Elucidating reaction mechanisms on quantum computers

Abstract

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

Keywords: quantum algorithms; quantum computing; reaction mechanisms.

Fig. 1.

(Left) X-ray crystal structure 4WES (21) of the nitrogenase MoFe protein from Clostridium pasteurianum taken from the protein database (the backbone is colored in green, and hydrogen atoms are not shown), (Middle) the close protein environment of the FeMoco, and (Right) the structural model of FeMoco considered in this work (C, gray; O, red; H, white; S, yellow; N, blue; Fe, brown; and Mo, cyan).

Fig. 2.

Generic flowchart of a computational reaction mechanism elucidation with a quantum computer part that delivers a quantum full configuration interaction (QFCI) energy in a (restricted) complete active orbital space (CAS). Once a structural model of the active chemical species (here FeMoco, top right) embedded in a suitable environment (the metalloprotein, top left) is chosen, structures of potential intermediates can be set up and optimized. Molecular orbitals are then optimized for a suitably chosen Fock operator. A four-index transformation from the atomic orbital to the molecular basis produces all integrals required for the second-quantized Hamiltonian. Once the quantum computer produces the (ground state) energy of this Hamiltonian, this energy can be supplemented by corrections that consider nuclear motion effects to yield enthalpic and entropic quantities at a given temperature according to standard protocols (e.g., from DFT calculations). The temperature-corrected energy differences between stable intermediates and transition structures then enter rate expressions for kinetic modeling. For complex chemical mechanisms, this modeling might point to the exploration of additional structures.

Fig. 3.

Hardware architectures for quantum computers. We show the architecture of a hybrid classical/quantum computer for quantum chemistry-type calculations. Shown are (A) a serial architecture using a single rotation factory and (B) a parallel architecture with multiple rotation factories. The quantum computer acts as an accelerator to the classical supercomputer. It consists of a classical control front end, a main quantum processor, and a number of auxiliary processing units. The devices labeled QRot build single-qubit rotations using $\pi /8$ rotations created in the T-gate factories labeled Tfac. Red arrows denote quantum communication, and blue arrows represent classical communication.