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Related Concept Videos

Quantum Numbers02:43

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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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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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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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Amides are synthesized by treating carboxylic acids with amines in the presence of dehydrating agents like dicyclohexylcarbodiimide (DCC).
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One of the common methods to prepare nitriles is the dehydration of amides. This method requires strong dehydrating agents like phosphorous pentoxide or boiling acetic anhydride for converting amides to nitriles. Another reagent namely, thionyl chloride also accomplishes the dehydration of amides, where amide acts as a nucleophile. The first step of the mechanism involves the nucleophilic attack by the amide on the thionyl chloride to form an intermediate. In the next step, the electron pairs...
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Overview
Epoxides result from alkene oxidation, which can be achieved by a) air, b) peroxy acids, c) hypochlorous acids, and d) halohydrin cyclization.
Epoxidation with Peroxy Acids
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How Difficult is it to Prepare a Quantum State?

Davide Girolami1

  • 1Los Alamos National Laboratory, Theoretical Division, P.O. Box 1663 Los Alamos, New Mexico 87545, USA and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106, USA.

Physical Review Letters
|April 24, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a geometric cost function to measure the difficulty of transforming quantum states. It establishes a lower bound on the number of operations needed, linking quantum state preparation to coherence and correlations.

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Area of Science:

  • Quantum Information Science
  • Quantum Control Theory

Background:

  • Quantum systems require precise control to transition between states.
  • Classical operations offer a baseline for understanding quantum control complexity.

Purpose of the Study:

  • To define a geometric cost function for quantum state preparation protocols.
  • To quantify the difference between quantum and classical processes.
  • To establish a lower bound on the number of unitary transformations.

Main Methods:

  • Identification of a geometric cost function.
  • Analysis of classical states and operations as free resources.
  • Derivation of a lower bound for commuting unitary transformations.

Main Results:

  • A geometric cost function is identified, quantifying protocol difficulty relative to classical processes.
  • A lower bound on the number of commuting unitary transformations is established.
  • The relationship between quantum state preparation and generated coherence/correlations is discussed.

Conclusions:

  • The geometric cost function provides a metric for quantum control efficiency.
  • The findings link the quantum nature of state preparation to inherent quantum properties in the target state.