Can a Quantum Computer Simulate Nuclear Magnetic Resonance Spectra Better than a Classical One?

TL;DR

The paper investigates whether a quantum computer can outperform classical methods in simulating NMR spectra. It introduces a spin-dependent cluster solver with linear scaling in the total number of spins for a fixed cluster size and benchmarks it against exact solutions and larger molecules, revealing strong accuracy in typical experimental regimes. The findings show that, at conventional high fields and reasonable broadening, the classical approach suffices, though highly symmetric, low-direct-coupling cases require extended clustering; zero-field NMR emerges as a potential regime where quantum advantage could be realized. This work clarifies where quantum resources may be beneficial for NMR spectroscopy and guides future investigations into quantum advantage in nonstandard magnetic-field regimes.

Abstract

The simulation of the spectra measured in nuclear magnetic resonance (NMR) spectroscopy experiments is a computationally non-trivial problem which, due to its natural interpretation as a quantum spin problem, maps in a straightforward way to a quantum computer. As such, it represents a problem for which such a device may provide some practical advantage over traditional computing methods. In order to understand the extent to which such problems may indeed provide examples of useful quantum advantage, it is important to understand the limitations of existing classical simulation methods. In this work, we benchmark our own classical solver designed to study such problems. This solver uses a clustering approximation to achieve a resource scaling which is linear in the total number of nuclear spins in a given molecule, for a fixed cluster size. The success of such an approximation would present a stark repudiation to the common claim that such problems require an exponential scaling of resources, the very claim which makes simulating an NMR spectra a candidate for quantum advantage. Our benchmarking results indicate that our approximation performs well throughout, and even somewhat beyond, the more typical experimental regimes. We discuss what implications this may have for future efforts to demonstrate quantum advantage in the context of NMR.

Figures (22)

• Figure 1: The convergence for selected molecules with 16 nuclear spins for the case of high broadening, for high, low, and very low field.
• Figure 2: The convergence for selected molecules with 16 nuclear spins for the case of low broadening, for high, low, and very low field.
• Figure 3: The convergence of the spectral function of Limonene as a function of cluster size, for low field and high broadening. The inverted horizontal axis is conventional in the chemistry literature.
• Figure 4: The molecule Triphenylphosphine oxide, with one phosphorous atom and fifteen hydrogen atoms.
• Figure 5: The computational time (on a logarithmic scale) required for selected molecules with 16 nuclear spins, for the case of very low field and low broadening.