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Related Concept Videos

Randomized Experiments01:13

Randomized Experiments

The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...
Ampere-Maxwell's Law: Problem-Solving01:17

Ampere-Maxwell's Law: Problem-Solving

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 the problem,...
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...

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Related Experiment Video

Updated: May 16, 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

Parameter tuning patterns for random graph coloring with quantum annealing.

Olawale Titiloye1, Alan Crispin

  • 1School of Computing, Mathematics and Digital Technology, Manchester Metropolitan University, Manchester, United Kingdom.

Plos One
|November 21, 2012
PubMed
Summary
This summary is machine-generated.

Quantum annealing, a quantum mechanics optimization method, can solve complex graph coloring problems. Tuning the acceptance ratio during Monte Carlo simulations leads to discovering solutions for long-standing benchmark instances.

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Last Updated: May 16, 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 computing
  • Combinatorial optimization
  • Computational complexity

Background:

  • Quantum annealing is a metaheuristic optimization algorithm inspired by quantum mechanics.
  • Combinatorial optimization problems, such as graph coloring, are computationally challenging.
  • Monte Carlo methods are widely used for simulating complex systems.

Purpose of the Study:

  • To investigate the effectiveness of quantum annealing for solving the k-coloring problem on large, dense random graphs.
  • To explore the relationship between the acceptance ratio in Monte Carlo quantum annealing and solution discovery.
  • To identify optimal tuning strategies for quantum annealing to solve benchmark k-coloring instances.

Main Methods:

  • Developed a spin model for the k-coloring problem applicable to large dense random graphs.
  • Employed Monte Carlo quantum annealing with field tuning.
  • Analyzed the behavior of the acceptance ratio during simulations.

Main Results:

  • Demonstrated that field tuning can cause the acceptance ratio to diverge during Monte Carlo quantum annealing, leading to ground state discovery.
  • Showed that simulations with a diverging acceptance ratio are more effective than those with declining or stagnating ratios.
  • Successfully discovered solutions for several benchmark k-coloring instances, some previously unsolved for nearly two decades.

Conclusions:

  • A diverging acceptance ratio during Monte Carlo quantum annealing is a key indicator of simulation effectiveness for graph coloring.
  • This approach provides a novel and effective strategy for solving challenging combinatorial optimization problems.
  • The findings open new avenues for utilizing quantum annealing in computational science and operations research.