Skip to content

Unitary Instructions

Name Operator Description Example
I \(I\) Identity gate builder.I(0)
H \(H\) Hadamard gate builder.H(0)
X \(X\) Pauli-X builder.X(0)
X90 \(X_{90}\) Rotation around the x-axis of \(\frac{\pi}{2}\) builder.X90(0)
mX90 \(X_{-90}\) Rotation around the x-axis of \(-\frac{\pi}{2}\) builder.mX90(0)
Y \(Y\) Pauli-Y builder.Y(0)
Y90 \(Y_{90}\) Rotation around the y-axis of \(\frac{\pi}{2}\) builder.Y90(0)
mY90 \(Y_{-90}\) Rotation around the y-axis of \(-\frac{\pi}{2}\) builder.mY90(0)
Z \(Z\) Pauli-Z builder.Z(0)
Z90 \(Z_{90}\) Rotation around the z-axis of \(\frac{\pi}{2}\) builder.Z90(0)
mZ90 \(Z_{-90}\) Rotation around the z-axis of \(-\frac{\pi}{2}\) builder.mZ90(0)
S \(S\) Phase gate builder.S(0)
Sdag \(S^\dagger\) S dagger gate builder.Sdag(0)
T \(T\) T gate builder.T(0)
Tdag \(T^\dagger\) T dagger gate builder.Tdag(0)
Rx \(R_x(\theta)\) Arbitrary rotation around x-axis builder.Rx(0, 0.23)
Ry \(R_y(\theta)\) Arbitrary rotation around y-axis builder.Ry(0, 0.23)
Rz \(R_z(\theta)\) Arbitrary rotation around z-axis builder.Rz(0, 2)
Rn \(R_\textbf{n}(n_x, n_y, n_z, \theta, \phi_g)\) Arbitrary rotation around specified axis builder.Rn(0)
U \(U(\theta, \phi,\lambda)\) Arbitrary unitary gate builder.U(0, 1, 2, 3)
CZ \(CZ\) Controlled-Z, Controlled-Phase builder.CZ(1, 2)
CR \(CR(\theta)\) Controlled phase shift (arbitrary angle) builder.CR(0, 1, 3.1415)
CRk \(CR_k(k)\) Controlled phase shift (\(\frac{\pi}{2^{k-1}}\)) builder.CRk(1, 0, 2)
SWAP \(SWAP\) SWAP gate builder.SWAP(1, 2)
CNOT \(CNOT\) Controlled-NOT gate builder.CNOT(1, 2)