论文标题
使用Chebyshev插值提高了Trotter模拟的精度
Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation
论文作者
论文摘要
量子计量学允许在最佳的海森堡极限下测量量子系统的性质。但是，当使用数字哈密顿模拟制备相关的量子状态时，应计算法错误将导致与此基本限制的偏差。在这项工作中，我们展示了如何通过使用标准的多项式插值技术来减轻由于Trotterized时间演化引起的算法误差。我们的方法是外推到零猪螺旋杆的步长大小，类似于用于减轻硬件错误的零噪声外推技术。我们对插值方法进行了严格的误差分析，以估计特征值和随时间推动的期望值，并证明Heisenberg极限已达到误差中的polyogarithmic因子。我们的工作表明，仅使用Trotter和经典资源来实现许多相关算法任务，就可以实现接近最先进的模拟算法的精度。
Quantum metrology allows for measuring properties of a quantum system at the optimal Heisenberg limit. However, when the relevant quantum states are prepared using digital Hamiltonian simulation, the accrued algorithmic errors will cause deviations from this fundamental limit. In this work, we show how algorithmic errors due to Trotterized time evolution can be mitigated through the use of standard polynomial interpolation techniques. Our approach is to extrapolate to zero Trotter step size, akin to zero-noise extrapolation techniques for mitigating hardware errors. We perform a rigorous error analysis of the interpolation approach for estimating eigenvalues and time-evolved expectation values, and show that the Heisenberg limit is achieved up to polylogarithmic factors in the error. Our work suggests that accuracies approaching those of state-of-the-art simulation algorithms may be achieved using Trotter and classical resources alone for a number of relevant algorithmic tasks.
