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Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

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Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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Thermal cycloadditions are reactions where the source of activation energy needed to initiate the reaction is provided in the form of heat. A typical example of a thermally-allowed cycloaddition is the Diels–Alder reaction, which is a [4 + 2] cycloaddition. In contrast, a [2 + 2] cycloaddition is thermally forbidden.
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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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Cycloaddition Reactions: Overview01:16

Cycloaddition Reactions: Overview

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Cycloadditions are one of the most valuable and effective synthesis routes to form cyclic compounds. These are concerted pericyclic reactions between two unsaturated compounds resulting in a cyclic product with two new σ bonds formed at the expense of π bonds. The [4 + 2] cycloaddition, known as the Diels–Alder reaction, is the most common. The other example is a [2 + 2] cycloaddition.
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Thermal and Photochemical Electrocyclic Reactions: Overview01:26

Thermal and Photochemical Electrocyclic Reactions: Overview

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Electrocyclic reactions are reversible reactions. They involve an intramolecular cyclization or ring-opening of a conjugated polyene. Shown below are two examples of electrocyclic reactions. In the first reaction, the formation of the cyclic product is favored. In contrast, in the second reaction, ring-opening is favored due to the high ring strain associated with cyclobutene formation.
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Maxam-Gilbert Sequencing01:05

Maxam-Gilbert Sequencing

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In the same year as the discovery of the Sanger sequencing method, another group of scientists, Allan Maxam and Walter Gilbert, demonstrated their chemical-cleavage method for DNA sequencing. The Maxam-Gilbert method relies on using different chemicals that can cleave the DNA sequence at specific sites, the separation of resulting DNA fragments of variable size using electrophoresis, and deciphering the DNA sequence from the resulting gel bands.
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Related Experiment Video

Updated: Aug 13, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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Entanglement-Assisted Quantum Codes from Cyclic Codes.

Francisco Revson F Pereira1, Stefano Mancini2,3

  • 1IQM Quantum Computers, Nymphenburger Str. 86, 80636 Munich, Germany.

Entropy (Basel, Switzerland)
|January 21, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for creating entanglement-assisted quantum-error-correcting (EAQEC) codes from cyclic codes. These novel EAQEC codes offer improved error correction capabilities, with some achieving maximal distance separable properties.

Keywords:
BCH codesReed–Solomon codesmaximal distance separablemaximal entanglementquantum codes

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Area of Science:

  • Quantum Information Science
  • Coding Theory
  • Quantum Error Correction

Background:

  • Entanglement-assisted quantum-error-correcting (EAQEC) codes leverage entanglement for enhanced error correction.
  • EAQEC codes offer advantages over traditional stabilizer codes.

Purpose of the Study:

  • To develop a general method for constructing EAQEC codes from cyclic codes.
  • To apply this method to specific code families like Reed-Solomon and BCH codes.

Main Methods:

  • A general construction framework for EAQEC codes from cyclic codes is presented.
  • Euclidean and Hermitian constructions are employed.
  • The quantum Singleton bound is used for comparison.

Main Results:

  • Three new families of EAQEC codes are generated.
  • Two families are maximal distance separable (MDS).
  • One family is almost MDS or almost near MDS.

Conclusions:

  • The proposed method provides a systematic way to construct powerful EAQEC codes.
  • The generated codes demonstrate competitive performance, particularly in relation to the quantum Singleton bound.