qml.labs.resource_estimation.ResourceToffoli

class ResourceToffoli(elbow=None, wires=None)

Bases: ResourceOperator

Resource class for the Toffoli gate.

Parameters:

• wires (Sequence[int], optional) – the subsystem the gate acts on

• elbow (Union[str, None]) – String identifier to determine if this is a special type of Toffoli gate (left or right elbow). Default value is None.

Resources:

If elbow is provided, resources are obtained from Figure 4 of Babbush 2018.

If elbow is None, the resources are obtained from Figure 1 of Jones 2012.

The circuit which applies the Toffoli gate on target wire ‘target’ with control wires (‘c1’, ‘c2’) is defined as:

    c1: ─╭●────╭X──T†────────╭X────╭●───────────────╭●─┤
    c2: ─│──╭X─│──╭●───T†─╭●─│──╭X─│────────────────╰Z─┤
  aux1: ─╰X─│──│──╰X───T──╰X─│──│──╰X────────────────║─┤
  aux2: ──H─╰●─╰●──T─────────╰●─╰●──H──S─╭●──H──┤↗├──║─┤
target: ─────────────────────────────────╰X──────║───║─┤
                                                 ╚═══╝

Specifically, the resources are defined as nine ResourceCNOT gates, three ResourceHadamard gates, one ResourceCZ gate, one ResourceS gate, two ResourceT gates and two adjoint ResourceT gates.

See also

Toffoli

Example

The resources for this operation are computed using:

>>> re.ResourceToffoli.resource_decomp()
[AllocWires(2), (9 x CNOT), (3 x Hadamard), (1 x S), (1 x CZ), (2 x T), (2 x Adjoint(T)), FreeWires(2)]

Attributes

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

num_wires = 3

resource_keys = {'elbow'}

resource_params

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

Returns:

• elbow (Union[str, None]): String identifier to determine if this is a special type of Toffoli gate (left or right elbow).

Return type:

A dictionary containing the resource parameters

Methods

adjoint_resource_decomp([elbow])	Returns a list representing the resources for the adjoint of the operator.
controlled_resource_decomp(...[, elbow])	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.
elbow_decomp([elbow])
pow_resource_decomp(pow_z[, elbow])	Returns a list representing the resources for an operator raised to a power.
queue([context])	Append the operator to the Operator queue.
resource_decomp([elbow])	Returns a list of GateCount objects representing the resources of the operator.
resource_rep([elbow])	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
textbook_resource_decomp([elbow])	Returns a list of GateCount objects representing the resources of 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(elbow=None, **kwargs)

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

Resources:

This operation is self-adjoint, so the resources of the adjoint operation results 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, elbow=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

• elbow (Union[str, None]) – String identifier to determine if this is a special type of Toffoli gate (left or right elbow). Default value is None.

Resources:

The resources are expressed as one general ResourceMultiControlledX gate.

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.

static elbow_decomp(elbow='left')

A function that prepares the resource decomposition obtained from Figure 4 of Babbush 2018.

Parameters:

elbow (str, optional) – One of “left” or “right”. Defaults to “left”.

Returns:

The resources of decomposing the elbow gates.

Return type:

list[GateCount]

classmethod pow_resource_decomp(pow_z, elbow=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:

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]

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

Append the operator to the Operator queue.

classmethod resource_decomp(elbow=None, **kwargs)

Returns a list of GateCount objects representing the resources of the operator. Each GateCount object specifies a gate type and its total occurrence count.

Resources:

If elbow is provided, resources are obtained from Figure 4 of arXiv:1805.03662.

If elbow is None, the resources are obtained from Figure 1 of Jones 2012.

The circuit which applies the Toffoli gate on target wire ‘target’ with control wires (‘c1’, ‘c2’) is defined as:

    c1: ─╭●────╭X──T†────────╭X────╭●───────────────╭●─┤
    c2: ─│──╭X─│──╭●───T†─╭●─│──╭X─│────────────────╰Z─┤
  aux1: ─╰X─│──│──╰X───T──╰X─│──│──╰X────────────────║─┤
  aux2: ──H─╰●─╰●──T─────────╰●─╰●──H──S─╭●──H──┤↗├──║─┤
target: ─────────────────────────────────╰X──────║───║─┤
                                                 ╚═══╝

Specifically, the resources are defined as nine ResourceCNOT gates, three ResourceHadamard gates, one ResourceCZ gate, one ResourceS gate, two ResourceT gates and two adjoint ResourceT gates.

classmethod resource_rep(elbow=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 textbook_resource_decomp(elbow=None, **kwargs)

Returns a list of GateCount objects representing the resources of the operator. Each GateCount object specifies a gate type and its total occurrence count.

Resources:

If elbow is provided, resources are obtained from Figure 4 of arXiv:1805.03662.

If elbow is None, the resources are taken from Figure 4.9 of Nielsen, M. A., & Chuang, I. L. (2010).

The circuit is defined as:

0: ───────────╭●───────────╭●────╭●──T──╭●─┤
1: ────╭●─────│─────╭●─────│───T─╰X──T†─╰X─┤
2: ──H─╰X──T†─╰X──T─╰X──T†─╰X──T──H────────┤

Specifically, the resources are defined as six ResourceCNOT gates, two ResourceHadamard gates, four ResourceT gates and three adjoint ResourceT gates.

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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