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Related Concept Videos

Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis. This...
Atomic Nuclei: Magnetic Resonance01:05

Atomic Nuclei: Magnetic Resonance

The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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 one, the...
NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
Nuclear Magnetic Resonance (NMR): Overview01:07

Nuclear Magnetic Resonance (NMR): Overview

Nuclear magnetic resonance (NMR) is a phenomenon exhibited by certain nuclei that can absorb characteristic radio frequency radiation under certain conditions. NMR has been extensively applied in molecular spectroscopy and medical diagnostic imaging. In both these applications, the molecule or subject under study is placed in a magnetic field and irradiated with radio frequency energy.
NMR spectroscopy generates a spectrum where the characteristic absorption frequencies of the sample are...

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Solving quantum ground-state problems with nuclear magnetic resonance.

Zhaokai Li1, Man-Hong Yung, Hongwei Chen

  • 1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230036, People's Republic of China.

Scientific Reports
|February 23, 2012
PubMed
Summary
This summary is machine-generated.

This study demonstrates a quantum approach to solve complex quantum ground-state problems using a variational wavefunction and phase estimation algorithm (PEA) on a quantum simulator. The method achieved high accuracy, showing quantum simulators can enhance classical trial wave functions.

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Area of Science:

  • Quantum Computing
  • Computational Physics
  • Quantum Chemistry

Background:

  • Many-body Hamiltonians present computationally intractable quantum ground-state problems.
  • Classical and quantum algorithms struggle with efficient solutions for these complex systems.
  • Trial wavefunctions approximating ground states are often available in physics and chemistry.

Purpose of the Study:

  • To experimentally implement a variational wavefunction approach for solving quantum ground-state problems.
  • To utilize the phase estimation algorithm (PEA) on a quantum simulator.
  • To assess the accuracy and fidelity of the quantum approach for the Heisenberg spin model.

Main Methods:

  • Employed a nuclear magnetic resonance (NMR) quantum simulator.
  • Implemented an iterative phase estimation procedure.
  • Utilized a variational wavefunction to approximate the ground state.

Main Results:

  • Achieved high accuracy for eigenenergies, precise to the 10⁻⁵ decimal digit.
  • Distilled ground-state fidelity exceeding 80%.
  • Reliably captured the singlet-to-triplet switching near the critical field.

Conclusions:

  • Quantum simulators can effectively leverage classical trial wave functions.
  • This approach offers a more efficient method than classical computers for certain quantum problems.
  • Demonstrates the practical application of PEA in quantum simulation for ground-state problems.