A variational quantum algorithm for nuclear dynamics on hybrid discrete-continuous quantum computers

We present a variational quantum algorithm (VQA) on hybrid discrete-continuous (HDC) quantum hardware for simulating Born-Oppenheimer dynamics. The approach represents the nuclear wave function as a superpositions of frozen Gaussians evolving according to the Kramer-Saraceno variational principle. The equations of motion involve matrix elements evaluated from measurements on HDC quantum circuits. The number of Gaussians in the wave function expansion increases exponentially with respect to the number ancilla qubits suggesting potentially more favorable scaling compared to analogous classical approaches. We benchmark the algorithm on a collection of harmonic and anharmonic model systems. For harmonic and Morse potentials, the algorithm converges to the numerically exact solution as the number of ancilla qubits increases. Our approach has also been implemented on a coupled qumode–qubit quantum platform simulating the photoelectron spectrum of sulfur dioxide. Finally, we show for a double-well potential, that while the VQA exhibits challenges in fully capturing wave function bifurcation, its accuracy improves as the number of ancilla qubits increases. Overall, this work establishes a promising pathway to simulating molecular dynamics on noisy intermediate-scale quantum devices.