A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

Abstract

The Heisenberg exchange coupling parameterJ(H= −2JSi·Sj) characterises the isotropic magnetic interaction between unpaired electrons, and it is one of the most important spin Hamiltonian parameters of multi-spin open shell systems. TheJvalue is related to the energy difference between high-spin and low-spin states, and thus computing the energies of individual spin states are necessary to obtain theJvalues from quantum chemical calculations. Here, we propose a quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing theJvalue directly, without calculating the energies of individual spin states. The BxB algorithm is composed of the quantum simulations of the time evolution of a broken-symmetry wave function under the Hamiltonian with an additional termjS2, the wave function overlap estimation with the SWAP test, and Bayesian optimisation of the parameterj. Numerical quantum circuit simulations for H2under a covalent bond dissociation, C, O, Si, NH, OH+, CH2, NF, O2, and triple bond dissociated N2molecule revealed that the BxB can compute theJvalue within 1 kcal mol−1of errors with less computational costs than conventional quantum phase estimation-based approaches.