Operator Relationship between Conventional Coupled Cluster and Unitary Coupled Cluster

The chemistry community has long sought the exact relationship between conventional and unitary coupled cluster ansatz for a single-reference system, especially given interest in performing quantum on computers. In this work, we show how one can use operator manipulations by exponential disentangling identity Hadamard lemma to relate factorized form of coupled-cluster approximation (the is required, because some amplitudes are operator-valued do not commute with other terms). By employing Trotter product formula, then standard ansatz. dependence also be removed at expense requiring even more higher-rank operators, finally yielding cluster. algebraic approach daunting carry out hand, but automated computer small enough systems.