Kökcü Efekan, Steckmann Thomas, Wang Yan, Freericks J K, Dumitrescu Eugene F, Kemper Alexander F
Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA.
Oak Ridge National Laboratory, Computational Sciences and Engineering Division, Oak Ridge, Tennessee 37831, USA.
Phys Rev Lett. 2022 Aug 12;129(7):070501. doi: 10.1103/PhysRevLett.129.070501.
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize limited quantum resources remains an open problem. We tackle this problem by presenting a constructive algorithm, based on Cartan decomposition of the Lie algebra generated by the Hamiltonian, which generates quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one-dimensional transverse field XY model, where O(n^{2})-gate circuits naturally emerge. Compared to product formulas with significantly larger gate counts, our algorithm drastically improves simulation precision. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
由于对内存要求很高，在经典计算机上模拟大型系统的量子动力学具有挑战性。在量子计算机上进行模拟是一种很有前途的替代方法，但完全优化量子电路以最小化有限的量子资源仍然是一个未解决的问题。我们通过提出一种基于哈密顿量生成的李代数的嘉当分解的构造性算法来解决这个问题，该算法生成具有与时间无关深度的量子电路。我们针对特殊类别的模型突出展示了我们的算法，包括一维横向场XY模型中的安德森局域化，其中自然会出现O(n²)门电路。与具有大得多的门数的乘积公式相比，我们的算法极大地提高了模拟精度。除了为广泛的自旋和费米子模型提供精确电路外，我们的算法还为最优哈密顿量模拟提供了广泛的分析和数值见解。
