Quantum Computing for Nuclear Dynamics

G. P. Berman, David K Campbell, Gary D. Doolen +1 more

Joseph A. Formaggio

Juan C. Dominguez, Ismael de Farias, Jorge A. Morales

We present the first step toward the quantum computing (QC) formulation of the electron nuclear dynamics (END) method within the variational quantum simulator (VQS) scheme: END/QC/VQS. END is a time-dependent, variational, on-the-flight, and non-adiabatic method to simulate chemical reactions. END represents nuclei with frozen Gaussian wave packets and electrons with a single-determinantal state in the Thouless non-unitary representation. Within the hybrid quantum/classical VQS, END/QC/VQS currently evaluates the metric matrix M and gradient vector V of the symplectic END/QC equations on the QC software development kit QISKIT, and calculates basis function integrals and time evolution on a classical computer. To adapt END to QC, we substitute the Thouless non-unitary representation with Fukutome unitary representation. We derive the first END/QC/VQS version for pure electronic dynamics in multielectron chemical models consisting of two-electron units with fixed nuclei. Therein, Fukutome unitary matrices factorize into triads of one-qubit rotational matrices, which leads to a QC encoding of one electron per qubit. We design QC circuits to evaluate M and V in one-electron diatomic molecules. In log2-log2 plots, errors and deviations of those evaluations decrease linearly with the number of shots and with slopes = −1/2. We illustrate an END/QC/VQS simulation with the pure electronic dynamics of H2+ We discuss the present results and future END/QC/QVS extensions.

Natalie Kloco

Ionel Stetcu

Description of quantum many-body dynamics is extremely challenging on classical computers, as it requires taking into account many degrees of freedom. In nuclear physics, this translates on a large number of break up channels that have to be taken into account depending on available energy. Even using classical computing exascale capabilities will not allow a full description of dynamical processes starting from internucleon interactions beyond drastic approximations. On the other hand, the dynamics can be naturally implemented on quantum hardware that is designed to easily handle unitary transformations, and hence the hope that in the future we will be able to obtain reaction observables from first principles. In this contribution, I describe the main steps involved in quantum algorithms and review our efforts to apply quantum computing to the nuclear many-body problem using realistic inter-nucleon interactions.

Anurag Dwivedi, A. J. Rasmusson, Philip Richerme +1 more

Quantum nuclear dynamics with wavepacket time evolution is classically intractable and viewed as a promising avenue for quantum information processing. Here, we use IonQ, Inc.'s 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 a 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 the 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 computation are in agreement with those obtained from classical simulations to within a fraction of a kilocalorie per mole, 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 of parallel quantum computation on a distributed set of ion-trap quantum computers.