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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Atomic Nuclei: Nuclear Spin State Population Distribution

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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Quantum Numbers02:43

Quantum Numbers

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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Atomic Nuclei: Nuclear Spin01:08

Atomic Nuclei: Nuclear Spin

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All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
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NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

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The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Approximately Symmetric Neural Networks for Quantum Spin Liquids.

Dominik S Kufel1,2, Jack Kemp1,2, DinhDuy Vu1,2

  • 1Harvard University, Department of Physics, 17 Oxford Street, Cambridge, Massachusetts 02138, USA.

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|August 18, 2025
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Summary

We developed new, efficient neural networks for quantum spin liquid problems. These networks outperform existing methods and can study complex systems beyond the reach of other techniques.

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Area of Science:

  • Quantum physics
  • Machine learning
  • Condensed matter theory

Background:

  • Quantum spin liquids are exotic states of matter with complex correlations.
  • Current computational methods face limitations in system size and scope for these problems.

Purpose of the Study:

  • To introduce a novel family of approximately symmetric neural networks tailored for quantum spin liquid investigations.
  • To demonstrate the efficiency, scalability, and superior performance of these networks compared to existing approaches.

Main Methods:

  • Development of parameter-efficient, scalable neural network architectures incorporating approximate symmetry.
  • Application to mixed-field toric code and PXP Rydberg Hamiltonian models.
  • Comparison with tensor network and quantum Monte Carlo methods.

Main Results:

  • The proposed neural networks significantly outperform symmetry-unaware architectures.
  • Performance is competitive with state-of-the-art tensor network and quantum Monte Carlo methods.
  • Exploration of large system sizes (N=480, N=1584) and Hamiltonians with sign problems inaccessible to other methods.

Conclusions:

  • The symmetric neural network approach offers a powerful new tool for quantum spin liquid research.
  • This method enables the study of complex quantum systems previously beyond computational reach.
  • Paves the way for interpretable neural network architectures in quantum physics.