Interference
Interference means amplitudes are added first, and only then squared into chances. So parts with the same sign build each other up, and parts with opposite signs cancel. In H–Z–H, the two parts heading to outcome 0 are +0.5 and −0.5. They cancel exactly. So a change in phase alone becomes a sure result of 1.
Why care? Interference is the engine inside every quantum algorithm. If you understand this one chapter, the algorithms stop looking like magic.
The rule that makes quantum computing different from ordinary random computing is one sentence long. To get an outcome's chance, first add every amplitude part flowing into that outcome. Then square the total. (An amplitude is a number you square to get a chance.)
Ordinary chances can only pile up. Say two routes each reach an outcome with chance 0.25. Together they give 0.25 + 0.25 = 0.5. But amplitudes carry signs, so their sum can be smaller than either part. Do the arithmetic:
- +0.5 and +0.5 add to 1.0, and 1.0² = 1. That is a sure thing. This is called constructive interference.
- +0.5 and −0.5 add to 0, and 0² = 0. The outcome is wiped out. This is called destructive interference.
Think of waves in a swimming pool. When two peaks meet, the water rises higher. When a peak meets a dip, the water goes flat. (Unlike pool water, amplitudes are not made of anything. They are numbers that decide chances.)
- Worked example: what happens in H–Z–H, one gate at a time?
- Destructive interference on outcome 0INTERACTIVE
- Remove the Z and the cancellation swaps sidesINTERACTIVE
- Does the qubit "try both paths at once"?
- Why do algorithms care about interference?
- Worked exampleINTERACTIVE
- Why does interference need a steady phase?
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