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What is meant by the term "quantum interference" in the context of quantum computing and quantum algorithms?

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The term is most often used in the context of the two-slit experiment. The interference pattern that you see, which is not simply what you'd get if you added the wavefunction ($\Psi_A$) associated with going through slit A to the wavefunction ($\Psi_B$) going through slit B, but there is a "mixed" term as follows:

$$ \tag{1} |\psi|^2 = |\psi_A + \psi_B|^2 = |\psi_A|^2 + |\psi_B|^2 + \psi_A^*\psi_B + \psi_A\psi_B^*. $$

This interference pattern occurs even when you reduce the number of photons until there's only one photon at a time! When there's only one photon at a time, what could it possibly be interfering with to cause the patter on the screen to be different from $P_A + P_B$?

We say the photon interferes with itself. This is a quantum mechanical phenomenon that doesn't exist in classical mechanics.

The two-slit experiment was used by Feynman when he explained the Feynman integral, because the Feynman integral is a sum/integral over paths which each have an amplitude. These amplitudes interfere with each other, which again is a signature of quantum mechanical effects, since classically there would only be one path in the Feynman integral: the path with the smallest Lagrangian action.

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  • $\begingroup$ thank you for your answer. Are you saying that quantum interference has no meaning in quantum computing, and this term is (and should) be used in the context of quantum physics? $\endgroup$
    – incud
    Mar 3 at 8:56
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    $\begingroup$ It doesn't have "no meaning" in quantum computing. The meaning is the same here. For example the Mach-Zender interferometer is frequently used to explain the concept of superposition of qubits for a photonic quantum computer: Without interference, there's no quantum computer. $\endgroup$ Mar 3 at 13:34
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    $\begingroup$ Whoa. Been reading a tiny bit and I actually understood that. Thank you for that point about Mach-Zender interferometer! Highly instructive. I want to learn more about self interference. The symbol |Ψ|² makes sense to me, as does your equation. I really like the clear way math is written in this field. $\endgroup$
    – DukeZhou
    Sep 5 at 5:05

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