Quantum Machine Learning and Grover's Algorithm for Quantum Optimization of Robotic Manipulators

TL;DR

The paper addresses the challenge of optimizing high-DoF robotic manipulators in complex configuration spaces by proposing a fully quantum-native framework that unifies quantum machine learning with Grover's search. A parameterized quantum circuit learns forward kinematics to construct a cost oracle, enabling Grover's algorithm to achieve a quadratic speedup in identifying optimal configurations over classical search. Demonstrations on 1-DoF, 2-DoF, and dual-arm tasks show substantial speedups as problem dimensionality grows—up to 93x compared with Nelder-Mead—while maintaining solution quality and meeting precision requirements. This work establishes a foundational bridge between quantum computing and robotics, highlighting potential for scalable quantum-enhanced optimization in precision automation, with future work focusing on hardware-aware circuit design and real-time deployment on advanced quantum processors.

Abstract

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 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.

Figures (7)

• Figure 1: Integration of QML and Grover's algorithm. The QML block uses parameterized gates $U_{\text{QML}}(\psi)$ to encode learned kinematic patterns, biasing the initial state. This feeds into Grover's, where the oracle $U(\psi)$ marks solutions, and the diffusion operator $D$ amplifies them over $\mathcal{O}(\sqrt{N})$ iterations. Measurement yields optimal configurations with high probability.
• Figure 2: A toroidal manifold $\mathbb{T}^2$ representing the configuration space of a two-link manipulator. Each point corresponds to a unique joint angle pair $(\theta_1, \theta_2)$, illustrating the periodicity and complexity of multi-DoF solution spaces.
• Figure 3: Quantum variational circuit (ansatz design) for optimizing a single-link manipulator to generate a circular workspace. The circuit uses parameterized rotations ($R_X$, $R_Y$) and CNOT gates across 9 qubits to encode solutions and evaluate their fitness through measurement, enabling iterative refinement of the joint angle. It is tailored to optimize the cost function, incorporating link length and other relevant parameters.
• Figure 4: Optimization results for one- and two-DoF manipulators. (x-axes represent optimization iterations; figures regenerated with continuous lines without markers for clarity.)
• Figure 5: Optimization results for the 2-DoF manipulator (quantum) and the dual-arm system (classical). (x-axes represent optimization iterations; figures regenerated with continuous lines without markers for clarity.)