Riemann-Hurwitz zeta函数的量子模拟
Quantum simulation of the Riemann-Hurwitz zeta function
摘要：
我们提出了一个简单的实现的量子模拟器的Riemann-Hurwitz（RH）的函数的基础上截断其Dirichlet表示。我们合成了一个最近邻相互作用哈密顿量，满足哈密顿量初始裸态的自相关函数的时间演化沿复平面的线σ+i ωt再现RH函数的性质，其中σ>1.紧束缚哈密顿量与工程跳跃率和网站的能量可以在各种物理系统，包括捕获离子系统和光波导阵列中实现。所提出的方法是可扩展的，这意味着模拟原则上可以任意准确。建议的计划，所产生的有限数量的晶格站点N和退相干的实际限制，进行了简要讨论。
英文摘要：
We propose a simple realization of a quantum simulator of the Riemann-Hurwitz (RH) ζ function based on a truncation of its Dirichlet representation. We synthesize a nearest-neighbour-interaction Hamiltonian, satisfying the property that the temporal evolution of the autocorrelation function of an initial bare state of the Hamiltonian reproduces the RH function along the line σ+i ωt of the complex plane, with σ>1. The tight-binding Hamiltonian with engineered hopping rates and site energies can be implemented in a variety of physical systems, including trapped ion systems and optical waveguide arrays. The proposed method is scalable, which means that the simulation can be in principle arbitrarily accurate. Practical limitations of the suggested scheme, arising from a finite number of lattice sites N and from decoherence, are briefly discussed.
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