01State vector
An n-qubit state is 2ⁿ complex numbers. A gate does not multiply a 2ⁿ×2ⁿ matrix — it walks pairs of amplitudes that differ in one bit. Sixteen qubits is 65 536 amplitudes; this phone does a gate in a millisecond. Twenty is a million; thirty would not fit in memory. That gap is the whole point of building the real thing.
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02Checked
Every preset matches the textbook to the last digit: Grover at sin²(5·asin(1/√8)) = 0.9453, teleportation preserving sin²(0.5), Fourier phases going exactly once around. Twelve random circuits of up to six qubits match a NumPy reference — built the slow way, by Kronecker products — to 10⁻¹⁵.
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03What this is not
A simulation, not a quantum computer. Amplitudes here are exact and there is no noise; a real device gives you only the histogram, and a noisy one. The simulation is what you use to know what the real machine should have said.
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Qubit 0 is the least significant bit, as in Qiskit, so outcomes read right to left: |101⟩ means qubit 2 = 1, qubit 1 = 0, qubit 0 = 1.
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