Optimal Control-Based Grover’s Algorithm for a Six-Jointed Articulated Robotic Arm

Abstract

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.