Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents?

Abstract

The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, its usual implementation in the projected form becomes nonvariational when the excitations are truncated and therefore fails to describe quantum states characterized by strong electronic correlations. Thanks to its exponential form, CC can be naturally adapted to quantum algorithms. In particular, the quantum unitary CC (q-UCC) is a popular wavefunction Ansatz for the Variational Quantum Eigensolver (VQE). The variational nature of this approach can lead to significant advantages compared to its classical equivalent (in the projected form), in particular for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCC, approximations need to be introduced in order to make this approach implementable in a stateof-the-art quantum computer. In this work, we propose several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems such as H 4 , H 2 O and N 2 molecules, as well as the one-dimensional periodic Fermi-Hubbard chain. The results, which are in good agreement with the exact solutions, promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.

Orbital optimized unitary coupled cluster theory for quantum computer

“…In this study, we implement OO-VQE using a quantum circuit simulator; we propose an orbital optimized unitary coupled cluster doubles (OO-UCCD) as a wave-function model for OO-VQE. It must be noted that after posting the initial manuscript of this work on the arXiv preprint server, an implementation of OO-UCCD by Sokolov et al was uploaded on arXiv [55]. Their study carefully performed the cost and accuracy analysis of several variants of OO-UCCD methods, while our work focused on its fully variational nature and computed analytical derivatives for geometry optimizations which are a vital part of quantum chemical calculations.…”

Hardware efficient quantum algorithms for vibrational structure calculations

“…74,75 However, there is still no clear evidence that Barren plateaus will play an important role when using the UVCC Ansatz, since physically motivated reductions of the number of variational parameters can be applied, at the cost of reducing the accuracy of the calculation. 54,55,[76][77][78][79] Additionally, the convergence rate when working with the UVCC Ansatz for larger, strongly anharmonic molecules may be improved by initializing the VQE parameters with a more accurate guess. As already suggested for the electronic-structure case, such a guess may be constructed from the VMP2 wavefunction.…”

“…Moreover, the number of excitations can be reduced using traditional approaches for the selection of the relevant subset. 54,55,[76][77][78][79] 3.3 Quantum computation of vibrational structures on existing hardware…”

Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor

“…The energy corresponding to a given set of parameters is obtained by computing the expectation value of the system Hamiltonian and becomes therefore a function of the gate variables. The VQE has already been successfully applied to the simulation of the ground-state properties of simple molecular systems on quantum hardware [12][13][14] and extended to more complex molecules in quantum simulators [15,16].…”