Lab 02 · Foundations · 30–40 minutes
Interference: Shape the Answer
How can an algorithm suppress unlikely answers and amplify useful ones? See the amplitudes change, then connect the result to quantum cryptography.
Classical simulation of ideal quantum math. No account needed.
Not guessing. Shaping the odds.
The word is interference. Inference means drawing a conclusion from evidence. Interference is what happens when quantum amplitudes combine: some reinforce, others cancel.
1. Possibilities have amplitudes, not just probabilities
An amplitude is a number associated with a possible outcome. Unlike a probability, it can have a sign or a direction called phase. To get a probability, square its magnitude. For example, +0.5 and −0.5 both give a probability of 0.25.
2. Add amplitudes first. Square afterward.
When different computational paths reach the same outcome, their amplitudes add. Same-phase contributions can reinforce. Opposite-phase contributions can cancel. This wave analogy shows that addition, not a full quantum state.
Two contributions, one outcome
Blue: contribution A · Gold: contribution B · Green: sum
+0.5 + (+0.5) = 1 → probability 1
These are illustrative contributions to one outcome, not independent outcomes. A complete normalized quantum state redistributes probability across all outcomes; probability does not disappear.
3. The algorithm must arrange the interference
A quantum computer does not recognize the answer by magic. The problem must be encoded in quantum operations. Grover uses a test that recognizes a solution; Shor uses a mathematical repeating structure. Their operations make useful outcomes more likely when measured.
Measurement gives one result, not a list of every answer. Superposition alone does not make searching fast.