从解析结构到量子复杂度：连续算子的Walsh-Pauli表示
From Analytic Structure to Quantum Complexity: Walsh-Pauli Representations of Continuum Operators
- University of Oxford（牛津大学）
- National Institute for Theoretical and Computational Sciences (NITheCS)（理论与计算科学国家研究所）
- Stellenbosch University（斯泰伦博斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出算子级生成函数框架，解析求解JLP动量算子的Walsh-Pauli谱，揭示支持规则与壳内层级，并应用于GUP运动学，展示谱权重向高Pauli权重扇区的重分布。
AI中文摘要：
连续算子结构如何出现在有限量子比特寄存器中？我们针对以二进制基表示的对角算子的解析函数来探讨此问题，重点关注Jordan-Lee-Preskill (JLP)动量算子，通过发展一个算子级生成函数框架来研究其Walsh-Pauli谱。该构造解析地确定了谱，并揭示了精确的支持和奇偶选择规则，以及由二进制编码引起的非平凡的壳内层级结构。这提供了对Walsh可压缩性及其与Pauli局域性关系的系统刻画。作为受控应用，我们考虑广义不确定性原理（GUP）运动学作为动量的可调非线性奇变形，展示高阶动量项如何将谱权重重新分布到逐渐更高的Pauli权重扇区。
英文摘要：
How does continuum operator structure appear in a finite qubit register? We address this question for analytic functions of diagonal operators represented in a binary basis, focusing on the Jordan--Lee--Preskill (JLP) momentum operator, by developing an operator-level generating-function framework for their Walsh-Pauli spectra. The construction determines the spectrum analytically and reveals exact support and parity selection rules, together with a nontrivial intra-shell hierarchy induced by the binary encoding. This provides a systematic characterization of Walsh compressibility and its relation to Pauli locality. As a controlled application, we consider generalized uncertainty-principle (GUP) kinematics as a tunable nonlinear odd deformation of momentum, showing how higher-order momentum terms redistribute spectral weight into progressively higher Pauli-weight sectors
