A Path to Solving Robotic Differential Equations Using Quantum Computing

Quantum Computing and Quantum Information Science is a burgeoning engineering field at the cusp of solving challenging robotic applications. This paper introduces a hybrid (gate-based) quantum computing and classical computing architecture to solve the motion propagation problem for a robotic system. This paper presents the quantum-classical architecture for linear differential equations defined by two types of linear operators: Unitary and Non-Unitary system matrices, thereby solving any linear ordinary differential equation. The ability to encode information using bits - or qubits - is essential in any computation problem. The results in this paper also introduce two novel approaches to encoding any arbitrary state vector or any arbitrary linear operator using qubits. Unlike other algorithms that solve ODEs using purely quantum or classical architectures, the ODE solver presented in this paper leverages the best of quantum and classical computing paradigms.