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Bits, qubits and notation
Kets, amplitudes and how a register of qubits is written down.
- Read |0⟩, |1⟩ and α|0⟩ + β|1⟩ aloud and say what each symbol means.
- Explain the normalisation rule |α|² + |β|² = 1.
- Write the state of a two-qubit register and map it to the labels QubitLab shows.
A classical bit is 0 or 1. A qubit is described by two complex numbers, called amplitudes, attached to the two classical outcomes. Physicists write the outcomes as kets: |0⟩ and |1⟩. The general state is a weighted sum of the two.
Kets are column vectors
Several qubits
Two qubits have four basis states: |00⟩, |01⟩, |10⟩, |11⟩, each with its own amplitude. n qubits have 2ⁿ. QubitLab labels states with the rightmost character being qubit 0, the same convention Qiskit uses, so |10⟩ means qubit 1 is 1 and qubit 0 is 0.
Read a statevector
Open this circuit and switch the results to the State tab. The table lists every basis state with its probability and phase; compare the labels with the qubit order on the wires.
OPENQASM 3.0; include "stdgates.inc"; qubit[2] q; x q[1]; h q[0];
A qubit is in the state (|0⟩ + |1⟩)/√2. What is the probability of measuring 1?
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How many amplitudes describe a 5-qubit register?
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A qubit is a unit vector with two complex entries; a register of n qubits is a unit vector with 2ⁿ entries. Probabilities are squared magnitudes of amplitudes.
Up next: Superposition and the Hadamard gate