Operator Ordering Ambiguity in Trotterized Unitary Coupled Cluster Theory and How to Take Advantage of It

The unitary coupled cluster (UCC) ansatz is an attractive choice for representing chemical wavefunctions on a quantum computer. In practice, a Trotter decomposition of the ansatz is necessary for convenient preparation on hardware. Finite-order Trotter decomposition of the same UCC ansatz, however, gives different Trotterized ansatz structures depending on the ordering of the individual operators in the Trotter product. We demonstrate that even after variationally optimizing these different parametrized ansatzë, one obtains dramatically different ground state energies, many of them superior to that of the un-Trotterized UCC energy. We consider our Adaptive, Derivative-Assembled, Pseudo-Trotterized Variational Quantum Eigensolver (ADAPT-VQE) through the lens of building a quasi-optimal, well-defined, Trotterized UCC-like ansatz, reflecting on why ADAPT is so much more parameter-efficient than UCC.