Error-Mitigation Enabled Multicomponent Quantum Simulations beyond the Born-Oppenheimer Approximation

We introduce a multicomponent unitary coupled cluster (mcUCC) framework for quantum simulations of molecular systems that incorporate both electronic and nuclear quantum effects beyond the Born-Oppenheimer approximation. Using the nuclear-electronic orbital formalism, we construct mcUCC ansätze for positronium hydride and molecular hydrogen with a quantum proton, and analyze hardware requirements for different excitation truncations. To further reduce resource costs effectively, we employ the local unitary cluster Jastrow ansatz and implement it experimentally on IBM Q's Heron superconducting hardware. With the Physics-Inspired Extrapolation error mitigation protocol, the computed ground-state energies remain within chemical accuracy, consistent with the stated uncertainty level. These results provide the first demonstration of error-mitigated multicomponent correlated simulations on quantum hardware and outline a path toward scalable algorithms unifying electronic and nuclear degrees of freedom.