Relativistic quantum chemistry on quantum computers

TL;DR

This paper introduces the first quantum algorithm for relativistic quantum chemistry, enabling efficient computation of molecular energies considering relativistic effects, demonstrated through simulations of spin-orbit splitting in SbH.

Contribution

It presents a novel quantum algorithm for solving the Dirac-Coulomb Hamiltonian, extending quantum chemistry computations into the relativistic regime.

Findings

Successfully simulated spin-orbit splitting in SbH

Proposed quantum circuits with 3 qubits and minimal CNOTs

Demonstrated potential for experimental realization

Abstract

Last years witnessed a remarkable interest in application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, even first proof-of-principle experimental realizations have been reported. However, so far only the non-relativistic regime (i.e. Schroedinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. In this letter we present the first quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with 3 qubits and 9 or 10 CNOTs, which implement a proof-of-principle relativistic quantum chemical calculation for this molecule and might be suitable for an experimental realization.