inputs below this reference, and quantum counting to estimate their number. The reference is iteratively updated using a sigmoid-based rule until only one input satisfies the condition, thereby ensuring convergence to the global minimum within the discretized control space. Although full quantum implementation is currently infeasible due to oracle complexity and hardware limitations, we simulate the process using a classical controller as a pseudo-oracle to illustrate the algorithmic structure. This work does not aim to demonstrate performance gains but rather to establish a foundational method for embedding control synthesis within Grover-based quantum circuits. The framework paves the way for scalable quantum control systems once hardware resources permit full realization.
This paper introduces a novel theoretical framework that reformulates optimal control as a quantum search problem using Grover’s algorithm, leveraging its quadratic speedup. Specifically, the method encodes all possible control inputs into a quantum superposition state and uses a reference value interpreted as a candidate minimum to evaluate which inputs yield a lower control cost. To guide the search, we integrate a quantum comparator circuit to identify the inputs below this reference, and quantum counting to estimate their number. The reference is iteratively updated using a sigmoid-based rule until only one input satisfies the condition, thereby ensuring convergence to the global minimum within the discretized control space. Although full quantum implementation is currently infeasible due to oracle complexity and hardware limitations, we simulate the process using a classical controller as a pseudo-oracle to illustrate the algorithmic structure. This work does not aim to demonstrate performance gains but rather to establish a foundational method for embedding control synthesis within Grover-based quantum circuits. The framework paves the way for scalable quantum control systems once hardware resources permit full realization.
Optimizing high-degree-of-freedom robotic manipulators requires searching complex, high-dimensional configuration spaces, a task that is computationally challenging for classical methods. This paper introduces a quantum-native framework that integrates Quantum Machine Learning (QML) with Grover's algorithm to solve kinematic optimization problems efficiently. A parameterized quantum circuit is trained to approximate the forward kinematics model, which then constructs an oracle to identify optimal configurations. Grover's algorithm leverages this oracle to provide a quadratic reduction in search complexity. Demonstrated on simulated 1-DoF, 2-DoF, and dual-arm manipulator tasks, the method achieves significant speedups-up to 93x over classical optimizers like Nelder-Mead-as problem dimensionality increases. This work establishes a foundational, quantum-native framework for robot kinematic optimization, effectively bridging quantum computing and robotics problems.
Particle Swarm Optimization (PSO) is a widely used solver for the Inverse Kinematics (IK) problem, offering competitive convergence rates compared to methods like Damped Least Squares and Forward and Backward Reaching Inverse Kinematics. However, PSO’s high computational cost per iteration remains a challenge. While many PSO variants focus on reducing the number of iterations, this work introduces a novel approach to decrease the computational cost per iteration by minimizing direct kinematics calculations. Leveraging quantum computing algorithms, specifically Quantum Amplitude Amplification (QAA), we developed Quantum-Grover PSO (QG-PSO), which identifies a suboptimal particle to guide the swarm. This approach capitalizes on QAA’s quadratic speedup for unstructured search problems. Simulated experiments demonstrate that QG-PSO significantly reduces computational costs compared to classical PSO when solving the IK problem for robotic manipulators with 7 and 15 joints, highlighting the potential of quantum computing in robotics. In addition to position correction, we considered orientation correction while respecting joint limits and avoiding obstacles.
Grover search is a renowned quantum search algorithm that leverages quantum superposition to find a marked item with quadratic speedup. However, when implemented on Noisy Intermediate-scale Quantum (NISQ) hardware, the required repeated iterations of the oracle and diffusion operators increase exponentially with the number of qubits, resulting in significant noise accumulation. To address this, we propose a hybrid quantum-classical architecture that replaces quantum iterations with updates from a classical optimizer. This optimizer minimizes the expectation value of an oracle Hamiltonian with respect to a parameterized quantum state representing the target bit string. Our parameterized quantum circuit is much shallower than Grover search circuit, and we found that it outperforms Grover search on noisy simulators and NISQ hardware. When the number of qubits is greater than 5, our approach still maintains usable success probability, while the success probability of Grover search is at the same level as random guessing.
This study evaluates quantum-inspired control strategies on classical hardware, specifically Quantum Sliding Mode Control (QSMC), Quantum Genetic Algorithm (QGA), and a Grover-based quantum search controller, to improve control of a six-degree-of-freedom robotic arm with nonlinear dynamics. Building upon quantum-analogous probabilistic principles, these methods offer significant potential across industries. To clarify the basis of these approaches, the analysis centers on quantum-computation concepts, such as probabilistic amplitude encoding and superposition, which can enhance robustness, trajectory smoothness, and energy efficiency in classical control systems. Consistent, noise-free simulation conditions and multiple independent trials ensured fairness and reproducibility throughout the study. Performance assessment relied on Integrated Absolute Error (IAE), which measures total error over time, and Average Control Energy (Eavg) for mean energy consumption. Compared with classical Sliding Mode Control (SMC), QSMC achieved an 11 % faster transient response. Additionally, QGA delivered 21 % lower IAE and 12.3 % lower average control energy, while the Grover-based controller provided balanced performance among convergence speed, tracking accuracy, and energy efficiency. Overall, these results suggest that quantum-inspired approaches can significantly advance trajectory precision, robustness, and energy efficiency, supporting the development of nextgeneration intelligent robotics.
The K-SAT problem is a fundamental challenge in computational theory, widely used in artificial intelligence, cryptography, and optimization. Classical algorithms struggle with exponential time complexity, making them inefficient for large-scale instances. In this research, we propose an efficient quantum computing approach based on Grover’s algorithm to enhance the search process for satisfiable solutions in K-SAT problems. Our implementation leverages quantum superposition and amplitude amplification to explore multiple possible solutions simultaneously, reducing the search complexity from O (2ⁿ) in classical methods to O(√2ⁿ) in quantum computing. We design a quantum oracle that encodes the K-SAT clauses and integrates it into Grover’s iterative search framework. The performance is evaluated through Qiskit simulations, demonstrating a significant improvement in search efficiency compared to classical brute-force techniques. The results highlight the potential of quantum algorithms in solving complex combinatorial problems with enhanced speed and accuracy. This study contributes to the development of quantum-accelerated optimization methods, paving the way for real-world applications in machine learning, cryptanalysis, and large-scale data processing.
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's search algorithm finds the target element in an unsorted database with quadratic speedup than classical search and has been proved to be optimal in terms of the number of queries to the database. The challenge, however, is that Grover's search algorithm leads to high numbers of quantum gates, which make it infeasible for the Noise-Intermediate-Scale-Quantum (NISQ) computers. In this paper, we propose a novel hardware efficient quantum search algorithm to overcome this challenge. Our key idea is to replace the global diffusion operation with low-cost local diffusions. Our analysis shows that our algorithm has similar oracle complexity to the original Grover's search algorithm while significantly reduces the circuit depth and gate count. The circuit cost reduction leads to a remarkable improvement in the system success rates, paving the way for quantum search on NISQ machines.