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

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum physics

Background:

• The Born-Oppenheimer approximation simplifies molecular simulations by separating electronic and nuclear motion.
• Accurately simulating molecular systems requires incorporating quantum effects for both electrons and nuclei.
• Current quantum computing hardware presents challenges for complex molecular simulations.

Purpose of the Study:

• To develop a multicomponent unitary coupled cluster (mcUCC) framework for quantum simulations.
• To include both electronic and nuclear quantum effects beyond the Born-Oppenheimer approximation.
• To demonstrate the feasibility and accuracy of these simulations on current quantum hardware.

Main Methods:

• Utilized the nuclear-electronic orbital formalism to construct mcUCC ansätze.
• Applied a local unitary cluster Jastrow ansatz to reduce resource costs.
• Implemented the framework on IBM Q's Heron superconducting quantum hardware.
• Employed the Physics-Inspired Extrapolation error mitigation protocol.

Main Results:

• Successfully performed mcUCC simulations for positronium hydride and molecular hydrogen with a quantum proton.
• Achieved ground-state energies within chemical accuracy, demonstrating the effectiveness of error mitigation.
• Analyzed hardware requirements for different excitation truncations in mcUCC.

Conclusions:

• This work provides the first demonstration of error-mitigated multicomponent correlated simulations on quantum hardware.
• The developed framework successfully unifies electronic and nuclear degrees of freedom in quantum simulations.
• Outlines a path toward scalable quantum algorithms for molecular systems incorporating quantum nuclear effects.