Title: Quantum Computing Algorithms for the Study of Quantum Nuclear Dynamics and Vibrational Spectroscopy

Abstract: This talk presents novel quantum algorithms for simulating quantum nuclear dynamics on near-term quantum simulators and quantum computers. Understanding the quantum behavior of nuclei is essential for accurately describing chemical reactions involving light elements like hydrogen. These processes are critical to a wide range of problems of technological, atmospheric, and biological significance. However, these quantum dynamical studies are hindered by the exponential scaling in the computational cost for (a) the accurate computation of the underlying potential energy landscapes and (b) the time evolution of the nuclear wavefunctions on these precisely computed surfaces. With recent theoretical and experimental advances in quantum information science, quantum computing appears to have the potential to address these otherwise intractable problems, though its advantage is still being explored. Recently, commercial quantum computing platforms have been developed, along with algorithms designed to simulate quantum mechanical processes. However, these approaches have largely been limited to strongly correlated electronic systems and chemical dynamics primarily within the harmonic approximation. Here, we present novel quantum computing protocols that enable the accurate simulation of quantum wavepacket dynamics on quantum computing architectures. The focus will be on both analog and digital quantum algorithms for chemical dynamics simulations. We develop a mapping protocol to effect the study of such quantum nuclear dynamic problems onto generalized Ising model Hamiltonian, realizable on an ion-trap quantum hardware, as well as other quantum hardware. Towards this, we inspect the symmetries within the generalized Ising model Hamiltonian onto which we map our quantum nuclear Hamiltonian. This study allows us to characterize the general class of problems that can be simulated using such hardware systems. We further discuss quantum circuit decomposition techniques that allow more accurate and general treatments of such problems on quantum hardware. The performance of our mapping protocol and circuit decomposition method is demonstrated for a range of hydrogen-bonded systems of significance in multiple chemical problems. Our mapping protocol also allows us to emulate the wavepacket dynamics on a two-qubit ion-trap quantum computer and subsequently extract vibrational properties of the shared proton within spectroscopic accuracies. The methods discussed here form the basis for multi-dimensional quantum nuclear studies.

*This work was conducted at Indiana University Bloomington under the supervision of Srinivasan Iyengar (Department of Chemistry) in collaboration with Phil Richerme (Department of Physics, Indiana University Bloomington) and Melissa Revelle (Sandia National Laboratories, Albuquerque, NM).

Lunch will be provided at 12:30 PM in EQuad J401.