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The Classiq platform provides many standard gates.
Some key standard gates are shown here in detail. reference manual .
Single Qubit Gates An example is given for X X X
The gates I I I X X X Y Y Y Z Z Z H H H T T T
For example: X Function: X
Arguments:
@qfunc def main ( q : Output[QBit]): allocate(q) X(q) qmod = create_model(main) qprog = synthesize(qmod)
Single Qubit Rotation Gates An example is given for R Z RZ RZ
The gates R X RX RX R Y RY R Y R Z RZ RZ
Parameter names for different rotation gates
RX: thetaRY: thetaRZ: phi
For example: RZ R Z ( θ ) = ( e − i θ 2 0 0 e i θ 2 ) \begin{split}RZ(\theta) = \begin{pmatrix}
{e^{-i\frac{\theta}{2}}} & 0 \\
0 & {e^{i\frac{\theta}{2}}} \\
\end{pmatrix}\end{split} RZ ( θ ) = ( e − i 2 θ 0 0 e i 2 θ ) Function: RZ
Arguments:
theta: CRealtarget: QBit
@qfunc def main ( q : Output[QBit]): allocate(q) theta = 1.9 RZ(theta, q) qmod = create_model(main) qprog = synthesize(qmod)
R Gate Rotation by θ \theta θ c o s ( ϕ ) X + s i n ( ϕ ) Y cos(\phi)X + sin(\phi)Y cos ( ϕ ) X + s in ( ϕ ) Y
R ( θ , ϕ ) = ( c o s ( θ 2 ) − i e − i ϕ s i n ( θ 2 ) − i e i ϕ s i n ( θ 2 ) c o s ( θ 2 ) ) \begin{split}R(\theta, \phi) = \begin{pmatrix}
cos(\frac{\theta}{2}) & -ie^{-i\phi}sin(\frac{\theta}{2}) \\
-ie^{i\phi}sin(\frac{\theta}{2}) & cos(\frac{\theta}{2}) \\
\end{pmatrix}\end{split} R ( θ , ϕ ) = ( cos ( 2 θ ) − i e i ϕ s in ( 2 θ ) − i e − i ϕ s in ( 2 θ ) cos ( 2 θ ) ) Parameters:
theta: CRealphi: CRealtarget: QBit
@qfunc def main ( q : Output[QBit]): allocate(q) theta = 1 phi = 2 R(theta, phi, q) qmod = create_model(main) qprog = synthesize(qmod)
Phase Gate Rotation about the Z axis by λ \lambda λ λ 2 \frac{\lambda}{2} 2 λ
P H A S E ( λ ) = ( 1 0 0 e i λ ) \begin{split}PHASE(\lambda) = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\lambda} \end{pmatrix}\end{split} P H A SE ( λ ) = ( 1 0 0 e iλ ) Parameters:
theta: CRealtarget: QBit
@qfunc def main ( q : Output[QBit]): allocate(q) theta = 1 PHASE(theta, q) qmod = create_model(main) qprog = synthesize(qmod)
Double Qubits Rotation Gates An example is given for R Z Z RZZ RZZ
The gates R X X RXX RXX R Y Y RYY R YY R Z Z RZZ RZZ
RZZ Gate Rotation about ZZ.
R Z Z ( θ ) = ( e − i θ 2 0 0 0 0 e i θ 2 0 0 0 0 e i θ 2 0 0 0 0 e − i θ 2 ) \begin{split}RZZ(\theta) = \begin{pmatrix}
{e^{-i\frac{\theta}{2}}} & 0 & 0 & 0 \\
0 & {e^{i\frac{\theta}{2}}} & 0 & 0 \\
0 & 0 & {e^{i\frac{\theta}{2}}} & 0 \\
0 & 0 & 0 & {e^{-i\frac{\theta}{2}}} \\
\end{pmatrix}\end{split} RZZ ( θ ) = e − i 2 θ 0 0 0 0 e i 2 θ 0 0 0 0 e i 2 θ 0 0 0 0 e − i 2 θ Parameters:
theta: CRealtarget: QArray[QBit]
@qfunc def main ( q : Output[QArray]): allocate( 2 , q) theta = 1 RZZ(theta, q) qmod = create_model(main) qprog = synthesize(qmod)
Controlled Gates An example is given for C X CX CX
The gates C X CX CX C Y CY C Y C Z CZ CZ C H CH C H C S X CSX CSX C C X CCX CCX
In C C X CCX CCX ctrl_state parameter receives a value suitable for 2 control qubits. for example: "01".
CX Gate The Controlled X X X
Applies X X X ∣ 1 ⟩ |1\rangle ∣1 ⟩
C X = ( 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 ) \begin{split}CX = \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 \\
\end{pmatrix}\end{split} CX = 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 Parameters:
control: QBittarget: QBit
@qfunc def main ( q_target : Output[QBit], q_control : Output[QBit]): allocate(q_target) allocate(q_control) CX(q_control, q_target) qmod = create_model(main) qprog = synthesize(qmod)
Controlled Rotations An example is given for C R X CRX CRX
The gates C R X CRX CRX C R Y CRY CR Y C R Z CRZ CRZ
CRX Gate Controlled rotation around the X axis.
C R X ( θ ) = ( 1 0 0 0 0 1 0 0 0 0 cos ( θ 2 ) − i sin ( θ 2 ) 0 0 − i sin ( θ 2 ) cos ( θ 2 ) ) \begin{split}CRX(\theta) = \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & \cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) \\
0 & 0 & -i\sin(\frac{\theta}{2}) & \cos(\frac{\theta}{2}) \\
\end{pmatrix}\end{split} CRX ( θ ) = 1 0 0 0 0 1 0 0 0 0 cos ( 2 θ ) − i sin ( 2 θ ) 0 0 − i sin ( 2 θ ) cos ( 2 θ ) Parameters:
theta: CRealcontrol: QBittarget: QBit
@qfunc def main ( q_target : Output[QBit], q_control : Output[QBit]): allocate(q_target) allocate(q_control) theta = 1 CRX(theta, q_control, q_target) qmod = create_model(main) qprog = synthesize(qmod)
Swap Gate Swaps between two qubit states.
S W A P = ( 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 ) \begin{split}SWAP = \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 \\
\end{pmatrix}\end{split} S W A P = 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 Parameters:
@qfunc def main ( q1 : Output[QBit], q2 : Output[QBit]): allocate(q1) allocate(q2) SWAP(q1, q2) qmod = create_model(main) qprog = synthesize(qmod)
U Gate The single-qubit gate applies phase and rotation with three Euler angles.
Matrix representation:
U ( γ , ϕ , θ , λ ) = e i γ ( cos ( θ 2 ) − e i λ sin ( θ 2 ) e i ϕ sin ( θ 2 ) e i ( ϕ + λ ) cos ( θ 2 ) ) U(\gamma,\phi,\theta,\lambda) = e^{i\gamma}\begin{pmatrix}
\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{pmatrix} U ( γ , ϕ , θ , λ ) = e iγ ( cos ( 2 θ ) e i ϕ sin ( 2 θ ) − e iλ sin ( 2 θ ) e i ( ϕ + λ ) cos ( 2 θ ) ) Parameters:
theta: CRealphi: CReallam: CRealgam: CRealtarget: QBit
@qfunc def main ( q : Output[QBit]): allocate(q) theta = 1 phi = 2 lam = 1.5 gam = 1.1 U(theta, phi, lam, gam, q) qmod = create_model(main) qprog = synthesize(qmod)
