Standard Gates¶

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

X Gate¶

The Pauli-X gate.

\[ \begin{split}X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\end{split} \]

Syntax¶

Function: XGate

Parameters: None

{
  "function": "XGate",
  "function_params": {}
}

Y Gate¶

The Pauli-Y gate.

\[ \begin{split}Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}\end{split} \]

Syntax¶

Function: YGate

Parameters: None

{
  "function": "YGate",
  "function_params": {}
}

Z Gate¶

The Pauli-Z gate.

\[ \begin{split}Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\end{split} \]

Syntax¶

Function: ZGate

Parameters: None

{
  "function": "ZGate",
  "function_params": {}
}

H Gate¶

The Hadamard gate converts \(|0\rangle\) to \(|+\rangle\) and \(|1\rangle\) to \(|-\rangle\).

\[ \begin{split}H = \frac{1}{\sqrt{2}}*\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}\end{split} \]

Syntax¶

Function: HGate

Parameters: None

{
  "function": "HGate",
  "function_params": {}
}

RZ Gate¶

Rotation around the Z axis is by a given angle \(\varphi\).

\[ \begin{split}{RZ(\varphi)} = \begin{pmatrix} {e^{-i\frac{\varphi}{2}}} & 0 \\ 0 & {e^{i\frac{\varphi}{2}}} \end{pmatrix}\end{split} \]

Syntax¶

Function: RZGate

Parameters:

phi: ParameterFloatType
The angle in a parameter type or a float.

CX Gate¶

The Controlled X gate.

Applies X Gate on the target qubit, based on the state of the control qubit (by default if the controlled state is \(|1\rangle\)).

\[ \begin{split}CX = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ \end{pmatrix}\end{split} \]

Syntax¶

Function: CXGate

Parameters:

ctrl_state: Optional[Union[str, PositiveOrZeroInt]]
The control state in decimal or as a bit string (e.g., ‘0’). If not specified, the control state is 1. The gate is performed if the state of the control qubits matches the control state.

{
  "function": "CXGate",
  "function_params": {
    "ctrl_state": "0"
  }
}

Example¶

This example shows a circuit built with several standard gates, both controlled and uncontrolled.

Textual ModelSDK

{
    "logic_flow": [
        {
            "function": "CCXGate",
            "function_params": {},
            "outputs": {"CTRL": "ccx_ctrl_out", "TARGET": "ccx_target_out"}
        },
        {
            "function": "RZGate",
            "function_params": {"phi": 1.9},
            "inputs": "ccx_target_out"
        },
        {
            "function": "SwapGate",
            "function_params": {},
            "inputs": "ccx_ctrl_out"
        }
    ]
    }

from classiq import Model
from classiq.builtin_functions import CCXGate, SwapGate, RZGate
from classiq.model import Constraints

constraints = Constraints(max_width=4, max_depth=50)
model = Model(constraints=constraints)

ccx_params = CCXGate()
ccx_out = model.CCXGate(ccx_params)
ccx_target_out = ccx_out["TARGET"]
ccx_ctrl_out = ccx_out["CTRL"]

rz_params = RZGate(phi=1.9)
model.RZGate(rz_params, in_wires={"TARGET": ccx_target_out})

swap_params = SwapGate()
model.SwapGate(swap_params, in_wires={"TARGET": ccx_ctrl_out})

circuit = model.synthesize()

circuit.show_interactive()

StandardGates example

Parametrized Rotations¶

Rotation gates can be performed on parameters. See Parameters.