标题： 公钥量子货币与快速实变换 显示英文标题

标题： Public-Key Quantum Money and Fast Real Transforms

摘要： 我们提出了一种基于群作用和哈特利变换的公钥量子货币方案。 我们的方案改编了Zhandry（2024）的量子货币方案，将傅里叶变换替换为哈特利变换。 这种替换确保了纸币具有实数振幅而非复数振幅，这可能带来计算和理论上的优势。 为了支持这一新构造，我们提出了一种新的验证算法，该算法使用群作用扭曲来解决由于切换到实数振幅而导致的验证失败问题。 我们还展示了如何使用一种基于连续时间量子行走的新算法高效计算与货币状态相关的序列号。 最后，我们提出了一种递归算法用于量子哈特利变换，其门复杂度低于之前的工作，并展示了如何使用量子哈特利变换作为子程序来计算其他实数量子变换，例如量子正弦变换。 显示英文摘要

摘要： We propose a public-key quantum money scheme based on group actions and the Hartley transform. Our scheme adapts the quantum money scheme of Zhandry (2024), replacing the Fourier transform with the Hartley transform. This substitution ensures the banknotes have real amplitudes rather than complex amplitudes, which could offer both computational and theoretical advantages. To support this new construction, we propose a new verification algorithm that uses group action twists to address verification failures caused by the switch to real amplitudes. We also show how to efficiently compute the serial number associated with a money state using a new algorithm based on continuous-time quantum walks. Finally, we present a recursive algorithm for the quantum Hartley transform, achieving lower gate complexity than prior work and demonstrate how to compute other real quantum transforms, such as the quantum sine transform, using the quantum Hartley transform as a subroutine.