Prospects for NMR spectral prediction on fault-tolerant quantum computers

Advanced atomic magnetometers have made it possible to acquire nuclear magnetic resonance spectra in zero to ultralow magnetic fields. This regime carries the benefit of compact, low-cost instrumentation with reduced spin relaxation effects and the ability to probe phenomena that are inaccessible in conventional high-field experiments. A trade-off is that the resulting spectra must be interpreted using simulations that are taxing for classical computation. Working by example for small-molecule and protein spectroscopy, we demonstrate that these simulations are a promising target for fault-tolerant quantum computation. Our holistic analysis spans from input selection to the construction of explicit circuits for qubitized quantum dynamics. By maintaining parity with experimental requirements, we demonstrate how certain cases might be especially promising for early fault-tolerant architectures. Notably, valuable natural products and small proteins could be simulated with a few hundred logical qubits and less than <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msup> <a:mn>10</a:mn> <a:mn>12</a:mn> </a:msup> <a:mo> </a:mo> <a:mi>T</a:mi> </a:math> gates, corresponding to days of runtime with foreseeable hardware based on spin or superconducting qubits.