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.

量子计算与量子信息科学是一门蓬勃发展的工程学科，正处于攻克高难度机器人应用难题的前沿。本文提出一种混合（基于量子门的）量子计算与经典计算架构，用于解决机器人系统的运动传播问题。本文针对由两类线性算子——酉（Unitary）系统矩阵与非酉（Non-Unitary）系统矩阵——定义的线性微分方程，提出了对应的量子-经典架构，从而可求解任意线性常微分方程。在各类计算问题中，利用比特（bits）或量子比特（qubits）编码信息的能力是不可或缺的。本文研究成果还提出了两种新颖的编码方案，可利用量子比特对任意态矢量或任意线性算子进行编码。与其他仅采用纯量子或纯经典架构求解常微分方程（ODE，Ordinary Differential Equation）的算法不同，本文提出的常微分方程求解器充分融合了量子与经典计算范式的最优特性。