Phase and Amplitude

Modifying Double Slit experiment

When two electrons are simultaneously launched to two different double slits, it leads to non-interference pattern

Wave Functions

Wave functions describe state of a Quantum Object represented as \(\psi\) . They form the core of Quantum Calculations. To wave functions, two important components exist.

  1. Amplitude: The height or size of a wave is termed as amplitude. Amplitude determines how likely it is to be measured.
  2. Phase Difference: The shift of a wave relative to another is called as phase. It determines the resultant wave after an interference. (In-phase waves interfere to from wave with larger amplitude hence constructive interference. Destructive interference is formed when out-phase interfere to reduce the resultant amplitude.)

Note: Quantum Computers use phase difference to solve questions. Quantum Computers use phase difference \(\phi\) and the amplitude of solutions. This makes the required solution to be constructively interfered and destructively interfere with others.

Gaming Example:

A superposition state of all possible state can be modified by interference (hence phase) to obtain desired combination or pattern. superposition-gaming-example

Superposition of wavefunctions:

superposition-of-wavefunctions

Note:

  1. Amplitudes can be theoretically predictable but in practice we can never know them with high certainty. Theoretical prediction can be done with the help of Born’s Rule which is given by:

    \[\text{For given wavefunction as: }ket{state} = a \ket{0} \ + \ b\ket{1} \ we \ state:\ prob(0) = a^2 \ and \ prob(1) = b^2\]

  2. We call Wave function collapse after a Quantum Measurement which is due to the fact that measurement force the q-object to take up a single state after which the object looses the information of it’s past superposition state (which translate to loss of information about the amplitude)