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FUNDAMENTALS / 02 / QUBITS

Classical bit vs qubit

Distinguish a stored bit from a quantum state and a measurement outcome.

Intuition

A classical bit has value 0 or 1. A qubit is described by a quantum state. Measuring it in the computational basis still gives just one bit: 0 or 1.

A superposition is not a way to read two answers at once. Quantum computations change amplitudes so that interference changes which outcomes are likely. Start with a definite state before exploring superposition.

The mathematics

∣0⟩=[10],∣1⟩=[01]|0\rangle=\begin{bmatrix}1\\0\end{bmatrix},\quad |1\rangle=\begin{bmatrix}0\\1\end{bmatrix}
Look a little deeper

These column vectors are an orthonormal basis for a two-dimensional complex vector space. Their entries are amplitudes, not the two possible results of a single measurement.

Use it

Start at |0⟩. Use one X gate to make measurement return 1 with certainty.

This exercise uses the same server-side state and circuit checks as its linked practice problem.

Build your circuit

Click a gate to append it, or drag it onto a wire. CX uses the selected control; SWAP uses it as the second operand. Basis order: |qₙ … q₀⟩.

q0

Returned logical circuit · before transpilation · q0 on top

0 / 32 gates · terminal measurement of all qubits

Connect to code

qc = QuantumCircuit(1)
qc.x(0)

These operations go inside a circuit-building program. Practice problems provide a complete solve() template.

Solve the linked Qiskit problem →

Check your understanding

A single computational-basis measurement of a qubit returns…

First complete the circuit exercise successfully.