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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...
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Ampere-Maxwell's Law: Problem-Solving01:17

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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.
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Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a cylinder...
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Portfolios of quantum algorithms.

S M Maurer1, T Hogg, B A Huberman

  • 1Physics Department, Stanford University, Stanford, California 94043, USA.

Physical Review Letters
|December 12, 2001
PubMed
Summary

Quantum computation can probabilistically solve hard problems. Portfolios of quantum algorithms, like financial ones, can reduce running time and uncertainty for complex tasks like 3-satisfiability.

Area of Science:

  • Quantum Computing
  • Computational Complexity Theory
  • Algorithm Optimization

Background:

  • Quantum computation offers potential solutions for intractable problems.
  • Many quantum algorithms are inherently stochastic, providing probabilistic solutions.
  • Algorithm efficiency requires evaluation of both completion time and variance.

Purpose of the Study:

  • To investigate methods for minimizing running time and uncertainty in quantum algorithms.
  • To explore the application of portfolio strategies to quantum algorithm selection.
  • To assess the performance of quantum algorithm portfolios on NP-complete problems.

Main Methods:

  • Developed a portfolio approach for quantum algorithms, drawing parallels with financial portfolio theory.

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  • Applied the portfolio strategy to NP-complete problems, specifically 3-satisfiability.
  • Analyzed the expected completion time and variance of the portfolio approach compared to single algorithms.
  • Main Results:

    • Quantum algorithm portfolios demonstrated superior performance over single algorithms.
    • The portfolio approach effectively reduced both the expected running time and its uncertainty.
    • Significant improvements were observed when applied to NP-complete problems like 3-satisfiability.

    Conclusions:

    • Portfolio strategies are a viable method for enhancing quantum algorithm efficiency.
    • This approach offers a promising direction for tackling complex computational problems using quantum computers.
    • Further research into quantum portfolio optimization could unlock new computational capabilities.