We present a quantum algorithm for simulating quantum chemistry with gate complexity \(\tilde {\cal{O}}(N^{1/3}\eta ^{8/3})\) where η is the number of electrons and N is the number of plane wave orbitals. In comparison, the most efficient prior algorithms for simulating electronic structure using plane waves (which are at least as efficient as algorithms using any other basis) have complexity \(\tilde {\cal{O}}(N^{8/3}{\mathrm{/}}\eta ^{2/3})\). We achieve our scaling in first quantization by performing simulation in the rotating frame of the kinetic operator using interaction picture techniques. Our algorithm is far more efficient than all prior approaches when N ≫ η, as is needed to suppress discretization error when representing molecules in the plane wave basis, or when simulating without the Born-Oppenheimer approximation.

我们提出一种用于模拟具有门复杂度\（\ tilde {\ cal {O}}（N ^ {1/3} \ eta ^ {8/3}）\）的量子化学的量子算法，其中η是电子数，N是平面波轨道数。相比之下，使用平面波模拟电子结构的最有效的现有算法（至少与使用任何其他基础的算法效率一样）具有复杂度\（\ tilde {\ cal {O}}（N ^ {8/3} {\ mathrm {/}} \ eta ^ {2/3}）\）。我们通过使用交互图像技术在动力学算子的旋转框架中执行模拟来实现第一次量化的缩放。我们的算法比以前的所有方法时更有效率ñ  »  η，以抑制在平面波基础上表示分子时或在不使用Born-Oppenheimer近似进行模拟时抑制离散化误差所需要的。