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WAVES
Waves can add or cancel
In step
They add up: constructive interference.
Opposite
They cancel: destructive interference.
Brightness
Goes as amplitude squared.
Quantum amplitudes interfere just like waves.
ONE QUBIT
Interference with a single photon
Two paths
The photon's paths are its |0⟩ and |1⟩.
Beam splitters
Act like Hadamard gates.
The phase
Decides which detector fires: cos2(φ/2).
Every photon takes both paths, and the paths interfere.
THE TRICK
The recipe behind quantum algorithms
Spread
Put every possible answer in superposition.
Mark
Flip the sign of the right answer's amplitude.
Interfere
Make wrong answers cancel and the right one grow, then measure.
It isn't 'trying every answer at once': it's choreographing the cancellations.
GROVER'S SEARCH
Finding a needle with interference
Classical
About N/2 tries to find one item in N.
Quantum
About (π/4)√N Grover steps.
Timing
Too many steps and the odds fall again.
A quadratic speedup: useful, but not magic.
SPEEDUPS
How much faster depends on the problem
Searching
Quadratic speedup.
Factoring and chemistry
Exponential speedups for some problems.
Everyday tasks
No speedup at all.
Quantum computers are specialists, not faster versions of your laptop.
UNIT 7 STUDY COMPLETE
🌊
Ready for the Fab Challenge?
You've used interference to steer photons and to find a hidden item with Grover's algorithm.