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Related Concept Videos

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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2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)01:19

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Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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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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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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¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)01:20

¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)

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When proton-coupled carbon-13 spectra are simplified by a broadband proton decoupling technique, structural information about the coupled protons is lost. Distortionless enhancement by polarization transfer (DEPT) is a technique that provides information on the number of hydrogens attached to each carbon in a molecule. While the DEPT experiment utilizes complex pulse sequences, the pulse delay and flip angle are specifically manipulated. The resulting signals have different phases depending on...
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Experimental quantum compressed sensing for a seven-qubit system.

C A Riofrío1, D Gross2,3, S T Flammia3

  • 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, D-14195 Berlin, Germany.

Nature Communications
|May 18, 2017
PubMed
Summary
This summary is machine-generated.

Quantum compressed sensing enables state reconstruction for large quantum systems, overcoming limitations in quantum tomography. This study demonstrates its effectiveness on a seven-qubit system, even with incomplete data and noise.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Metrology

Background:

  • Quantum tomography, essential for characterizing quantum devices, faces scalability challenges with increasing system size.
  • Current quantum technologies are hindered by the inability to fully reconstruct complex quantum states and processes.

Purpose of the Study:

  • To experimentally implement compressed sensing for quantum state tomography on a multi-qubit system.
  • To demonstrate the feasibility of reconstructing quantum states from incomplete measurement data under realistic noisy conditions.

Main Methods:

  • Experimental realization of compressed tomography on a seven-qubit topological color code using trapped ion architecture.
  • Utilizing a highly incomplete set of 127 Pauli basis measurements with 100 repetitions per setting.
  • Applying low-rank estimation techniques adapted for noisy quantum data.

Main Results:

  • Successful reconstruction of a seven-qubit quantum state from significantly undersampled measurement data.
  • Demonstration that low-rank estimates are effective even when compressed sensing's original assumptions of few non-zero eigenvalues are not met.
  • Characterization of noise effects, showing remaining eigenvectors are consistent with a random-matrix model.

Conclusions:

  • Compressed sensing is a viable and powerful technique for overcoming the scalability limitations of quantum tomography.
  • Low-rank estimation provides a robust framework for quantum state reconstruction in the presence of noise and incomplete data.
  • This work paves the way for characterizing larger and more complex quantum systems essential for quantum technology development.