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

Area of Science:

• Quantum Computing
• Molecular Biophysics
• Nuclear Magnetic Resonance (NMR) Spectroscopy

Background:

• Inferring molecular nuclear spin Hamiltonians is crucial for understanding molecular structure and dynamics.
• Classical simulation of anisotropic dipolar interactions within Hamiltonians presents significant computational challenges.
• Nuclear magnetic resonance (NMR) provides time-resolved measurements of spin-spin correlators, a key data source for Hamiltonian inference.

Purpose of the Study:

• To develop and demonstrate a quantum algorithm for inferring molecular nuclear spin Hamiltonians.
• To focus on learning the anisotropic dipolar term, which is computationally intensive for classical methods.
• To explore the application of quantum computation for analyzing molecular structures using NMR data.

Main Methods:

• Proposing a quantum algorithm utilizing time-resolved spin-spin correlator measurements from NMR.
• Implementing algorithms for both noisy near-term and fault-tolerant quantum computers.
• Estimating the Jacobian and Hessian of the learning problem directly on a quantum computer to learn Hamiltonian parameters.
• Benchmarking the method on a protein (ubiquitin) confined on a membrane, analyzing small spin clusters.

Main Results:

• Demonstrated the quantum algorithm's ability to learn Hamiltonian parameters by estimating Jacobian and Hessian.
• Showcased the algorithm's convergence on a model system (spin clusters of ubiquitin).
• Observed a correlation between the multifractal dimension of eigenstates and the learnability of Hamiltonian parameters across a phase transition.

Conclusions:

• The developed quantum algorithm offers a promising approach for inferring molecular nuclear spin Hamiltonians, particularly the anisotropic dipolar term.
• Quantum computation, especially on near-term devices, shows potential as an early beyond-classical application for molecular structure analysis.
• The findings suggest that quantum methods could enhance the interpretation and development of novel NMR techniques.