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6 results for “qubit”

Formulae (6)

|\psi\rangle = \alpha|0\rangle + \beta|1\rangle

General state of a single qubit as a superposition of the computational basis states.

|\alpha|^2 + |\beta|^2 = 1

The squared amplitudes of a qubit must sum to 1, ensuring total probability is 100 %.

H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}

Puts a qubit into an equal superposition — the most common single-qubit gate.

CNOT = \begin{pmatrix} 1&0&0&0 \\ 0&1&0&0 \\ 0&0&0&1 \\ 0&0&1&0 \end{pmatrix}

Two-qubit gate that flips the target qubit only when the control qubit is |1⟩.

|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)

Maximally entangled two-qubit state — measuring one qubit instantly determines the other.

\text{States} = 2^n

Number of basis states an n-qubit register can be in superposition of simultaneously.