具有最大对易initialHamiltonians的分子能量的量子Zeno方法
Quantum Zeno approach for molecular energies with maximum commuting initialHamiltonians
摘要：
我们提出用量子绝热和模拟退火框架来计算小分子的基态。算法的初始哈密顿量取泡利基下分子全哈密顿量中最大对易项集所构成的最大对易哈密顿量。我们考虑两个变量。在第一种方法中，我们将初始态作为最大对易哈密顿量的基态，对得到的与时间或路径相关的哈密顿量进行绝热演化。然而，由于简并性和沿哈密顿路径的能级交叉，这种方法确实遭受绝热量子计算的常见问题。这个问题通过Zeno方法减轻，即，利用量子模拟退火中的一系列本征态投影，在路径依赖的哈密顿量中增加Pauli X项，Pauli X项的贡献在路径的起始和终止处消失，除了基态外，还可以用量子Zeno方法得到与基态同样精确的低激发态.
英文摘要：
We propose to use a quantum adiabatic and simulated-annealing framework to compute theground state of small molecules. The initial Hamiltonian of our algorithms is taken to be themaximum commuting Hamiltonian that consists of a maximal set of commuting terms in the fullHamiltonian of molecules in the Pauli basis. We consider two variants. In the first method, weperform the adiabatic evolution on the obtained time- or path-dependent Hamiltonian with theinitial state as the ground state of the maximum commuting Hamiltonian. However, this methoddoes suffer from the usual problems of adiabatic quantum computation due to degeneracy andenergy-level crossings along the Hamiltonian path. This problem is mitigated by a Zeno method,i.e., via a series of eigenstate projections used in the quantum simulated annealing, with the path-dependent Hamiltonian augmented by a sum of Pauli X terms, whose contribution vanishes at thebeginning and the end of the path. In addition to the ground state, the low lying excited states canbe obtained using this quantum Zeno approach with equal accuracy to that of the ground state.
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