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The Classiq platform provides many standard gates. Some key standard gates are shown here in detail.
All gates are covered in the reference manual. 
from classiq import *

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Single Qubit Gates

An example is given for XX gate. The gates II, XX, YY, ZZ, HH, TT are used in the same way.

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For example: X

Function: X Arguments:
  • target: QBit
@qfunc
def main(q: Output[QBit]):
    allocate(q)

    X(q)


qmod = create_model(main)
qprog = synthesize(qmod)

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Single Qubit Rotation Gates

An example is given for RZRZ gate. The gates RXRX, RYRY, RZRZ are used in the same way except for parameter name.

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Parameter names for different rotation gates

  • RX: theta
  • RY: theta
  • RZ: phi

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For example: RZ

RZ(θ)=(e−iθ200eiθ2)\begin{split}RZ(\theta) = \begin{pmatrix} {e^{-i\frac{\theta}{2}}} & 0 \\ 0 & {e^{i\frac{\theta}{2}}} \\ \end{pmatrix}\end{split} Function: RZ Arguments:
  • theta: CReal
  • target: QBit
@qfunc
def main(q: Output[QBit]):
    allocate(q)

    theta = 1.9
    RZ(theta, q)


qmod = create_model(main)
qprog = synthesize(qmod)

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R Gate

Rotation by θ\theta around the cos(ϕ)X+sin(ϕ)Ycos(\phi)X + sin(\phi)Y axis. R(θ,ϕ)=(cos(θ2)−ie−iϕsin(θ2)−ieiϕsin(θ2)cos(θ2))\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} Parameters:
  • theta: CReal
  • phi: CReal
  • target: QBit
@qfunc
def main(q: Output[QBit]):
    allocate(q)

    theta = 1
    phi = 2
    R(theta, phi, q)


qmod = create_model(main)
qprog = synthesize(qmod)

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Phase Gate

Rotation about the Z axis by λ\lambda with global phase of λ2\frac{\lambda}{2}. PHASE(λ)=(100eiλ)\begin{split}PHASE(\lambda) = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\lambda} \end{pmatrix}\end{split} Parameters:
  • theta: CReal
  • target: QBit
@qfunc
def main(q: Output[QBit]):
    allocate(q)

    theta = 1
    PHASE(theta, q)


qmod = create_model(main)
qprog = synthesize(qmod)

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Double Qubits Rotation Gates

An example is given for RZZRZZ gate. The gates RXXRXX, RYYRYY, RZZRZZ are used in the same way.

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RZZ Gate

Rotation about ZZ. RZZ(θ)=(e−iθ20000eiθ20000eiθ20000e−iθ2)\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} Parameters:
  • theta: CReal
  • target: QArray[QBit]
@qfunc
def main(q: Output[QArray]):
    allocate(2, q)

    theta = 1
    RZZ(theta, q)


qmod = create_model(main)
qprog = synthesize(qmod)

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Controlled Gates

An example is given for CXCX gate. The gates CXCX, CYCY, CZCZ, CHCH, CSXCSX, CCXCCX are used in a similar way. In CCXCCX Gate the ctrl_state parameter receives a value suitable for 2 control qubits. for example: "01".

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CX Gate

The Controlled XX gate. Applies XX Gate on the target qubit, based on the state of the control qubit (by default if the controlled state is ∣1⟩|1\rangle). CX=(1000010000010010)\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} Parameters:
  • control: QBit
  • target: 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)

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Controlled Rotations

An example is given for CRXCRX gate. The gates CRXCRX, CRYCRY, CRZCRZ, CPhase are used in the same way.

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CRX Gate

Controlled rotation around the X axis. CRX(θ)=(1000010000cos⁡(θ2)−isin⁡(θ2)00−isin⁡(θ2)cos⁡(θ2))\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} Parameters:
  • theta: CReal
  • control: QBit
  • target: 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)

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Swap Gate

Swaps between two qubit states. SWAP=(1000001001000001)\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} Parameters:
  • qbit0: QBit
  • qbit1: QBit
@qfunc
def main(q1: Output[QBit], q2: Output[QBit]):
    allocate(q1)

    allocate(q2)

    SWAP(q1, q2)


qmod = create_model(main)
qprog = synthesize(qmod)

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U Gate

The single-qubit gate applies phase and rotation with three Euler angles. Matrix representation: U(γ,ϕ,θ,λ)=eiγ(cos⁡(θ2)−eiλsin⁡(θ2)eiϕsin⁡(θ2)ei(ϕ+λ)cos⁡(θ2))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} Parameters:
  • theta: CReal
  • phi: CReal
  • lam: CReal
  • gam: CReal
  • target: 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)