Zhao Hongzheng, Bukov Marin, Heyl Markus, Moessner Roderich
School of Physics, <a href="https://ror.org/02v51f717">Peking University</a>, 100871 Beijing, China.
<a href="https://ror.org/01bf9rw71">Max Planck Institute for the Physics of Complex Systems</a>, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Phys Rev Lett. 2024 Jul 5;133(1):010603. doi: 10.1103/PhysRevLett.133.010603.
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical trade-off between improved accuracy for finer time steps, and increased error rate on account of the larger circuit depth. We present an adaptive Trotterization algorithm to cope with time dependent Hamiltonians, where we propose a concept of piecewise "conserved" quantities to estimate errors in the time evolution between two (nearby) points in time; these allow us to bound the errors accumulated over the full simulation period. They reduce to standard conservation laws in the case of time independent Hamiltonians, for which we first developed an adaptive Trotterization scheme [H. Zhao et al., Making Trotterization adaptive and energy-self-correcting for NISQ devices and beyond, PRX Quantum 4, 030319 (2023).2691-339910.1103/PRXQuantum.4.030319]. We validate the algorithm for a time dependent quantum spin chain, demonstrating that it can outperform the conventional Trotter algorithm with a fixed step size at a controlled error.
数字量子模拟依靠 Trotter 化方法将时间演化离散为基本量子门。在当前具有显著门缺陷的量子处理器上，在更精细时间步长下提高精度与由于电路深度增加而导致的错误率上升之间存在关键权衡。我们提出一种自适应 Trotter 化算法来处理含时哈密顿量，在此我们提出分段“守恒”量的概念，以估计两个（相邻）时间点之间时间演化中的误差；这些使我们能够界定整个模拟周期内累积的误差。在哈密顿量与时间无关的情况下，它们简化为标准守恒定律，针对这种情况我们首先开发了一种自适应 Trotter 化方案[H. 赵等人，《为含噪声中等规模量子设备及更高级情况使 Trotter 化自适应且能量自校正》，《物理评论X量子》4，030319 (2023).2691 - 339910.1103/PRXQuantum.4.030319]。我们针对含时量子自旋链验证了该算法，表明它能够在可控误差下优于具有固定步长的传统 Trotter 算法。
