Operator Relationship between Conventional Coupled Cluster and Unitary Coupled Cluster
Operator Relationship between Conventional Coupled Cluster and Unitary Coupled Cluster
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DOI：
10.3390/sym14030494
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发表时间：
2022-03-01
期刊：
影响因子：
2.7
通讯作者：
Freericks, James K.
中科院分区：
文献类型：
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作者：
Freericks, James K.
长期以来，化学界一直在寻找单一参照系的传统团簇和么正耦合团簇之间的确切关系，特别是考虑到人们对在量子计算机上执行量子化学的兴趣。在这项工作中，我们展示了如何使用指数解纠缠恒等式和Hadamard引理给出的算符操作来将么正耦合团簇近似的因式分解形式与传统耦合团簇近似的因式分解形式联系起来(因式分解形式是必需的，因为一些振幅是算子值的，并且不与其他项交换)。通过使用Trotter乘积公式，我们可以将因式分解形式与么正耦合簇的标准形式联系起来。耦合簇近似的因式分解形式的运算符依赖也可以被消除，但代价是需要更多的更高阶运算符，最终产生传统的耦合簇。这种方法的代数操作很难手工执行，但对于足够小的系统，可以在计算机上实现自动化。
The chemistry community has long sought the exact relationship between the conventional and the unitary coupled cluster ansatz for a single-reference system, especially given the interest in performing quantum chemistry on quantum computers. In this work, we show how one can use the operator manipulations given by the exponential disentangling identity and the Hadamard lemma to relate the factorized form of the unitary coupled-cluster approximation to a factorized form of the conventional coupled cluster approximation (the factorized form is required, because some amplitudes are operator-valued and do not commute with other terms). By employing the Trotter product formula, one can then relate the factorized form to the standard form of the unitary coupled cluster ansatz. The operator dependence of the factorized form of the coupled cluster approximation can also be removed at the expense of requiring even more higher-rank operators, finally yielding the conventional coupled cluster. The algebraic manipulations of this approach are daunting to carry out by hand, but can be automated on a computer for small enough systems.