qml.estimator.ops.Hadamard

class Hadamard(wires=None)

Bases: ResourceOperator

Resource class for the Hadamard gate.

Parameters:

wires (Sequence[int] | int | None) – the wire the operation acts on

Resources:

The Hadamard gate is treated as a fundamental gate and thus it cannot be decomposed further. Requesting the resources of this gate raises a ResourcesUndefinedError error.

See also

The corresponding PennyLane operation Hadamard.

Attributes

num_wires
resource_params	Returns a dictionary containing the minimal information needed to compute the resources.

num_wires = 1

resource_params

Returns a dictionary containing the minimal information needed to compute the resources.

Returns:

Empty dictionary. The resources of this operation don’t depend on any additional parameters.

Return type:

dict

Methods

adjoint_resource_decomp([target_resource_params])	Returns a list representing the resources for the adjoint of the operator.
controlled_resource_decomp(num_ctrl_wires, ...)	Returns a list representing the resources for a controlled version of the operator.
pow_resource_decomp(pow_z[, ...])	Returns a list representing the resources for an operator raised to a power.
resource_decomp()	Returns a list representing the resources of the operator.
resource_rep()	Returns a compressed representation containing only the parameters of the operator that are needed to compute the resources.

classmethod adjoint_resource_decomp(target_resource_params=None)

Returns a list representing the resources for the adjoint of the operator.

Parameters:

target_resource_params (dict | None) – A dictionary containing the resource parameters of the target operator.

Resources:

This operation is self-adjoint, so the resources of the adjoint operation results are same as the original operation.

Returns:

A list of GateCount objects, where each object represents a specific quantum gate and the number of times it appears in the decomposition.

Return type:

list[GateCount]

classmethod controlled_resource_decomp(num_ctrl_wires, num_zero_ctrl, target_resource_params=None)

Returns a list representing the resources for a controlled version of the operator.

Parameters:

• num_ctrl_wires (int) – the number of qubits the operation is controlled on

• num_zero_ctrl (int) – the number of control qubits, that are controlled when in the \(|0\rangle\) state

• target_resource_params (dict | None) – A dictionary containing the resource parameters of the target operator.

Resources:

For a single control wire, the cost is a single instance of CH. Two additional X gates are used to flip the control qubit if it is zero-controlled. In the case where multiple controlled wires are provided, the resources are derived from the following identities:

\[\begin{split}\begin{align} \hat{H} &= \hat{R}_{y}(\frac{\pi}{4}) \cdot \hat{Z} \cdot \hat{R}_{y}(\frac{-\pi}{4}), \\ \hat{Z} &= \hat{H} \cdot \hat{X} \cdot \hat{H}. \end{align}\end{split}\]

Specifically, the resources are given by two RY gates, two Hadamard gates and a X gate. By replacing the X gate with MultiControlledX gate, we obtain a controlled-version of this identity.

Returns:

A list of GateCount objects, where each object represents a specific quantum gate and the number of times it appears in the decomposition.

Return type:

list[GateCount]

classmethod pow_resource_decomp(pow_z, target_resource_params=None)

Returns a list representing the resources for an operator raised to a power.

Parameters:

• pow_z (int) – the power that the operator is being raised to

• target_resource_params (dict | None) – A dictionary containing the resource parameters of the target operator.

Resources:

The Hadamard gate raised to even powers produces identity and raised to odd powers it produces itself.

Returns:

A list of GateCount objects, where each object represents a specific quantum gate and the number of times it appears in the decomposition.

Return type:

list[GateCount]

classmethod resource_decomp()

Returns a list representing the resources of the operator. Each object represents a quantum gate and the number of times it occurs in the decomposition.

Resources:

The Hadamard gate is treated as a fundamental gate and thus it cannot be decomposed further. Requesting the resources of this gate raises a ResourcesUndefinedError error.

Raises:

ResourcesUndefinedError – This gate is fundamental, no further decomposition defined.

classmethod resource_rep()

Returns a compressed representation containing only the parameters of the operator that are needed to compute the resources.

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