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Hybridization of Atomic Orbitals II03:35

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sp3d and sp3d 2 Hybridization
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Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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Atomic Orbitals02:44

Atomic Orbitals

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An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
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The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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Ampere-Maxwell's Law: Problem-Solving01:17

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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...
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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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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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リッドバーグ原子配列を用いた最大独立集合の量子最適化

S Ebadi1, A Keesling1,2, M Cain1

  • 1Department of Physics, Harvard University, Cambridge, MA 02138, USA.

Science (New York, N.Y.)
|May 5, 2022
PubMed
まとめ
この要約は機械生成です。

研究者はリッドバーグの原子配列を使用して,最大独立集合問題を解くための量子アルゴリズムを調査しました. 難しいグラフで超線形量子加速を観測し 量子コンピューティングの優位性を示しました

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関連する実験動画

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科学分野:

  • 量子情報科学
  • 量子コンピューティング
  • 計算上の複雑さ

背景:

  • 計算上難しい問題を解くことは 重要な課題です
  • 量子アルゴリズムはスピードアップの 可能性を秘めています
  • Rydbergの原子配列は量子計算のための有望なプラットフォームです.

研究 の 目的:

  • 最大独立集合の問題の量子アルゴリズムを実験的に調査する.
  • リッドバーグ原子配列を用いたプログラム可能なグラフ上のこれらのアルゴリズムの性能を探求する.
  • 古典的な方法と比較して 量子性能を比較する

主な方法:

  • 289クビットまでのライドバーグ原子配列を利用した.
  • リッドバーグの封鎖を利用した ハードウェア効率の良い暗号化
  • 変数量子アルゴリズムのクローズドループ最適化を実装した.
  • プログラム可能な接続性を持つグラフでテストされたアルゴリズム.
  • 典型的なシミュレート annealingに対してベンチマーク.

主要な成果:

  • 問題の硬さにおける重要な要因として,溶液の退化と局所的な最小値を特定した.
  • 最も難しいグラフの正確な解を見つけるのに 超線形量子加速が観測されました
  • 観測された量子加速の起源を 分析した

結論:

  • Rydbergの原子配列は 実験的に量子アルゴリズムを 難しい計算問題で実現できます
  • 量子アルゴリズムは,特定の問題のインスタンスに対して,古典的な方法よりも大きなスピードアップの可能性を示しています.
  • この研究は,組み合わせ最適化のための量子アプローチの性能とスケーラビリティの洞察を提供します.