Superposition

4 Key excerpts on "Superposition"

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  Foundations of Physics

  • Steve Adams(Author)
  • 2019(Publication Date)
  • Mercury Learning and Information

    (Publisher)

  15

  Superposition Effects

  15.0   Superposition Effects

   

  Superposition is what happens when two or more waves are present at the same point. This might occur because they originate from different sources or because of reflection. If the waves are of the same type, the resultant disturbance at that point is the vector sum of the disturbances from each individual wave. This is called the principle of Superposition. We can determine the effects of Superposition graphically, by adding phasors or by calculation. Many important phenomena are linked to Superposition, including interference and diffraction and the formation of standing (stationary) waves.

  15.1   Two-Source Interference

   

  If waves of the same type with equal wavelength, frequency, and amplitude are emitted from two sources placed a short distance apart (comparable to a few wavelengths), then a regular interference pattern is formed. The pattern consists of regions where the waves reinforce to produce maximum intensity (constructive interference) and regions where they cancel to produce minimum intensity (destructive interference).

  The famous double slit experiment carried out by Thomas Young in 1801 provided strong evidence for the wavelength of light and enabled Young to calculate its wavelength. A similar setup with sound can be used to demonstrate Superposition patterns and, in a modified form, to create noise-cancelling headphones.

  In order for stable clear interference effects to be created, the two sources must be coherent.

  Coherent sources maintain a constant phase relationship.

  This means that they must be the same type of wave and have the same wavelength and frequency. The sources do not have to be in phase, but the phase difference between them must be constant. They must also have comparable amplitudes; if one wave has a much greater amplitude than the other, then variations in intensity will be hard to detect.

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  eBook - ePub

  Quantum Computing in Action

  • Johan Vos(Author)
  • 2022(Publication Date)
  • Manning

    (Publisher)

  4 Superposition

  This chapter covers

  • Understanding why Superposition allows quantum systems to process exponentially more data
  • Processing data via quantum gates
  • Using the Hadamard gate

  In the previous chapter, we briefly mentioned Superposition, which is a fundamental concept of quantum computing. It is one of the reasons quantum computers are expected to be able to run some applications much faster than classical computers.

  In this chapter, you learn what Superposition is and how it is relevant in creating quantum algorithms. We talk about a specific gate that brings a qubit into a Superposition state, and we show a simple but relevant example that demonstrates Superposition. The flow of the chapter is explained in figure 4.1.

  Figure 4.1 From Superposition to the Hadamard gate

  We try to keep the physical explanations to a minimum. The scientific work behind the physics is mind-boggling, but it requires different skills and is less relevant to software development. Keep in mind that even for the most knowledgeable people, quantum computing (QC) and its concepts are difficult to grasp, so do not worry if the physical concepts behind Superposition are not clear. What matters to developers is how to use these concepts and write more suitable applications.

  4.1 What is Superposition?

  A qubit can be in different states. We’ve mentioned before that a qubit can hold the value 0, the value 1, and also some sort of combination of the values 0 and 1. There are important restrictions on what combinations are allowed, though, and we discuss these now.

  We said earlier that when a qubit is measured, it always returns the value 0 or the value 1. But that doesn’t say everything about what is happening before we measure it.

  To understand this, we’ll make a short detour to the world of quantum physics. Remember that what software developers call a qubit is backed by real-world phenomena. The software behavior and properties of a qubit, therefore, have to correspond somehow with the behavior and properties of the real-world phenomena (figure 4.2).

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  No longer available |Learn more

  Foundations of Physics

  • Steve Adams(Author)
  • 2023(Publication Date)
  • Mercury Learning and Information

    (Publisher)

  15

  SUPERPOSITION EFFECTS

  15.0 Superposition EFFECTS

  Superposition is what happens when two or more waves are present at the same point. This might occur because they originate from different sources or because of reflection. If the waves are of the same type the resultant disturbance at that point is the vector sum of the disturbances from each individual wave. This is called the “principle of Superposition.” We can determine the effects of Superposition graphically, by adding phasors or by calculation. Many important phenomena are linked to Superposition including interference and diffraction and the formation of standing (stationary) waves.

  15.1 TWO-SOURCE INTERFERENCE

  If waves of the same type with equal wavelength, frequency, and amplitude are emitted from two sources placed a short distance apart (comparable to a few wavelengths) then a regular interference pattern is formed. The pattern consists of regions where the waves reinforce to produce maximum intensity (constructive interference) and regions where they cancel to produce minimum intensity (destructive interference).

  The famous double slit experiment carried out by Thomas Young in 1801 provided strong evidence for the wavelength of light and enabled Young to calculate its wavelength. A similar set up with sound can be used to demonstrate Superposition patterns and, in a modified form to create noise-canceling headphones.

  In order for stable clear interference effects to be created the two sources must be coherent. Coherent sources maintain a constant phase relationship.

  This means that they must be the same type of wave, and have the same wavelength and frequency. The sources do not have to be in phase but the phase difference between them must be constant. They must also have comparable amplitudes; if one wave has a much greater amplitude than the other then variations in intensity will be hard to detect.

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  eBook - PDF

  Sneaking a Look at God's Cards

  Unraveling the Mysteries of Quantum Mechanics - Revised Edition

  • Giancarlo Ghirardi, Gerald Malsbary(Authors)
  • 2021(Publication Date)
  • Princeton University Press

    (Publisher)

  79 C H A P T E R F O U R The Superposition Principle and the Conceptual Structure of the Theory The assumption of Superposition relationships between the states leads to a mathematical theory in which the equations that define a state are linear in the unknowns. In consequence of this, people have tried to establish analogies with systems in classical mechanics, such as vibrating strings or membranes, which are governed by linear equations and for which, therefore, a Superposition principle holds. Such analogies have led to the name “Wave Mechanics” being sometimes given to quantum mechanics. It is important to remember, however, that the Superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum Superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation. The analogies are thus liable to be misleading. —Paul Adrien Maurice Dirac W e can now deepen our analysis of the most innovative point of the new theory: the Superposition principle. In the preceding chapters we have shown that the formal structure of the theory is such as to permit the “sum-mation” of quantum states. In particular, our attention has been drawn to the fact that, for instance, the polarization state |45° > of a photon is the “sum” of the states |V > and |H > (for “vertical” and “horizontal,” respec- tively). Analogously, it was asserted that the state of a particle with upward spin along the direction of the x axis is the “sum” of the states correspond-ing to upward and downward spin along the z axis.

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