A hybrid quantum algorithm to detect conical intersections

TL;DR

This paper introduces a hybrid quantum algorithm that efficiently detects conical intersections in molecular systems by estimating the Berry phase through a variational approach, enabling verification with bounded error.

Contribution

It presents a novel quantum algorithm leveraging variational methods and the Hadamard test to detect conical intersections via Berry phase estimation in molecular Hamiltonians.

Findings

Algorithm successfully detects conical intersections in toy models.

Bounded error allows for efficient verification of results.

Numerical demonstrations on small molecules validate the approach.

Abstract

Conical intersections are topologically protected crossings between the potential energy surfaces of a molecular Hamiltonian, known to play an important role in chemical processes such as photoisomerization and non-radiative relaxation. They are characterized by a non-zero Berry phase, which is a topological invariant defined on a closed path in atomic coordinate space, taking the value $\pi$ when the path encircles the intersection manifold. In this work, we show that for real molecular Hamiltonians, the Berry phase can be obtained by tracing a local optimum of a variational ansatz along the chosen path and estimating the overlap between the initial and final state with a control-free Hadamard test. Moreover, by discretizing the path into $N$ points, we can use $N$ single Newton-Raphson steps to update our state non-variationally. Finally, since the Berry phase can only take two discrete values (0 or $\pi$), our procedure succeeds even for a cumulative error bounded by a constant; this allows us to bound the total sampling cost and to readily verify the success of the procedure. We demonstrate numerically the application of our algorithm on small toy models of the formaldimine molecule (\ce{H2C=NH}).