Quantum computation of molecular geometry via many-body nuclear spin echoes

TL;DR

This work introduces a quantum-information-inspired framework to extract long-range molecular structure information from nuclear spin dynamics via out-of-time-ordered correlators (OTOCs). It combines NMR OTOC experiments on labeled organic molecules in nematic solvents with classical molecular dynamics and quantum simulation on a superconducting processor, using TARDIS pulse sequences and Pauli-path zero-noise extrapolation to learn structural parameters. The authors demonstrate learning ortho-meta C–C distances and dihedral-angle distributions with OTOCs that rival conventional methods, and validate these insights with independent MQC data. By leveraging a swap-network quantum simulator and AlphaEvolve-optimized circuits, the study shows that quantum computation can mitigate classical-cost barriers in interpreting complex many-body spin dynamics and enable long-range structural constraints in chemistry and materials science.

Abstract

Quantum-information-inspired experiments in nuclear magnetic resonance spectroscopy may yield a pathway towards determining molecular structure and properties that are otherwise challenging to learn. We measure out-of-time-ordered correlators (OTOCs) [1-4] on two organic molecules suspended in a nematic liquid crystal, and investigate the utility of this data in performing structural learning tasks. We use OTOC measurements to augment molecular dynamics models, and to correct for known approximations in the underlying force fields. We demonstrate the utility of OTOCs in these models by estimating the mean ortho-meta H-H distance of toluene and the mean dihedral angle of 3',5'-dimethylbiphenyl, achieving similar accuracy and precision to independent spectroscopic measurements of both quantities. To ameliorate the apparent exponential classical cost of interpreting the above OTOC data, we simulate the molecular OTOCs on a Willow superconducting quantum processor, using AlphaEvolve-optimized [5] quantum circuits and arbitrary-angle fermionic simulation gates. We implement novel zero-noise extrapolation techniques based on the Pauli pathing model of operator dynamics [6], to repeat the learning experiments with root-mean-square error $0.05$ over all circuits used. Our work highlights a computational protocol to interpret many-body echoes from nuclear magnetic systems using low resource quantum computation.

Figures (57)

• Figure 1: Making a longer molecular ruler with an out-of-time-ordered correlator (OTOC). a,b) A comparison between conventional spin transport measurements that infer distance restraints from single couplings, and OTOC measurements, which probe the growth of large quantum coherences through the H spin network. By utilizing all the couplings in the spin network, the OTOC is not limited in distance by the $1/r^3$ scaling that limits the distances measurable by conventional techniques. c) Our proposal to use a quantum computer to assist in processing OTOC (or other challenging-to-classically-simulate) data from a large spin cluster. Following nuclear magnetic resonance (NMR) data collection, the quantum computer provides an artificial system that is iteratively tuned ---via classical feedback--- until it matches experiment.
• Figure 2: Benchmarking the structural sensitivity of out-of-time-ordered correlators (OTOCs) in $[4-^{13}$C$]$-toluene. a) Description of the OTOC protocol (top) as implemented in a nuclear magnetic resonance (NMR) spectrometer (bottom). b) Cartoon showing the spread of the spin cluster through the molecule following the sequence in a). c) OTOC (red) and Loschmidt echo data (yellow) from the NMR experiment. Points show NMR experiment data with 1$\sigma$ confidence intervals (CI), compared to numerical simulations (lines). d) Sensitivity of the OTOC experiment to an artificial stretch of benzene between the ortho and meta carbon atoms (inset), with experimental data from b) overlaid (red). e) Simulated learning of the ortho-meta H-H distance $z_{\mathrm{om}}$ from OTOC data. (top) Red triangles show the covariance weighted mean error between simulation and NMR experiment, line shows a cubic fit with $1\sigma$ CI shaded. (bottom) Estimate of $z_{\mathrm{om}}$ (red) compared to reference data from the literature (gray), with bootstrapped $2\sigma$ CI.
• Figure 3: Alleviating the exponential cost of out-of-time-ordered correlator (OTOC) simulation with a quantum computer. a) Approximating nuclear spin evolution on superconducting quantum hardware. A Trotterized digital quantum simulation of the double quantum Hamiltonian is executed by compiling individual couplings with swap gates that permute spin indices. The compiled gate is executed using a pulse train divided into a Z rotation, partial population swap, and conditional phase gate. b) Error-mitigated simulations of the first five points of the OTOC curve on quantum hardware, swept over the same range of ortho-meta C-C bond lengths $z_{\mathrm{om}}$ as in Fig. \ref{['fig:fig2_sensitivity']}(c). The target simulation at $z_{\mathrm{om,\,r}}=2.46$ Å is emphasized (solid blue line), error bars are $1\sigma$ confidence intervals (CI). c) (upper) Comparison of the learning experiment using quantum and classical data. Fits (lines) are from a bootstrapped Gaussian process regression, with $1\sigma$ CI shaded. (lower) Comparison of two estimates of $z_{\mathrm{om}}$ to reference data, with bootstrapped $2\sigma$ CI.
• Figure 4: Refining a molecular mechanics model of the torsion free energy of [1-${}^{13}$C]-3',5'-dimethylbiphenyl (DMBP), validated by multiple quantum coherence (MQC) experiments. a) Workflow diagram identifying whether a task is performed in the nuclear magnetic resonance spectrometer (red), on the quantum computer (blue), or classically (yellow). b) Plots of the 9 potential of mean-force (PMF) candidate functions of the dihedral angle of DMBP. c) Out of time ordered correlators (OTOC) of DMBP, comparing experimental NMR data (red points), OTOC simulations run on the Willow chip using the most likely PMF (blue points), and classical simulations with added RF inhomogeneity (lines). d) Root-mean-square error (RMSE) of the OTOC or MQC peak position for the 9 candidate free energy surfaces shown in (b); lines are a Gaussian process fit. Error bars in all plots are $1\sigma$ CI except for the estimates of the PMF minimum which are shown with $2\sigma$ CI from bootstrapping.
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