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arXiv:2510.19550

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

Chuanwei Zhang, Rodrigo G. Cortiñas, Amir H. Karamlou, Noll, N., Justin Provazza, Johannes Bausch, S. Shirobokov, White, A., Martin Claassen, S. H. Kang, Andrew Senior, Nenad Tomašev, Jonathan A. Gross, K. Lee, Schuster, T., William J. Huggins, Celik, H., Alex Greene, Borislav M. Kozlovskii, Francisco J. H. Heras, Andreas Bengtsson, Alejandro Grajales Dau, I. V. Drozdov, Bicheng Ying, Livingstone, W., Volodymyr Sivak, Noureldin Yosri, C. Quintana, Dmitry A. Abanin, Abbas, A., Rajeev Acharya, Laleh Aghababaie Beni, Georg Aigeldinger, Alcaraz, R., Alcaraz, S., Trond I. Andersen, M. Ansmann, Frank Arute, Kunal Arya, Walt Askew, Nikita Astrakhantsev, Juan Atalaya, Ballard, B., Joseph C. Bardin, Bates, H., Karimi, M. Bigdeli, Alexander Bilmes, Simon Bilodeau, Felix Borjans, Alexandre Bourassa, Jenna Bovaird, Bowers, D., L. Brill, Brooks, P., Michael Broughton, Browne, D. A., Brett Buchea, Bob B. Buckley, Tim Burger, Brian Burkett, Jamal Busnaina, Nicholas Bushnell, A. Cabrera, Juan Campero, Chang, H. -S., Chen, S., Z. Chen, Benjamin Chiaro, Liang-Ying Chih, Agnetta Y. Cleland, Cochrane, B., Cockrell, M., J. G. Cogan, Roberto Collins, P. Conner, Cook, H., William Courtney, A. L. Crook, Ben Curtin, Sayan Das, Martin Damyanov, Dripto M. Debroy, Luis Lorenzo, Sean Demura, De Rose, L. B., Agustín Di Paolo, Donohoe, P., A. Dunsworth, Valerie Ehimhen, Alec Eickbusch, Aviv Moshe Elbag, Lior Ella, Mahmoud Elzouka, Enriquez, D., Catherine Erickson, V. S. Ferreira, Flores, M., Leslie Flores Burgos, Ebrahim Forati, Ford, J.

Published Oct 22, 2025• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.2510.19550

