Fluid fermionic fragments for optimizing quantum measurements of electronic Hamiltonians in the variational quantum eigensolver
Fluid fermionic fragments for optimizing quantum measurements of electronic Hamiltonians in the variational quantum eigensolver
复制标题
用于优化变分量子本征解算器中电子哈密顿量的量子测量的流体费米子片段
DOI：
10.22331/q-2023-01-03-889
复制
发表时间：
2022
期刊：
影响因子：
6.4
通讯作者：
A. Izmaylov
中科院分区：
文献类型：
--
作者：
Seonghoon Choi;Ignacio Loaiza;A. Izmaylov
测量分子电子哈密顿量的期望值是变分量子本征求解器的挑战性部分之一。一种广泛使用的策略是使用费米子算子代数将哈密顿量表示为可测量片段的总和。此类片段具有保存分子对称性的优点，可用于减少错误。获得哈密顿期望值所需的测量次数与片段方差之和成正比。在这里，我们引入了一种通过利用片段形式的灵活性来降低片段方差的新方法。由于占据数算子的幂等性，二电子片段的某些部分可以变成单电子片段，然后可以将其部分收集在纯单电子片段中。这种重新分配不会影响哈密顿量的期望值，但对每个片段的方差有非零贡献。所提出的方法通过使用量子波函数的经典有效代理估计的方差来找到最佳重新分配。对多个分子的数值测试表明，单电子项的重新分配使测量次数减少了一个数量级以上。
Measuring the expectation value of the molecular electronic Hamiltonian is one of the challenging parts of the variational quantum eigensolver. A widely used strategy is to express the Hamiltonian as a sum of measurable fragments using fermionic operator algebra. Such fragments have an advantage of conserving molecular symmetries that can be used for error mitigation. The number of measurements required to obtain the Hamiltonian expectation value is proportional to a sum of fragment variances. Here, we introduce a new method for lowering the fragments' variances by exploiting flexibility in the fragments' form. Due to idempotency of the occupation number operators, some parts of two-electron fragments can be turned into one-electron fragments, which then can be partially collected in a purely one-electron fragment. This repartitioning does not affect the expectation value of the Hamiltonian but has non-vanishing contributions to the variance of each fragment. The proposed method finds the optimal repartitioning by employing variances estimated using a classically efficient proxy for the quantum wavefunction. Numerical tests on several molecules show that repartitioning of one-electron terms lowers the number of measurements by more than an order of magnitude.
影响因子：
6.4
作者：
Preskill, John
通讯作者：
Preskill, John
影响因子：
7.6
作者：
Motta, Mario;Ye, Erika;Chan, Garnet Kin-Lic
通讯作者：
Chan, Garnet Kin-Lic