Simulating quantum chemistry in the seniority-zero space on qubit-based quantum computers

Abstract

Accurate quantum chemistry simulations remain challenging on classical computers for problems of industrially relevant sizes and there is reason for hope that quantum computing may help push the boundaries of what is technically feasible. While variational quantum eigensolver (VQE) algorithms may already turn noisy intermediate scale quantum (NISQ) devices into useful machines, one has to make all efforts to use the scarce quantum resources as efficiently as possible. We combine the so-called restricted approximation from computational quantum chemistry with techniques for simulating molecular chemistry on gate-based quantum computers and thereby obtain a much more resource efficient algorithm with little accuracy loss. In fact, we show that using the quantum resources freed up by means of the restricted approximation for increasing the basis set can lead to more accurate results and reductions in the necessary number of quantum computing runs (shots) by several orders of magnitude, already for a simple system such as lithium hydride.

A quantum computing view on unitary coupled cluster theory

“…Compared to similar classically solvable models ( e.g. UpCCD 128 ) the corresponding circuits are significantly lower in depth. Hence, while a quantum advantage in the long term is not to be expected, this ansatz can prove valuable for state preparation.…”

The prospects of quantum computing in computational molecular biology

“…In the 3 years since that publication, algorithmic advances have already lowered the time requirements by several orders of magnitude [149]. In addition to more powerful electronic structure methods, faster versions of current approximate methods that have been explored recently [150,151] may well accelerate prototyping, which would be of use for example in exploring reaction coordinates of enzymatic reactions, a problem that predates computational enzymology [152]. Moreover, through better understanding of intermolecular interactions, catalyzed by access to fully correlated calculations, or by access to faster throughput that improves parametrization, quantum simulations may well indirectly improve nonquantum simulation methods like force fields.…”

Simulating the electronic structure of spin defects on quantum computers

“…The expectation values of all Pauli correlators were obtained by measuring 8192 times N c independent circuits, where N c is the number of groups of Pauli correlators that contain commuting operators. The number of electrons may be determined simultaneously from the group of operators that only contains diagonal Pauli correlators (those with only I and Z gates) [104]. In our calculations we discard all measurement outcomes that do not conserve the number of electrons.…”

“…enforcement of the post-selection rule all measured energies turn out to be higher than the reference value for the ground state. Interestingly, the same post-selection method has also been adopted in the calculation of the total energy of LiH [104], yielding a notable improvement in the accuracy of energy measurements, with a small overall error of about 1 kcal/mol.…”