论文标题
NISQ设备上可实现的量子泊松求解器（改进版本）
A quantum Poisson solver implementable on NISQ devices (improved version)
论文作者
论文摘要
求解微分方程是量子计算的最引人注目的应用之一。人们认为，针对普通和部分微分方程的大多数现有量子算法被认为太昂贵了，无法成功执行嘈杂的中间量子量子（NISQ）设备。在这里，我们提出了一种基于简单旋转的一维泊松方程来求解一维泊松方程的紧凑型量子算法。主要操作是根据概率幅度进行的。因此，本算法避免了进行相位估计，哈密顿模拟和算术的需求。解决方案误差仅来自泊松方程的有限差近似。我们的量子泊松求解器（QPS）在Qubits中具有3N的栅极复合度，在一个和两倍的门中具有4n^3的栅极复合度，其中n是方程式线性系统维度的对数。就解决方案误差ε而言，复杂性是Qubits中的log（1/ε）和操作中的poly（log（1/ε）），这与最著名的结果组成。当前的QP可以代表NISQ设备上的潜在应用。
Solving differential equations is one of the most compelling applications of quantum computing. Most existing quantum algorithms addressing general ordinary and partial differential equations are thought to be too expensive to execute successfully on Noisy Intermediate-Scale Quantum (NISQ) devices. Here we propose a compact quantum algorithm for solving one-dimensional Poisson equation based on simple Ry rotation. The major operations are performed on probability amplitudes. Therefore, the present algorithm avoids the need to do phase estimation, Hamiltonian simulation and arithmetic. The solution error comes only from the finite difference approximation of the Poisson equation. Our quantum Poisson solver (QPS) has gate-complexity of 3n in qubits and 4n^3 in one- and two-qubit gates, where n is the logarithmic of the dimension of the linear system of equations. In terms of solution error ε, the complexity is log(1/ε) in qubits and poly(log(1/ε)) in operations, which is consist with the best known results. The present QPS may represent a potential application on NISQ devices.
