论文标题
常规耦合群集与统一耦合群之间的操作员关系
Operator relationship between conventional coupled cluster and unitary coupled cluster
论文作者
论文摘要
化学界长期以来一直在寻求单一参考系统的常规耦合群集ANSATZ之间的确切关系，尤其是考虑到有兴趣在量子计算机上执行量子化学。在这项工作中，我们展示了如何使用通过指数解脱的身份和Hadamard Lemma给出的操作员的操作，将单一耦合簇近似值的分解形式与传统偶联群集的分解形式的分解形式联系起来（需要分解形式（需要分解的形式），因为某些放大器是运算符和其他良好的频率，并且是其他方向的。通过采用托特产品公式，可以将分解形式与单一耦合群集Ansatz的标准形式联系起来。还可以以更高级别的运算符为代价去除耦合群集近似的分解形式的算子依赖性，最后产生常规的耦合群集。这种方法的代数操纵令人生畏，可以手工执行，但可以在计算机上自动化，以适应足够小的系统。
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.
