Multicomponent Unitary Coupled Cluster and Equation-of-Motion for Quantum Computation

The variational quantum eigensolver (VQE) algorithm combined with the unitary coupled cluster (UCC) ansatz has been developed for the quantum computation of molecular energies and wave functions within the Born-Oppenheimer approximation. Herein, this approach is extended to multicomponent systems to enable the quantum mechanical treatment of more than one type of particle, such as electrons and positrons or electrons and nuclei, without invoking the Born-Oppenheimer approximation. Specifically, we introduce the multicomponent unitary coupled cluster (mcUCC) method combined with the VQE algorithm for the calculation of ground-state energies and wave functions as well as the multicomponent equation-of-motion (mcEOM) method for the calculation of excitation energies. These methods are developed within the nuclear-electronic orbital (NEO) framework and are formulated in the qubit basis to enable implementations on quantum computers. Moreover, these methods are used to calculate the ground-state energy and excitation energies of positronium hydride, where both electrons and the positron are treated quantum mechanically, as well as the H-2 molecule, where both electrons and one proton are treated quantum mechanically. These applications validate the implementation and provide benchmark data for future calculations. The errors due to Trotterization of the mcUCC ansatz are also analyzed. This formalism, as well as the accompanying computer code, will serve as the basis for applications to more complex multicomponent systems, such as simulations of photoinduced nonadiabatic molecular processes, on both classical and quantum computers.

Automated summary

The VQE algorithm combined with the UCC ansatz has been extended to multicomponent systems for quantum mechanical treatment of more than one type of particle. The methods developed, such as mcUCC and mcEOM, enable calculation of ground-state energies, wave functions, and excitation energies in a nuclear-electronic orbital framework formulated in the qubit basis for implementation on quantum computers. Applications to positronium hydride and H-2 molecules validate the implementation and provide benchmark data for future calculations, while errors due to Trotterization of the mcUCC ansatz are also analyzed. This formalism and accompanying computer code will serve as the basis for applications to more complex multicomponent systems on both classical and quantum computers.