qml.estimator.ops.MultiControlledX

class MultiControlledX(num_ctrl_wires=None, num_zero_ctrl=0, wires=None)

Bases: ResourceOperator

Resource class for the MultiControlledX gate.

Parameters:

• num_ctrl_wires (int | None) – 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

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

Resources:

The resources are obtained based on the unary iteration technique described in Babbush et al. (2018). Specifically, the resources are defined as the following rules:

• If there are no control qubits, treat the operation as a X gate.

• If there is only one control qubit, treat the resources as a CNOT gate.

• If there are two control qubits, treat the resources as a Toffoli gate.

• If there are three or more control qubits (\(n\)), the resources obtained based on the unary iteration technique described in Babbush et al. (2018). Specifically, it requires \(n - 2\) clean qubits, and produces \(n - 2\) elbow gates and a single Toffoli.

See also

The corresponding PennyLane operation MultiControlledX.

Example

The resources for this operation are computed using:

>>> qml.estimator.MultiControlledX.resource_decomp(num_ctrl_wires=5, num_zero_ctrl=2)
[(4 x X), Allocate(3), (3 x TemporaryAND), (3 x Adjoint(TemporaryAND)), (1 x Toffoli), Deallocate(3)]

Attributes

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

resource_keys = {'num_ctrl_wires', 'num_zero_ctrl'}

resource_params

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

Returns:

A dictionary containing the resource 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

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(num_ctrl_wires, num_zero_ctrl)	Returns a list representing the resources of the operator.
resource_rep(num_ctrl_wires, num_zero_ctrl)	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)

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

Parameters:

target_resource_params (dict) – 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 originial 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)

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

Parameters:

• num_ctrl_wires (int) – the number of control qubits of the operation

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

• target_resource_params (dict) – A dictionary containing the resource parameters of the target operator.

Resources:

The resources are derived by combining the control qubits, control-values and into a single instance of MultiControlledX gate, controlled on the whole set of control-qubits.

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)

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) – A dictionary containing the resource parameters of the target operator.

Resources:

This operation is self-inverse, thus when raised to even integer powers acts like the identity operator 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(num_ctrl_wires, num_zero_ctrl)

Returns a list representing the resources 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

Resources:

The resources are obtained based on the unary iteration technique described in Babbush et al. (2018). Specifically, the resources are defined as the following rules:

• If there are no control qubits, treat the operation as a X gate.

• If there is only one control qubit, treat the resources as a CNOT gate.

• If there are two control qubits, treat the resources as a Toffoli gate.

• If there are three or more control qubits (\(n\)), the resources obtained based on the unary iteration technique described in Babbush et al. (2018). Specifically, it requires \(n - 2\) clean qubits, and produces \(n - 2\) elbow gates and a single Toffoli.

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_rep(num_ctrl_wires, num_zero_ctrl)

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

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

Returns:

the operator in a compressed representation

Return type:

CompressedResourceOp

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