Supported Gates

pytket-custatevec natively implements the following unitary gates using NVIDIA's cuStateVec kernels.

Single Qubit Gates

Gate	Symbol	Matrix Representation
I	\(I\)	\(\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\)
X	\(X\)	\(\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\)
Y	\(Y\)	\(\begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}\)
Z	\(Z\)	\(\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}\)
H	\(H\)	\(\frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}\)
S	\(S\)	\(\begin{bmatrix} 1 & 0 \\ 0 & i \end{bmatrix}\)
Sdg	\(S^\dagger\)	\(\begin{bmatrix} 1 & 0 \\ 0 & -i \end{bmatrix}\)
T	\(T\)	\(\begin{bmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{bmatrix}\)
V / SX	\(\sqrt{X}\)	\(\frac{1}{\sqrt{2}}\begin{bmatrix} 1 & -i \\ -i & 1 \end{bmatrix}\)

Gate	Definition	Matrix Form
Rx	\(R_x(\theta)\)	\(\begin{bmatrix} \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{bmatrix}\)
Ry	\(R_y(\theta)\)	\(\begin{bmatrix} \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ \sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{bmatrix}\)
Rz	\(R_z(\theta)\)	\(\begin{bmatrix} e^{-i\theta/2} & 0 \\ 0 & e^{i\theta/2} \end{bmatrix}\)
U1	\(U1(\lambda)\)	\(\begin{bmatrix} 1 & 0 \\ 0 & e^{i\lambda} \end{bmatrix}\)
U3	\(U3(\theta, \phi, \lambda)\)	\(\begin{bmatrix} \cos\frac{\theta}{2} & -e^{i\lambda}\sin\frac{\theta}{2} \\ e^{i\phi}\sin\frac{\theta}{2} & e^{i(\phi+\lambda)}\cos\frac{\theta}{2} \end{bmatrix}\)
PhasedX	\(R_x(\theta, \phi)\)	\(R_z(\phi) R_x(\theta) R_z(-\phi)\)
TK1	\(TK1(\alpha, \beta, \gamma)\)	\(R_z(\alpha) R_x(\beta) R_z(\gamma)\)

Gate	Description	Matrix / definition
SWAP	Swap states	\(\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}\)
ECR	Echoed Cross-Resonance	\(\frac{1}{\sqrt{2}} \begin{bmatrix} 0 & 0 & 1 & i \\ 0 & 0 & i & 1 \\ 1 & -i & 0 & 0 \\ -i & 1 & 0 & 0 \end{bmatrix}\)
ZZMax	Maximal Entanglement	\(e^{-i \frac{\pi}{4} Z \otimes Z} = \text{diag}(e^{-i\pi/4}, e^{i\pi/4}, e^{i\pi/4}, e^{-i\pi/4})\)
XXPhase	Ising XX	\(e^{-i \frac{\theta}{2} X \otimes X}\)
YYPhase	Ising YY	\(e^{-i \frac{\theta}{2} Y \otimes Y}\)
ZZPhase	Ising ZZ	\(e^{-i \frac{\theta}{2} Z \otimes Z}\)
ISWAP	Swap + Phase	\(\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & c & i s & 0 \\ 0 & i s & c & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}, \small{c=\cos(\frac{\theta}{2}), s=\sin(\frac{\theta}{2})}\)

Standard controlled gates are supported. The backend handles the control logic natively.