Why people believe this
Quantum computers are more powerful than classical ones. Therefore they should be faster at everything — sorting, searching, optimization, machine learning, simulation.
The correction
Quantum speedup applies to a specific and limited class of problems. Grover's algorithm gives quadratic speedup for unstructured search. Shor's gives exponential speedup for factoring. HHL gives exponential speedup for linear systems under strong conditions. But for most practically important problems — general optimization, neural network training, data analytics — no quantum speedup is known, and for many there are lower bound proofs showing no substantial speedup is possible. The problems where quantum computers excel are structurally different from everyday computing tasks.
Try it in the simulator
What to do
Run the Grover preset and note the quadratic speedup: 2 qubits means 4 possible states, Grover finds the answer in O(sqrt(4)) = 2 iterations instead of 4. Now think about what this means for a 50-qubit system: sqrt(2^50) iterations instead of 2^50. That is a speedup, but it is quadratic not exponential — and it only applies when you have an oracle for the target.
Research notes
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