Resolution of the Relative Energies of the Benzyne Isomers on a Quantum Computer Using a Contracted Schr\"odinger Equation
Scott E. Smart, Jan-Niklas Boyn, David A. Mazziotti · arXiv (Cornell University) · 2021
The simulation of strongly correlated many-electron systems is one of the most promising applications for near-term quantum devices. Here we develop and apply a family of quantum simulation algorithms for electronic structure, based on the integration (or contraction) of the Schr\odinger equation onto the two-electron space. We showcase the family of algorithms by resolving the energy splittings of the ortho-, meta-, and para-isomers of benzyne ${\textrm C_6} {\textrm H_4}$ including the strongly correlated biradical para-benzyne. The quantum solution of the anti-Hermitian part of the contracted Schr\odinger equation (qACSE) provides a scalable approach with low circuit depth and few variational parameters that has its foundations in two-electron reduced density matrix (2-RDM) theory. Error in the 2-RDM is mitigated through projection of the 2-RDM measured by tomography onto the approximate set of physically realistic 2-RDMs defined by the 2-positive $N$-representability conditions. The relative energies exhibit single-digit millihartree errors, and the computed natural-orbital occupations capture significant differences in the electron correlation of the isomers including the biradical nature of the {\em para}-isomer.