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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

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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 Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

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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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Thermal expansion and Thermal stress: Problem Solving01:27

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San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55...
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Thermal Strain01:19

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Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature...
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Integration by Parts: Indefinite Integrals01:26

Integration by Parts: Indefinite Integrals

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Integration by parts is a fundamental technique in calculus for evaluating integrals involving the product of two functions. It is particularly useful when direct integration is not feasible. The method is based on the product rule for differentiation, which states that the derivative of a product equals the derivative of the first function times the second, plus the first function times the derivative of the second. By integrating this identity and rearranging terms, the integration by parts...
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Thermal Expansion01:22

Thermal Expansion

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The expansion of alcohol in a thermometer is one of many commonly encountered examples of thermal expansion, which is the change in size or volume of a given system as its temperature changes. The most visible example is the expansion of hot air. When air is heated, it expands and becomes less dense than the surrounding air, which then exerts an upward force on the hot air to, for example, make steam and smoke rise, and hot air balloons float. The same behavior happens in all liquids and gases,...
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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Quantum Annealing and Thermalization: Insights from Integrability.

Fuxiang Li1, Vladimir Y Chernyak2, Nikolai A Sinitsyn3

  • 1School of Physics and Electronics, Hunan University, Changsha 410082, China, Theoretical Division, Los Alamos National Laboratory, B213, Los Alamos, New Mexico 87545, USA and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

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Summary

This study presents a quantum annealing model with key features for computation, demonstrating how quantum correlations accelerate processing and achieve perfect microstate distribution.

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Area of Science:

  • Quantum computation
  • Quantum annealing
  • Spin Hamiltonian

Background:

  • Quantum annealing is a metaheuristic optimization algorithm that uses quantum fluctuations to find the global minimum of an objective function.
  • Developing efficient quantum annealing models is crucial for advancing quantum computation.

Purpose of the Study:

  • To solve a quantum annealing model with essential features for computation.
  • To analyze nonadiabatic excitations and their scaling with annealing rate and system size.
  • To demonstrate the role of quantum correlations in accelerating computations.

Main Methods:

  • Solving a model Hamiltonian with programmable Ising parameters.
  • Characterizing nonadiabatic excitations nonperturbatively.
  • Analyzing the scaling of excitations with annealing rate and system size.

Main Results:

  • The model exhibits ground state entanglement and a constant energy gap during evolution.
  • Exact characterization of nonadiabatic excitations is achieved.
  • Quantum correlations are shown to accelerate computations.
  • The annealing protocol results in a perfect Gibbs distribution of microstates.

Conclusions:

  • The developed quantum annealing model provides a framework for efficient quantum computation.
  • Quantum correlations are vital for accelerating quantum annealing processes.
  • The model ensures accurate characterization of quantum states and computation outcomes.