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Related Concept Videos

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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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Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
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meta-Directing Deactivators: –NO2, –CN, –CHO, –⁠CO2R, –COR, –CO2H01:13

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All meta-directing substituents are deactivating groups. These substituents withdraw electrons from the aromatic ring, making the ring less reactive toward electrophilic substitution. For example, the nitration of nitrobenzene is 100,000 times slower than that of benzene because of the deactivating effect of the nitro group. The first step in an electrophilic aromatic substitution is the addition of an electrophile to form a resonance-stabilized carbocation. The energy diagrams for...
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Traverse angle computations are a critical component of surveying, used to compute the internal angles within a closed traverse. A traverse consists of a series of connected lines forming a closed loop, often used for land boundary delineation or mapping. Calculating the internal angles ensures accuracy in the traverse geometry and is essential for checking survey data integrity.The process begins with known azimuths and bearings of the traverse sides. Internal angles at each vertex are...
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Secondary amines react with nitrous acid to form N-nitrosamines, as depicted in Figure 1. Nitrous acid, a weak and unstable acid, is formed in situ from an aqueous solution of sodium nitrite and strong acids, such as hydrochloric acid or sulfuric acid, in cold conditions. In the presence of an acid, the nitrous acid gets protonated. The subsequent loss of water results in the formation of the electrophile known as nitrosonium ion.
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Qudit-Basis Universal Quantum Computation Using χ^{(2)} Interactions.

Murphy Yuezhen Niu1,2, Isaac L Chuang1,2,3, Jeffrey H Shapiro1,3

  • 1Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review Letters
|May 15, 2018
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Summary
This summary is machine-generated.

Universal quantum computation is achievable using linear optics and three-wave mixing interactions. This method enables universal gate sets for qubits and qutrits, paving the way for scalable quantum computing.

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Area of Science:

  • Quantum Information Science
  • Quantum Optics
  • Quantum Computation

Background:

  • Linear optics and nonlinear interactions are crucial for quantum computation.
  • Achieving universal quantum computation with minimal resources is a key challenge.

Purpose of the Study:

  • To demonstrate universal quantum computation using only linear optics and three-wave mixing (χ(2)) interactions.
  • To establish a universal gate set for qubit and qudit bases within specific photon subspaces.

Main Methods:

  • Utilizing χ(2) interactions for quantum gate operations.
  • Proving universality for qubit and qutrit bases in n-pump-photon subspaces.
  • Employing proof by induction and coherent photon manipulation.

Main Results:

  • A strictly universal gate set for the qubit basis in the one-pump-photon subspace was identified.
  • Qutrit-basis universality was demonstrated in the two-pump-photon subspace, showing generation of the u(3) Lie algebra.
  • A route for preparing high-photon-number Fock states from single-photon states was presented.

Conclusions:

  • Universal quantum computation is realizable with linear optics and χ(2) interactions.
  • The proposed methods provide a scalable approach for quantum information processing.
  • Coherent photon injection offers practical advantages for state preparation.