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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.

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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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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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Hybridization of Atomic Orbitals I

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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Related Experiment Video

Updated: Sep 4, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Generalized Quantum Subspace Expansion.

Nobuyuki Yoshioka^1,2, Hideaki Hakoshima^3,4, Yuichiro Matsuzaki^3,5

¹Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

Physical Review Letters

|July 22, 2022

Summary

This summary is machine-generated.

We developed a new quantum error mitigation technique to combat noise in quantum computers. This generalized quantum subspace expansion method effectively reduces errors without needing to know the noise details.

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Area of Science:

Quantum Computing
Quantum Information Science
Error Mitigation

Background:

Controlling noise is a major challenge for current quantum computers.
Developing practical, hardware-friendly quantum error mitigation (QEM) is crucial for non-fault-tolerant quantum resources.

Purpose of the Study:

Propose a novel generalized quantum subspace expansion method.
Address stochastic, coherent, and algorithmic errors in quantum computers.
Mitigate noise in Hamiltonian spectra without prior noise information.

Main Methods:

Utilize a generalized quantum subspace expansion.
Exploit an extended subspace for noise suppression.
Implement practical setups using powers of the noisy state (ρ^m) and error-boosted states.

Main Results:

Demonstrated significant error suppression (orders of magnitude) in numerical simulations.
Successfully mitigated noise in practical quantum computing setups.
Showcased the method's effectiveness without requiring noise characterization.

Conclusions:

The proposed method offers an efficient approach to quantum error mitigation.
It inherits advantages from previous error-agnostic QEM techniques.
It overcomes limitations of existing QEM methods, improving noise resilience.