arXiv 2402.093762024-02-14quant-phphysics.chem-ph

由李代数直和得到的精确可解哈密顿量片段

Exactly solvable Hamiltonian fragments obtained from a direct sum of Lie algebras

Smik Patel, Artur F. Izmaylov

AI总结：

本研究提出更一般的精确可解量子比特哈密顿量，其通过so(N)李代数直和定义，并结合酉算子、Clifford酉与线路中途测量进行测量，应用于分子电子哈密顿量分解后显著减少了估计期望值所需的总测量次数。

摘要：

精确可解哈密顿量在使用量子计算机研究量子多体系统时非常有用。在变分量子本征求解器中，将目标哈密顿量分解为精确可解片段，可通过重复量子测量来评估能量。在本研究中，我们应用了比以往考虑的更一般的精确可解量子比特哈密顿量类别，以解决哈密顿量测量问题。最一般的精确可解哈密顿量由以下条件定义：在一组Pauli对称性的每个同时本征空间内，哈密顿量有效地作为so(N)李代数直和的一个元素，因此可以使用相关李群中的酉算子、Clifford酉算子和线路中途测量的组合来测量。将此类哈密顿量通过图划分技术应用于分解分子电子哈密顿量，与以往使用的精确可解量子比特哈密顿量相比，显示出估计期望值所需的总测量次数减少。

英文摘要：

Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. In the variational quantum eigensolver, a decomposition of the target Hamiltonian into exactly solvable fragments can be used for evaluation of the energies via repeated quantum measurements. In this work, we apply more general classes of exactly solvable qubit Hamiltonians than previously considered to address the Hamiltonian measurement problem. The most general exactly solvable Hamiltonians are defined by the condition that, within each simultaneous eigenspace of a set of Pauli symmetries, the Hamiltonian acts effectively as an element of a direct sum of so(N) Lie algebras, and can therefore be measured using a combination of unitaries in the associated Lie group, Clifford unitaries, and mid-circuit measurements. Application of such Hamiltonians to decomposing molecular electronic Hamiltonians via graph partitioning techniques shows a reduction in the total number of measurements required to estimate the expectation value compared with previously used exactly solvable qubit Hamiltonians.

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