qml.labs.resource_estimation.ResourceRZ

class ResourceRZ(precision=None, wires=None)

Bases: ResourceOperator

Resource class for the RZ gate.

Keyword Arguments:

• precision (float) – error threshold for clifford plus T decomposition of this operation

• wires (Any, Wires, optional) – the wire the operation acts on

Resources:

A single qubit rotation gate can be approximately synthesised from Clifford and T gates. The resources are approximating the gate with a series of T gates. The expected T-count is taken from (the ‘Simulation Results’ section) Efficient Synthesis of Universal Repeat-Until-Success Circuits. The cost is given as:

\[T_{count} = \lceil(1.149 * log_{2}(\frac{1}{\epsilon}) + 9.2)\rceil\]

See also

RZ

Example

The resources for this operation are computed using:

>>> op = plre.estimate(plre.ResourceRZ)()
>>> op
--- Resources: ---
 Total qubits: 1
 Total gates : 21
 Qubit breakdown:
  clean qubits: 0, dirty qubits: 0, algorithmic qubits: 1
 Gate breakdown:
  {'T': 21}

The operation does not require any parameters directly, however, it will depend on the single qubit error threshold, which can be set using a config dictionary.

>>> config = {"error_rz": 1e-4}
>>> op = plre.estimate(plre.ResourceRZ, config=config)()
>>> print(op)
--- Resources: ---
 Total qubits: 1
 Total gates : 24
 Qubit breakdown:
  clean qubits: 0, dirty qubits: 0, algorithmic qubits: 1
 Gate breakdown:
  {'T': 24}

Attributes

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

num_wires = 1

resource_keys = {'precision'}

resource_params

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

Returns:

• precision (Union[float, None]): error threshold for the approximation

Return type:

A dictionary containing the resource parameters

Methods

adjoint_resource_decomp([precision])	Returns a list representing the resources for the adjoint of the operator.
controlled_resource_decomp(...[, precision])	Returns a list representing the resources for a controlled version of the operator.
dequeue(op_to_remove[, context])	Remove the given resource operator(s) from the Operator queue.
pow_resource_decomp(pow_z[, precision])	Returns a list representing the resources for an operator raised to a power.
queue([context])	Append the operator to the Operator queue.
resource_decomp([precision])	Returns a list representing the resources of the operator.
resource_rep([precision])	Returns a compressed representation containing only the parameters of the Operator that are needed to compute the resources.
resource_rep_from_op()	Returns a compressed representation directly from the operator
tracking_name(*args, **kwargs)	Returns a name used to track the operator during resource estimation.
tracking_name_from_op()	Returns the tracking name built with the operator's parameters.

classmethod adjoint_resource_decomp(precision=None, **kwargs)

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

Resources:

The adjoint of a single qubit rotation changes the sign of the rotation angle, thus the resources of the adjoint operation result in 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(ctrl_num_ctrl_wires, ctrl_num_ctrl_values, precision=None, **kwargs)

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

Parameters:

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

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

• precision (float, optional) – error threshold for clifford plus T decomposition of this operation

Resources:

For a single control wire, the cost is a single instance of ResourceCRY. Two additional ResourceX 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 obtained from Figure 1b of the paper T-count and T-depth of any multi-qubit unitary. They are derived from the following identity:

\[\hat{RZ}(\theta) = \hat{X} \cdot \hat{RZ}(- \theta) \cdot \hat{X}.\]

By replacing the X gates with multi-controlled X gates, we obtain a controlled-version of this identity. Thus we are able to constructively or destructively interfere the gates based on the value of the 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]

static dequeue(op_to_remove, context=<class 'pennylane.queuing.QueuingManager'>)

Remove the given resource operator(s) from the Operator queue.

classmethod pow_resource_decomp(pow_z, precision=None, **kwargs)

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

Resources:

Taking arbitrary powers of a single qubit rotation produces a sum of rotations. The resources simplify to just one total single qubit rotation.

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]

queue(context=<class 'pennylane.queuing.QueuingManager'>)

Append the operator to the Operator queue.

classmethod resource_decomp(precision=None, **kwargs)

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:

A single qubit rotation gate can be approximately synthesised from Clifford and T gates. The resources are approximating the gate with a series of T gates. The expected T-count is taken from (the ‘Simulation Results’ section) Efficient Synthesis of Universal Repeat-Until-Success Circuits. The cost is given as:

\[T_{count} = \lceil(1.149 * log_{2}(\frac{1}{\epsilon}) + 9.2)\rceil\]

Parameters:

precision (float) – error threshold for clifford plus T decomposition of this operation

classmethod resource_rep(precision=None)

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

resource_rep_from_op()

Returns a compressed representation directly from the operator

classmethod tracking_name(*args, **kwargs)

Returns a name used to track the operator during resource estimation.

tracking_name_from_op()

Returns the tracking name built with the operator’s parameters.

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