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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 0.050.050.05 over all circuits used. Our work highlights a computational protocol to interpret many-body echoes from nuclear magnetic systems using low resource quantum computation.
We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging to classically simulate in some contexts. We demonstrate the ability to directly estimate the Jacobian and Hessian of the corresponding learning problem on a quantum computer, allowing us to learn the Hamiltonian parameters. We develop algorithms for performing this computation on both noisy near-term and future fault-tolerant quantum computers. We argue that the former is promising as an early beyond-classical quantum application since it only requires evolution of a local spin Hamiltonian. We investigate the example of a protein (ubiquitin) confined on a membrane as a benchmark of our method. We isolate small spin clusters, demonstrate the convergence of our learning algorithm on one such example, and then investigate the learnability of these clusters as we cross the ergodic to non-ergodic phase transition by suppressing the dipolar interaction. We see a clear correspondence between a drop in the multifractal dimension measured across many-body eigenstates of these clusters, and a transition in the structure of the Hessian of the learning cost function (from degenerate to learnable). Our hope is that such quantum computations might enable the interpretation and development of new NMR techniques for analyzing molecular structure.
Out-of-time-ordered correlators (OTOCs) are widely used to investigate information scrambling in quantum systems. However, directly computing OTOCs with classical computers is an expensive procedure. This is due to the need to classically simulate the dynamics of quantum many-body systems, which entails computational costs that scale rapidly with system size. Similarly, exact simulation of the dynamics with a quantum computer (QC) will either only be possible for short times with noisy intermediate-scale quantum devices or require a fault-tolerant QC which is currently beyond technological capabilities. This motivates a search for alternative approaches to determine OTOCs and related quantities. In this paper, we explore four parameterized sets of Hamiltonians describing local one-dimensional quantum systems of interest in condensed matter physics. For each set, we investigate whether classical kernel methods can accurately learn the XZ\mathit{XZ}XZ-OTOC and a particular sum of OTOCs as functions of the Hamiltonian parameters. We frame the problem as a regression task, generating small batches of labeled data with classical tensor network methods for quantum many-body systems with up to 40 qubits. Using this data, we train a variety of standard kernel machines and observe that the Laplacian and radial basis function kernels perform best, achieving a coefficient of determination (R2{R}^{2}R2) on testing sets of at least 0.7167, with averages between 0.8112 and 0.9822 for the various sets of Hamiltonians, together with small root mean squared error and mean absolute error. Hence, after training, the models can replace further uses of tensor networks for calculating an OTOC function of a system within the parameterized sets. Accordingly, the proposed method can assist with extensive evaluations of an OTOC function.
The dynamics of quantum many-body systems is characterized by quantum observables that are reconstructed from correlation functions at separate points in space and time1–3. In dynamics with fast entanglement generation, however, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. To circumvent this limitation and enable access to relevant dynamics in experimental systems, repeated time-reversal protocols have been successfully implemented4. Here we experimentally measure the second-order out-of-time-order correlators (OTOC(2))5–18 on a superconducting quantum processor and find that they remain sensitive to the underlying dynamics at long timescales. Furthermore, OTOC(2) manifests quantum correlations in a highly entangled quantum many-body system that are inaccessible without time-reversal techniques. This is demonstrated through an experimental protocol that randomizes the phases of Pauli strings in the Heisenberg picture by inserting Pauli operators during quantum evolution. The measured values of OTOC(2) are substantially changed by the protocol, thereby revealing constructive interference between Pauli strings that form large loops in the configuration space. The observed interference mechanism also endows OTOC(2) with high degrees of classical simulation complexity. These results, combined with the capability of OTOC(2) in unravelling useful details of quantum dynamics, as shown through an example of Hamiltonian learning, indicate a viable path to practical quantum advantage. Experimental measurements of high-order out-of-time-order correlators on a superconducting quantum processor show that these correlators remain highly sensitive to the quantum many-body dynamics in quantum computers at long timescales.
With the latest advances in quantum computing technology, we are gradually moving from the noisy intermediate-scale quantum (NISQ) era characterized by hardware limited in the number of qubits and plagued with quantum noise, to the age of quantum utility where both the newest hardware and software methods allow for tackling problems which have been deemed difficult or intractable with conventional classical methods. One of these difficult problems is the simulation of one-dimensional (1D) nuclear magnetic resonance (NMR) spectra, a major tool to learn about the structure of molecules, helping the design of new materials or drugs. Using advanced error mitigation and error suppression techniques from Q-CTRL together with the latest commercially available superconducting-qubit quantum computer from IBM and trapped-ion quantum computer from IonQ, we present the quantum Hamiltonian simulation of liquid-state 1D NMR spectra in the high-field regime for spin systems up to 34 spins. Our pipeline has a major impact on the ability to execute deep quantum circuits with the reduction of quantum noise, improving mean square error by a factor of 22. It allows for the execution of deep quantum circuits and obtaining salient features of the 1D NMR spectra for both 16-spin and 22-spin systems, as well as a 34-spin system, which lies beyond the regime where unrestricted full Liouvillespace simulations are practical (32 spins, the Liouville limit). Our work is a step toward near-term quantum utility in NMR spectroscopy.
Out-of-time-order correlator (OTOC), been suggested as a measure of quantum information scrambling in quantum many-body systems, has received enormous attention recently. The experimental measurement of OTOC is quite challenging. The existing theoretical protocols consist in implementing time-reversal operations or using ancillary quantum systems, therefore only a few experiments have been reported. Recently, a new protocol to detect OTOC using statistical correlations between randomized measurements was put forward. In this work, we detect the OTOCs of a kicked-Ising model using this new measurement method on a 4-qubit nuclear magnetic resonance quantum simulator. In experiment, we use random Hamiltonian evolutions to generate the random operations that are required by the randomized OTOC detection protocol. Our experimental results are in good agreement with the theoretical predictions, thus confirming the feasibility of the protocols. Therefore, our work represents a step in exploring realistic quantum chaotic dynamics in complicated quantum systems.
The idea of the out-of-time-order correlator (OTOC) has recently emerged in the study of both condensed matter systems and gravitational systems.It not only plays a key role in investigating the holographic duality between a strongly interacting quantum system and a gravitational system, it also diagnoses the chaotic behavior of many-body quantum systems and characterizes information scrambling.Based on OTOCs, three different concepts-quantum chaos, holographic duality, and information scrambling-are found to be intimately related to each other.Despite its theoretical importance, the experimental measurement of the OTOC is quite challenging, and thus far there is no experimental measurement of the OTOC for local operators.Here, we report the measurement of OTOCs of local operators for an Ising spin chain on a nuclear magnetic resonance quantum simulator.We observe that the OTOC behaves differently in the integrable and nonintegrable cases.Based on the recent discovered relationship between OTOCs and the growth of entanglement entropy in the many-body system, we extract the entanglement entropy from the measured OTOCs, which clearly shows that the information entropy oscillates in time for integrable models and scrambles for nonintgrable models.With the measured OTOCs, we also obtain the experimental result of the butterfly velocity, which measures the speed of correlation propagation.Our experiment paves a way for experimentally studying quantum chaos, holographic duality, and information scrambling in many-body quantum systems with quantum simulators.