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Quantum Numbers

Quantum Numbers

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.

Chirality

Chirality

Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

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.

Chirality in Nature

Chirality in Nature

Chirality is the most intriguing yet essential facet of nature, governing life’s biochemical processes and precision. It can be observed from a snail shell pattern in a macroscopic world to an amino acid, the minutest building block of life. Most of the snails around the world have right-coiled shells because of the intrinsic chirality in their genes. All the amino acids present in the human body exist in an enantiomerically pure state, except for glycine - the sole achiral amino acid.

Chirality at Nitrogen, Phosphorus, and Sulfur

Chirality at Nitrogen, Phosphorus, and Sulfur

Chirality is most prevalent in carbon-based tetrahedral compounds, but this important facet of molecular symmetry extends to sp3-hybridized nitrogen, phosphorus and sulfur centers, including trivalent molecules with lone pairs. Here, the lone pair behaves as a functional group in addition to the other three substituents to form an analogous tetrahedral center that can be chiral.
A consequence of chirality is the need for enantiomeric resolution. While this is theoretically possible for all...

Molecules with Multiple Chiral Centers

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Molecules that possess multiple chiral centers can afford a large number of stereoisomers. For instance, while some molecules like 2-butanol have one chiral center, defined as a tetrahedral carbon atom with four different substituents attached, several molecules like butane-2,3-diol have multiple chiral centers. A simple formula to predict the number of stereoisomers possible for a molecule with n chiral centers is 2n. However, there can be a lower number where some of the stereoisomers are...

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Gradient Echo Quantum Memory in Warm Atomic Vapor

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Published on: November 11, 2013

Topological quantum computation based on chiral Majorana fermions.

Biao Lian^1,2, Xiao-Qi Sun^2,3, Abolhassan Vaezi^2,3

¹Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544-0001.

Proceedings of the National Academy of Sciences of the United States of America

|October 10, 2018

Summary

Chiral Majorana fermions, observed in hybrid topological materials, can perform quantum computations. Their propagation mimics Majorana zero mode braiding, enabling quantum gates like Hadamard and phase gates.

Keywords:

Majorana quantum computing topological

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Area of Science:

Condensed Matter Physics
Quantum Computing
Topological Matter

Background:

Chiral Majorana fermions are massless, self-conjugate fermions found as edge states in 2D topological matter.
They have been experimentally observed in hybrid devices combining quantum anomalous Hall insulators and superconductors.
Majorana zero modes, a related concept, are key to topological quantum computation.

Purpose of the Study:

To demonstrate that chiral Majorana fermions can be utilized for quantum computation.
To propose a platform for performing quantum computations using these fermions.
To show the equivalence between chiral Majorana fermion propagation and Majorana zero mode braiding.

Main Methods:

Utilizing a Corbino ring junction in a hybrid device.
Employing quantum coherent chiral Majorana fermions.
Analyzing junction conductance for qubit state readout.

Main Results:

The propagation of chiral Majorana fermions achieves the same unitary transformation as Majorana zero mode braiding.
A platform for quantum computation with chiral Majorana fermions is proposed.
The Corbino ring junction successfully implements the Hadamard and phase gates.
Junction conductance provides a natural readout mechanism for the qubit state.

Conclusions:

Chiral Majorana fermions offer a viable route for implementing quantum gates and performing quantum computations.
The proposed platform leverages the unique properties of these fermions for scalable quantum information processing.
This work bridges the gap between fundamental physics of topological matter and practical quantum computing applications.