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

Abstract

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.

Iterative quantum phase estimation with variationally prepared reference state

“…While the state preparation through VQE has assumed an ideal quantum environment, one may also take into account the effect of finite number of measurements during the state preparation. Furthermore, it would be interesting to study the success probability of prepared state with more robust and low depth unitary ansätze (like k‐UpCCGSD [28], UiCCSDn [51]). These will be highlighted in one of our future publications.…”

Machine learning assisted construction of a shallow depth dynamic ansatz for noisy quantum hardware

“…The interwoven structure of the ansatz that includes high rank correlation through its decomposition into lower rank operators is reminiscent of a double exponential (factorized) coupled cluster ansatz 41 and its unitarized variant. 7 Such double exponential structure of the waveoperator in terms of two-body operators is crucial for the exactness of the wavefunction for which the variational minimum analytically satises the contracted Schrödinger equation (CSE) 42 a necessary and sufficient condition for the wavefunction to satisfy the Schrödinger equation. Contrarily, the wavefunctions generated from a single exponential with generalized two-body operators 43,44 do not satisfy the CSE.…”

“…For this comparison, we do not use additional error mitigation techniques. 35,[58][59][60][61][62][63] 4 Conclusions and future outlook…”

Deep Neural Network Assisted Quantum Chemistry Calculations on Quantum Computers

“…Recent works have proposed novel ways to improve the efficiency of the VQE algorithm, such as (i) proposing newer chemically inspired ansatzes like k-UpCCGSD with lower circuit depths than that of the UCCSD ansatz, (ii) modifying the existing UCCSD ansatz through operator screening or by using the newer variants of UCCSD like dual exponential variant for reducing the circuit depth, − and (iii) by employing embedding schemes and entanglement forging techniques for reducing the qubit requirement while working with larger molecules. , Specific to the issue with the parameter optimization in VQE, Tao et al proposed the deep neural network (DNN)-VQE method, where a DNN model is used to predict the final optimized variational parameters for the quantum circuit . Using such parameters as the initial point for a VQE calculation, the authors showed that the DNN-VQE method is able to accurately construct the PESs of several small molecules such as H 2 , LiH, BeH 2 , and H 4 .…”