  Quantum nuclear dynamics with wavepacket time-evolution is classically
intractable and viewed as a promising avenue for quantum information
processing. Here, we use an IonQ 11-qubit trapped-ion quantum computer,
Harmony, to study the quantum wavepacket dynamics of a shared-proton within a
short-strong hydrogen-bonded system. We also provide the first application of
distributed quantum computing for chemical dynamics problems, where the
distributed set of quantum processes is constructed using a tensor network
formalism. For a range of initial states, we experimentally drive the ion-trap
system to emulate the quantum nuclear wavepacket as it evolves along the
potential surface generated from electronic structure. Following the
experimental creation of the nuclear wavepacket, we extract measurement
observables such as its time-dependent spatial projection and its
characteristic vibrational frequencies to good agreement with classical
results. Vibrational eigenenergies obtained from quantum computational are in
agreement with those obtained from classical simulations to within a fraction
of a kcal/mol, thus suggesting chemical accuracy. Our approach opens a new
paradigm for studying the quantum chemical dynamics and vibrational spectra of
molecules and also provides the first demonstration for parallel quantum
computation on a distributed set of ion-trap quantum computers.
