In this paper, we have developed a unitary variant of a double exponential coupled cluster theory, which is capable of handling molecular strong correlation with arbitrary electronic complexity. With the Hartree-Fock determinant taken as the reference, we introduce a sequential product of parametrized unitary ansatze. While the first unitary, containing the excitation operators, acts directly on the reference determinant, the second unitary, containing a set of rank-two, vacuum-annihilating scattering operators, has nontrivial action only on certain entangled states. We demonstrate the theoretical bottleneck of such an implementation in a classical computer, whereas, the same is implemented in the hybrid quantum-classical variational quantum eigensolver framework with a reasonably shallow quantum circuit without any additional approximation. We have further introduced a number of variants of the proposed ansatz with different degrees of sophistication by judiciously approximating the scattering operators. With a number of applications on strongly correlated molecules, we have shown that all our schemes can perform uniformly well throughout the molecular potential energy surface without significant additional implementation cost over the conventional unitary coupled cluster approach with single and double excitations.
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.
The iterative quantum phase estimation algorithm (IQPE) is theoretically appealing in its wide scope of being able to handle electronic correlation. However, the quality of the initial input state strongly enhances the probability of landing on the desired eigenstate. In this work, we systematically study two different parametrization schemes of the unitary coupled cluster (UCC) ansätz in the variational quantum eigensolver (VQE) framework toward the reference state preparation for IQPE. The efficacy of the UCC variants toward an appropriate state preparation is studied with prototypical H4 molecule on a circle. While the conventional UCC ansätz can lead to high success probability across various degrees of electronic complexity, a resource efficient minimally parametrized UCC ansätz consisting of active space excitations is shown to incorporate the essential static correlation in the reference state description. We demonstrate that such a carefully prepared initial state can significantly reduce the effects of noise due to sampling in the estimation of the desired eigenphase.
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