Relativistic quantum chemistry on quantum computers

Libor Veis (1, 2) , Jakub Viŝňák (1) , Timo Fleig (3) , Stefan Knecht (4) , Trond Saue (3) , Lucas Visscher (5) , Jiří Pittner (1)

1 J. Heyrovský Institute of Physical Chemistry of the ASCR
2 UK - Univerzita Karlova [Praha, Česká republika] = Charles University [Prague, Czech Republic]
3 GMO - Groupe THEO (LCPQ)
4 SDU - University of Southern Denmark
5 Amsterdam Center for Multiscale Modeling

The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only the nonrelativistic regime (i.e., the Schrödinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a 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 three qubits and nine or ten controlled-not (cnot) gates, which implement a proof-of-principle relativistic quantum chemical calculation for this molecule and might be suitable for an experimental realization.

Mots clés: ALGORITHM; COMPUTATION; SIMULATION

Domaines: Chimie théorique et/ou physique

Libor Veis, Jakub Viŝňák, Timo Fleig, Stefan Knecht, Trond Saue, et al.. Relativistic quantum chemistry on quantum computers. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2012, 85, pp.030304. ⟨10.1103/PhysRevA.85.030304⟩. ⟨hal-00760654⟩