Why people believe this
Classical computing uses AND, OR, NOT, XOR. Quantum computing has X (NOT), CNOT (controlled-NOT), and Toffoli (AND). The mapping seems direct.
The correction
Classical gates and quantum gates differ in a fundamental way: classical gates can be irreversible (AND, OR lose information), while all quantum gates except measurement must be unitary and therefore reversible. A classical AND gate maps 4 inputs to 2 outputs — this information loss cannot be represented as a unitary matrix. The Toffoli gate simulates AND reversibly by keeping all input bits and adding an output bit. Additionally, quantum gates include operations with no classical equivalent — Hadamard, phase gates, and rotations that create and manipulate superposition.
Try it in the simulator
What to do
Place an H gate on q0 and run it. The output is a superposition — no classical bit operation does this. Now place H then Z then H — the result is X (bit flip). This H-Z-H sequence has no direct classical analog; it works through quantum interference of amplitudes.
Research notes
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