论文标题
时间依赖的哈密顿
Minimum Trotterization Formulas for a Time-Dependent Hamiltonian
论文作者
论文摘要
当时间传播器$ e^{ΔTA} $ for disuation $ΔT$由两个非交换零件组成$ a = x+y $时，trotterization大约将繁殖物分解为$ x $ and $ y $的指数的产物。量子和经典计算机已使用了各种Trotterization公式，但与时间有关的发电机$ a（t）$的Trotterization众所周知。在这里，对于由两个运营商$ x $和$ y $的$ a（t）$，具有时间依赖于时间的系数$ a（t）= x（t）x（t）x + y（t）y $，我们开发了一种系统的方法来衍生高阶Trotterterization Formulas，以最小的指数指数。特别是，我们分别获得了涉及七个指数和15个指数的四阶和六阶小型化公式，这些公式不比时间无关的发电机。我们还构建了另一个四阶公式，该公式由九个指数较小的指数组成。最后，我们在数值上基准在量子链的哈密顿模拟中基准的四阶公式，表明9指数公式比众所周知的铃木公式伴随着每个局部量子门较小的误差。
When a time propagator $e^{δt A}$ for duration $δt$ consists of two noncommuting parts $A=X+Y$, Trotterization approximately decomposes the propagator into a product of exponentials of $X$ and $Y$. Various Trotterization formulas have been utilized in quantum and classical computers, but much less is known for the Trotterization with the time-dependent generator $A(t)$. Here, for $A(t)$ given by the sum of two operators $X$ and $Y$ with time-dependent coefficients $A(t) = x(t) X + y(t) Y$, we develop a systematic approach to derive high-order Trotterization formulas with minimum possible exponentials. In particular, we obtain fourth-order and sixth-order Trotterization formulas involving seven and fifteen exponentials, respectively, which are no more than those for time-independent generators. We also construct another fourth-order formula consisting of nine exponentials having a smaller error coefficient. Finally, we numerically benchmark the fourth-order formulas in a Hamiltonian simulation for a quantum Ising chain, showing that the 9-exponential formula accompanies smaller errors per local quantum gate than the well-known Suzuki formula.
