Intractability of Electronic Structure in a Fixed Basis
Intractability of Electronic Structure in a Fixed Basis
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DOI：
10.1103/prxquantum.3.020322
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发表时间：
2022-05-02
期刊：
影响因子：
9.7
通讯作者：
Fefferman, Bill
中科院分区：
文献类型：
--
作者：
O'Gorman, Bryan;Irani, Sandy;Fefferman, Bill
寻找受外部电场影响的电子的基态能量是计算化学中的一个基本问题。虽然 QMA 完备性理论有助于理解在多体量子系统中寻找基态的复杂性，但在这项工作之前，尚不清楚是否可以利用分子电子结构的哈密顿量的特殊形式来有效地寻找基态，或者对于这种特殊情况该问题是否仍然困难。我们证明，当限制于固定的单粒子基础和固定数量的电子时，电子结构问题是 QMA 完备的。在我们的证明中，局部哈密顿量被编码在用于离散电子结构哈密顿量的空间轨道的选择中。相比之下，Schuch 和 Verstraete 通过在特定位点磁场中的量子位上编码局部哈密顿量，证明了使用额外的特定位点外部磁场来解决电子结构问题的难度，但不受固定基础的限制。我们还表明，对于固定基础上的电子结构哈密顿量，最低能量 Slater 行列式状态（即 Hartree-Fock 状态）的能量估计是非确定性多项式时间 (NP) 完全的。
Finding the ground-state energy of electrons subject to an external electric field is a fundamental problem in computational chemistry. While the theory of QMA-completeness has been instrumental in understanding the complexity of finding ground states in many-body quantum systems, prior to this work it has been unknown whether or not the special form of the Hamiltonian for the electronic structure of molecules can be exploited to find ground states efficiently or whether the problem remains hard for this special case. We prove that the electronic-structure problem, when restricted to a fixed single-particle basis and a fixed number of electrons, is QMA-complete. In our proof, the local Hamiltonian is encoded in the choice of spatial orbitals used to discretize the electronic-structure Hamiltonian. In contrast, Schuch and Verstraete have proved hardness for the electronic-structure problem with an additional site-specific external magnetic field, but without the restriction to a fixed basis, by encoding a local Hamiltonian on qubits in the site-specific magnetic field. We also show that estimation of the energy of the lowest-energy Slater-determinant state (i.e., the Hartree-Fock state) is nondeterministic polynomial time (NP)-complete for the electronic-structure Hamiltonian in a fixed basis.