Day 1 Dec-2 2021
Session 2 14:00-14:45



Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments

*† Thomas E. O’Brien, ‡ Lev. B. Ioffe, ‡ Yuan Su, § David Fushman, ‡ Hartmut Neven, ‡ Ryan Babbush, and ‡ Vadim Smelyanskiy
*lead presenter
† teobrien@google.com, Google Quantum AI, Munich, Germany
‡ Google Quantum AI, California, USA
§ University of Maryland, Maryland, USA

We propose a quantum algorithm (ArXiv:2109.02163) for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging to classically simulate in some contexts. We demonstrate the ability to directly estimate the Jacobian and Hessian of the corresponding learning problem on a quantum computer, allowing us to learn the Hamiltonian parameters. We develop algorithms for performing this computation on both noisy near-term and future fault-tolerant quantum computers. We argue that the former is promising as an early beyond-classical quantum application since it only requires evolution of a local spin Hamiltonian. We investigate the example of a protein (ubiquitin) confined in a membrane as a benchmark of our method. We isolate small spin clusters, demonstrate the convergence of our learning algorithm on one such example, and then investigate the learnability of these clusters as we cross the ergodic-MBL phase transition by suppressing the dipolar interaction. We see a clear correspondence between a drop in the multifractal dimension measured across many-body eigenstates of these clusters, and a transition in the structure of the Hessian of the learning cost-function (from degenerate to learnable). Our hope is that such quantum computations might enable the interpretation and development of new NMR techniques for analyzing molecular structure.



FIG. 1. Cartoon of the “phases of learnability” of a quantum Hamiltonian. In the red region, the set of experimental data is insufficient to distinguish candidate Hamiltonians. In the blue region, the experimental data is sufficient to learn Hamiltonian structure, but this learning may be achieved classically, rendering a quantum computer unnecessary. The intermediary green region is the area we target with our quantum assisted Hamiltonian learning algorithm.

Reference:

M.J. Pacholski, G. Lemut, O. Ovdat, I. Adagideli, and C.W.J. Beenakker Phys. Rev. Lett. 126, 226801 (2021).







Tom is a research scientist at Google Quantum AI with a focus on developing new algorithms and finding new applications for quantum computers, and leading collaborations with industrial and academic partners in EMEA and APAC. Tom completed his undergraduate studies in Australia (University of Wollongong / University of Queensland), his masters at the Perimeter Institute in Waterloo, Canada, and his PhD (cum laude) at Leiden University. Before joining Quantum AI, Tom was a faculty member at Leiden University, where he was a founding member of the Applied Quantum Algorithms group and remains in a guest position.