Standard Gates

The Classiq platform provides many standard gates to the user. Some key standard gates will be shown here in detail. All gates can be seen 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.

This 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 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 will be performed if the state of the control qubits matches the control state.

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

Example

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

Textual ModelSDK

{
    "constraints": {
      "max_width": 4,
      "max_depth": 50
    },
    "logic_flow": [
        {
            "function": "CCXGate",
            "function_params": {},
            "outputs": {"CTRL_OUT": "ccx_ctrl_out", "TARGET_OUT": "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 ModelDesigner
from classiq.builtin_functions.standard_gates import CCXGate, SwapGate, RZGate
from classiq.interface.generator.model import Constraints

constraints = Constraints(max_width=4, max_depth=50)
model_designer = ModelDesigner(constraints=constraints)

ccx_params = CCXGate()
ccx_out = model_designer.CCXGate(ccx_params)
ccx_target_out = ccx_out["TARGET_OUT"]
ccx_ctrl_out = ccx_out["CTRL_OUT"]

rz_params = RZGate(phi=1.9)
model_designer.RZGate(rz_params, in_wires={"IN": ccx_target_out})

swap_params = SwapGate()
model_designer.SwapGate(swap_params, in_wires={"IN": ccx_ctrl_out})

circuit = model_designer.synthesize()

circuit.show()

Parametrized Rotations

Rotation Gates can be performed on classiq parameters.

Example

Textual ModelSDK

    {
        "logic_flow": [
            {
                "function": "RZGate",
                "function_params": {
                    "phi": {"name": "x"}
                }
            }
        ]
    }

from classiq import ModelDesigner
from classiq.builtin_functions import Parameter
from classiq.builtin_functions.standard_gates import RZGate

model_designer = ModelDesigner()
rz_params = RZGate(phi=Parameter(name="x"))
model_designer.RZGate(rz_params)
model_designer.synthesize()