The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analyzed as a multivariate time-discrete map where the concept of time appears in an implicit manner. With the observation that the cluster amplitudes have difference in their relaxation timescales with respect to the distributions of their magnitudes, the coupled cluster iteration dynamics are considered as a synergistic motion of coexisting slow and fast relaxing modes, manifesting a dynamical hierarchical structure. With the identification of the highly damped auxiliary amplitudes, their time variation can be neglected compared to the principal amplitudes which take much longer time to reach the fixed points. We analytically establish the adiabatic approximation where each of these auxiliary amplitudes are expressed as unique parametric functions of the collective principal amplitudes, allowing us to study the optimization with the latter taken as the independent degrees of freedom. Such decoupling of the amplitudes significantly reduces the computational scaling without sacrificing the accuracy in the ground state energy as demonstrated by a number of challenging molecular applications. A road-map to treat higher order post-adiabatic effects is also discussed.
Recent advancements in quantum information and quantum technology have stimulated a good deal of interest in the development of quantum algorithms toward the determination of the energetics and properties of many-fermionic systems. While the variational quantum eigensolver is the most optimal algorithm in the noisy intermediate scale quantum era, it is imperative to develop compact Ansätze with low-depth quantum circuits that are physically realizable in quantum devices. Within the unitary coupled cluster framework, we develop a disentangled Ansatz construction protocol that can dynamically tailor an optimal Ansatz using the one- and two-body cluster operators and a selection of rank-two scatterers. The construction of the Ansatz may potentially be performed in parallel over multiple quantum processors through energy sorting and operator commutativity prescreening. With a significant reduction in the circuit depth toward the simulation of molecular strong correlation, our dynamic Ansatz construction protocol is shown to be highly accurate and resilient to the noisy circumstances of the near-term quantum hardware.
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