A hybrid quantum algorithm to detect conical intersections

Quantum, vol. 8, pp. 1259

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 π 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 π ), 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 ( H 2 C = N H ).

Authors 6

1. Emiel Koridon Aachen Instituut-Lorentz

   Leiden University · Vrije Universiteit Amsterdam

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, 2300RA Leiden, The Netherlands

   Theoretical Chemistry, Vrije Universiteit, 1081HV Amsterdam, The Netherlands

2. Joana Fraxanet

   Institute of Photonic Sciences

   Affiliation as printed

   ICFO - Institut de Ciències Fotòniques, 08860 Castelldefels (Barcelona), Spain

3. Alexandre Dauphin

   Institute of Photonic Sciences · Pasqal (France)

   Affiliation as printed

   ICFO - Institut de Ciències Fotòniques, 08860 Castelldefels (Barcelona), Spain

   PASQAL SAS, 2 av. Augustin Fresnel Palaiseau, 91120, France

4. Lucas Visscher

   Vrije Universiteit Amsterdam

   Affiliation as printed

   Theoretical Chemistry, Vrije Universiteit, 1081HV Amsterdam, The Netherlands

5. Thomas E. O apos Brien Aachen Instituut-Lorentz

   Leiden University · Google (United States)

   Affiliation as printed

   Google Research, Munich, 80636 Bavaria, Germany

   Instituut-Lorentz, Universiteit Leiden, 2300RA Leiden, The Netherlands

6. Stefano Polla Aachen Instituut-Lorentz

   Leiden University · Google (United States)

   Affiliation as printed

   Google Research, Munich, 80636 Bavaria, Germany

   Instituut-Lorentz, Universiteit Leiden, 2300RA Leiden, The Netherlands