A quantum mechanical NMR simulation algorithm for protein-scale spin systems

Abstract

Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling simulation methods have not so far been available. Here, we report such a method and illustrate its performance by simulating common 2D and 3D liquid state NMR experiments (including accurate description of spin relaxation processes) on isotopically enriched human ubiquitin - a protein containing over a thousand nuclear spins forming an irregular polycyclic three-dimensional coupling lattice. The algorithm uses careful tailoring of the density operator space to only include nuclear spin states that are populated to a significant extent. The reduced state space is generated by analyzing spin connectivity and decoherence properties: rapidly relaxing states as well as correlations between topologically remote spins are dropped from the basis set. In the examples provided, the resulting reduction in the quantum mechanical simulation time is by many orders of magnitude.

Submitted for publication

References in corpus (1)

• The density-matrix renormalization group in the age of matrix product states

Cited by in corpus (6)

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• Auxiliary matrix formalism for interaction representation transformations, optimal control and spin relaxation theories
• Exact NMR simulation of protein-size spin systems using tensor train formalism
• Digital quantum simulation of NMR experiments
• Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments
• Bang-Bang Optimal Control of Large Spin Systems: Enhancement of ${}^{13}$C-${}^{13}$C Singlet-Order at Natural Abundance