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Related Concept Videos

The Quantum-Mechanical Model of an Atom02:45

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. Schrödinger...
Reaction Quotient02:35

Reaction Quotient

The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient (Q). For a reversible reaction described by m A + n B ⇌ x C + y D, the reaction quotient is derived directly from the stoichiometry of the balanced equation as
Atomic Orbitals02:44

Atomic Orbitals

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.
The Aufbau Principle and Hund's Rule03:02

The Aufbau Principle and Hund's Rule

To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the subshell of...
Rationalizing Substitutions01:29

Rationalizing Substitutions

Integrals involving non-rational functions are often difficult to evaluate using standard techniques, especially when radicals appear in the integrand. Rationalizing substitution provides a systematic method for simplifying such integrals by converting them into rational forms that are easier to handle.Consider a rod whose linear mass density depends on a constant linear density, a characteristic length, and the distance from the left end of the rod. Determining the total mass requires...
Quantum Numbers02:43

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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Related Experiment Video

Updated: Jun 4, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Quantum logic operations and algorithms in a single 25-level atomic qudit.

Pei Jiang Low1,2,3, Nicholas C F Zutt1,2, Gaurav A Tathed1,2

  • 1Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada.

Nature Communications
|June 2, 2026
PubMed
Summary
This summary is machine-generated.

Researchers explored using 25-dimensional barium-ion qudits for quantum computing. This approach enhances performance and efficiency by utilizing more quantum states, showing promise for future quantum computers.

Related Experiment Videos

Last Updated: Jun 4, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

  • Quantum Information Science
  • Atomic Physics
  • Quantum Computing

Background:

  • Scaling quantum computers is a major challenge.
  • Utilizing higher-dimensional quantum systems (qudits) can improve performance and efficiency.

Purpose of the Study:

  • To experimentally investigate the potential of 25-dimensional 137Ba+ ion qudits for quantum information processing.
  • To analyze error scaling with qudit dimension and identify primary error sources.
  • To demonstrate high-dimensional quantum operations.

Main Methods:

  • Experimental realization of a 25-dimensional trapped-ion qudit using 137Ba+.
  • High-fidelity state preparation and readout of qudit levels.
  • Probing superpositions of up to 24 states to study error scaling.
  • Implementation of quantum algorithms (Bernstein-Vazirani) and gates (Toffoli) using high-dimensional qudits.

Main Results:

  • Achieved high-fidelity state preparation and readout for a 25-dimensional 137Ba+ ion qudit.
  • Investigated error scaling with increasing qudit dimension (d).
  • Successfully demonstrated high-dimensional qudit operations, including a 3-qubit Bernstein-Vazirani algorithm and a 4-qubit Toffoli gate with a single ion.

Conclusions:

  • 137Ba+ ions are a viable platform for creating large-dimensional qudits.
  • High-dimensional qudit systems offer a promising pathway for enhanced quantum computing performance and hardware efficiency.
  • Further research into error mitigation in qudit systems is warranted.