What is Quantum Interference?

What happens when a π/2-pulse is applied to the second qubit. There are two cases to consider:

• If the second qubit is in the spin-up state, a π/2 pulse applied along the y-axis will rotate the spin from the north pole down to the equator.  This aligns the spin with the +x direction, creating the equal superposition state (|↑> + |↓>)/√2 with a "+" sign.

• If the second qubit is instead in the spin-down state, a π/2 pulse applied along the y-axis will rotate the spin in the same counter-clockwise direction, bringing it from the south pole up to the equator.  This aligns the spin in the -x direction, creating the equal superposition state (|↑> - |↓>)/√2  , this time with a corresponding "-" sign.

  

The probability amplitudes now add and subtract one another.  Suppose there are two coefficients with equal values, for example, c3 = c4.

In this case, there is a complete cancellation of the probability amplitude for |↑↓> . Such a reduction of the probability amplitude is called “destructive quantum interference."

On the other hand, there is a doubling of the probability amplitude in front of |↑↑>.  Such an enhancement of the probability amplitude is called “constructive quantum interference."

Since the constructive and destructive quantum interference happens across the entire state space, this is also an example of quantum parallelism.