自然轨道与量子互信息的稀疏性
Natural orbitals and sparsity of quantum mutual information
AI总结：
本文利用 WAHTOR 方法研究量子计算关联拟设，证明收敛轨道即自然轨道，并使量子互信息矩阵最大稀疏化，从而以更少量子比特对编码电子关联。
摘要：
自然轨道在电子结构和量子化学中被定义为使基态的单粒子约化密度矩阵对角化的（分子）轨道，几十年来一直被推测为描述电子关联的理想参考轨道。在本工作中，我们应用 Wavefunction-Adapted Hamiltonian Through Orbital Rotation（WAHTOR，通过轨道旋转的波函数适配哈密顿量）方法，研究用于量子计算的关联经验拟设。在所有考察的代表性分子中，我们表明收敛后的轨道与自然轨道一致。有趣的是，在此类轨道上构建的量子互信息矩阵也具有最大稀疏性，这清楚地表明这种轨道选择确实能够提供描述电子关联的最优基。因此，关联被编码在数量更少的、对量子互信息矩阵有贡献的量子比特对中。
英文摘要：
Natural orbitals, defined in electronic structure and quantum chemistry as the (molecular) orbitals diagonalizing the one-particle reduced density matrix of the ground state, have been conjectured for decades to be the perfect reference orbitals to describe electron correlation. In the present work we applied the Wavefunction-Adapted Hamiltonian Through Orbital Rotation (WAHTOR) method to study correlated empirical ansätze for quantum computing. In all representative molecules considered, we show that the converged orbitals are coinciding with natural orbitals. Interestingly, the resulting quantum mutual information matrix built on such orbitals is also maximally sparse, providing a clear picture that such orbital choice is indeed able to provide the optimal basis to describe electron correlation. The correlation is therefore encoded in a smaller number of qubit pairs contributing to the quantum mutual information matrix.
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