保结构的量子电路架构用于机器人运动学

中文摘要 AI 辅助

结构化空间数据需要能够保持几何关系、暴露可测量观测量、并可在有限深度硬件上实现的量子编码。本工作引入了一种用于刚体变换的量子表示和电路架构，并将其专门应用于串联开链机械臂的Denavit-Hartenberg运动学。每个平移贡献被分解为一个经典度量幅值和一个由单量子比特Bloch向量编码的带符号单位方向，而参数化旋转则再现了坐标系方向的有序传播。一个选择器寄存器制备与贡献幅值成比例的概率，指定读出量子比特的约化态编码其归一化加权和。保留的经典尺度随后重构度量末端执行器位置。另外两个读出量子比特编码末端坐标系轴，提供紧凑且几何可解释的位姿接口。在理想的期望值层面，测量的Pauli观测量再现了相应的经典运动学量。替代电路架构以量子比特数、电路深度、受控操作和测量要求的不同权衡实现相同的表示。在串联机械臂上的验证在理想模拟下产生了数值上可忽略的位置和方向重构误差。有限次测量模拟、噪声执行、转译分析和硬件演示进一步表征了统计误差、噪声敏感性和实现开销，而未声称计算优势。

英文摘要

Structured spatial data require quantum encodings that preserve geometric relations, expose measurable observables, and remain implementable on finite-depth hardware. This work introduces a quantum representation and circuit architecture for rigid-body transformations and specializes it to Denavit--Hartenberg kinematics of serial open-chain manipulators. Each translational contribution is factorized into a classical metric magnitude and a signed unit direction encoded by a single-qubit Bloch vector, while parameterized rotations reproduce the ordered propagation of frame directions. A selector register prepares probabilities proportional to the contribution magnitudes, and the reduced state of a designated readout qubit encodes their normalized weighted sum. The retained classical scale then reconstructs the metric end-effector position. Two additional readout qubits encode terminal-frame axes, providing a compact and geometrically interpretable pose interface. At the ideal expectation-value level, measured Pauli observables reproduce the corresponding classical kinematic quantities. Alternative circuit architectures realize the same representation with different tradeoffs in qubit count, circuit depth, controlled operations, and measurement requirements. Validation on a serial manipulator yields numerically negligible position and orientation reconstruction errors under ideal simulation. Finite-shot simulations, noisy executions, transpilation analysis, and a hardware demonstration further characterize statistical error, noise sensitivity, and implementation overhead without asserting computational advantage.

发表机构

• University of Naples Federico II（那不勒斯费德里科二世大学）

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