Table 1 Summary of common single-qubit and two-qubit quantum gates
From: A novel image classification framework based on variational quantum algorithms
Quantum gate | Matrix expression | Symbol |
|---|---|---|
Pauli-X gate | \(\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\) |
|
Pauli-Y gate | \(\begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}\) |
|
Pauli-Z gate | \(\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}\) |
|
\(R_x\) gate | \(\begin{bmatrix} \cos (\theta /2) & -i\sin (\theta /2) \\ -i\sin (\theta /2) & \cos (\theta /2) \end{bmatrix}\) |
|
\(R_y\) gate | \(\begin{bmatrix} \cos (\theta /2) & -\sin (\theta /2) \\ \sin (\theta /2) & \cos (\theta /2) \end{bmatrix}\) |
|
\(R_z\) gate | \(\begin{bmatrix} e^{-i\theta /2} & 0 \\ 0 & e^{i\theta /2} \end{bmatrix}\) |
|
Hadamard gate | \(\frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}\) |
|
CNOT gate | \(\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) |
|
