Low rank representations for quantum simulation of electronic structure
Low rank representations for quantum simulation of electronic structure
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DOI：
10.1038/s41534-021-00416-z
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发表时间：
2021-05-27
影响因子：
7.6
通讯作者：
Chan, Garnet Kin-Lic
中科院分区：
文献类型：
--
作者：
Motta, Mario;Ye, Erika;Chan, Garnet Kin-Lic
量子化学的量子模拟是量子计算机的一个很有前途的应用。然而，对于N个分子轨道，O（N-4）门的复杂性进行哈密尔顿和单一耦合集群特罗特步骤，使模拟的基础上，这样的原语的挑战。我们大大降低了门的复杂性，这样的原语通过两步低秩因式分解的哈密顿算子和集群运营商，伴随着截断的小项。使用截断，招致低于化学精度的错误，允许一个执行特罗特步骤的任意基础电子结构哈密顿与O（N-3）门复杂性在小的模拟，这减少到O（N-2）门复杂性在渐近制度;和单一耦合簇特罗特步骤与O（N-3）门复杂性作为一个函数的基础大小增加一个给定的分子。在Hamilton Trotter步骤的情况下，这些电路在线性连接的阵列上具有O（N-2）深度，这比假设没有截断的O（N-3）缩放有所改进。作为一个实际的例子，我们表明，一个化学精确的哈密顿Trotter步骤的50量子位分子模拟可以在分子轨道的基础上进行，只有4000层的平行最近邻两量子位门，包括少于10（5）非克利福德旋转。我们还将我们的算法应用于铁硫簇相关的阐明金属酶的作用模式。
The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the O(N-4) gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy allow one to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with O(N-3) gate complexity in small simulations, which reduces to O(N-2) gate complexity in the asymptotic regime; and unitary Coupled Cluster Trotter steps with O(N-3) gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have O(N-2) depth on a linearly connected array, an improvement over the O(N-3) scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 10(5) non-Clifford rotations. We also apply our algorithm to iron-sulfur clusters relevant for elucidating the mode of action of metalloenzymes.