Quantum computer succeeds where a classical algorithm fails
People have performed many mathematical proofs to show that a quantum computer will vastly outperform traditional computers on a number of algorithms. But the quantum computers we have now are error-prone and don't have enough qubits to allow for error correction. The only demonstrations we've had involve quantum computing hardware evolving out of a random configuration and traditional computers failing to simulate their normal behavior. Useful calculations are an exercise for the future.
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