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

Abstract

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 in 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.

arXiv comment20 pages, 6 page appendix with some FT and NISQ algorithm details, 7 figures

References in corpus (78)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Many-body localization, thermalization, and entanglement
• A Quantum Approximate Optimization Algorithm
• Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
• NMR Techniques for Quantum Control and Computation
• Strong quantum computational advantage using a superconducting quantum processor
• Quantum random access memory
• Local conservation laws and the structure of the many-body localized states
• On the Power of One Bit of Quantum Information
• Hamiltonian Simulation by Qubitization
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Elucidating Reaction Mechanisms on Quantum Computers
• Towards Practical Quantum Variational Algorithms
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
• Toward the first quantum simulation with quantum speedup
• The approach to thermal equilibrium in quantized chaotic systems
• Area laws in a many-body localized state and its implications for topological order
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
• A random compiler for fast Hamiltonian simulation
• Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• Unification of Dynamical Decoupling and the Quantum Zeno Effect
• Practical characterization of quantum devices without tomography
• Information Scrambling in Computationally Complex Quantum Circuits
• Even more efficient quantum computations of chemistry through tensor hypercontraction
• Multifractal Scalings across the Many-Body Localization Transition
• Exploring Localization in Nuclear Spin Chains
• Information-theoretic bounds on quantum advantage in machine learning
• Simulating Large Quantum Circuits on a Small Quantum Computer
• Low Depth Quantum Simulation of Electronic Structure
• Quantum computing enhanced computational catalysis
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• Experimental Quantum Hamiltonian Learning
• Provably efficient machine learning for quantum many-body problems
• Hamiltonian Learning and Certification Using Quantum Resources
• Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
• Robust Online Hamiltonian Learning
• Optimal Quantum Measurements of Expectation Values of Observables
• Nearly optimal lattice simulation by product formulas
• Learning a local Hamiltonian from local measurements
• Parahydrogen enhanced zero-field nuclear magnetic resonance
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Fermionic partial tomography via classical shadows
• Resource-efficient digital quantum simulation of $d$-level systems for photonic, vibrational, and spin-$s$ Hamiltonians
• Non-ergodic phases in strongly disordered random regular graphs
• Variational Thermal Quantum Simulation via Thermofield Double States
• Near-zero-field nuclear magnetic resonance
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Quantum algorithm for simulating real time evolution of lattice Hamiltonians
• Robust Calibration of a Universal Single-Qubit Gate-Set via Robust Phase Estimation
• Robust Dynamic Hamiltonian Engineering of Many-Body Spin Systems
• Optical detection of NMR J-spectra at zero magnetic field
• Fault-Tolerant Quantum Simulations of Chemistry in First Quantization
• Non-ergodic metallic and insulating phases of Josephson junction chains
• Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization
• Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States
• Quantum Hamiltonian Learning Using Imperfect Quantum Resources
• Faster Digital Quantum Simulation by Symmetry Protection
• Emergent prethermalization signatures in out-of-time ordered correlations
• Accurately computing electronic properties of a quantum ring
• Learning models of quantum systems from experiments
• Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks
• Hamiltonian tomography for quantum many-body systems with arbitrary couplings
• A quantum mechanical NMR simulation algorithm for protein-scale spin systems
• Parameter Estimation with Mixed-State Quantum Computation
• Non-ergodic extended phase of the Quantum Random Energy model
• Effectiveness of classical spin simulations for describing NMR relaxation of quantum spins
• Digital quantum simulation of NMR experiments
• Scalable Bayesian Hamiltonian learning
• Hybrid quantum-classical method for simulating high-temperature dynamics of nuclear spins in solids
• Optimizing qubit Hamiltonian parameter estimation algorithms using PSO
• Composite pulses in NMR quantum computation
• Meta Hamiltonian Learning

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• Learning out-of-time-ordered correlators with classical kernel methods