Noise-independent route toward the genesis of a COMPACT ansatz for molecular energetics: A dynamic approach.

Recent advances in quantum information and quantum science have inspired the development of various compact, dynamically structured ansätze that are expected to be realizable in Noisy Intermediate-Scale Quantum (NISQ) devices. However, such ansätze construction strategies hitherto developed involve considerable measurements, and thus, they deviate significantly in the NISQ platform from their ideal structures. Therefore, it is imperative that the usage of quantum resources be minimized while retaining the expressivity and dynamical structure of the ansatz that can adapt itself depending on the degree of correlation. We propose a novel ansatz construction strategy based on the ab initio many-body perturbation theory that requires no pre-circuit measurement and, thus, remains structurally unaffected by any hardware noise. The accuracy and quantum complexity associated with the ansatz are solely dictated by a pre-defined perturbative order, as desired, and, hence, are tunable. Furthermore, the underlying perturbative structure of the ansatz construction pipeline enables us to decompose any high-rank excitation that appears in higher perturbative orders into the product of various low-rank operators, and it thus keeps the execution gate-depth to its minimum. With a number of challenging applications on strongly correlated systems, we demonstrate that our ansatz performs significantly better, both in terms of accuracy, parameter count, and circuit depth, in comparison to the allied unitary coupled cluster based ansätze.

Development of a compact Ansatz via operator commutativity screening: Digital quantum simulation of molecular systems.

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.

A Synergistic Approach towards Optimization of Coupled Cluster Amplitudes by Exploiting Dynamical Hierarchy.

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.

Dual exponential coupled cluster theory: Unitary adaptation, implementation in the variational quantum eigensolver framework and pilot applications.

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 parameterized unitary Ansätze. 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.