qml.estimator.templates.Qubitization

class Qubitization(prep_op, select_op, wires=None)

Bases: ResourceOperator

Resource class for the Qubitization operator. The operator is also referred to as the Quantum Walk operator.

The operator is constructed by encoding a Hamiltonian, written as a linear combination of unitaries, into a block encoding (see Figure 1 in arXiv:1805.03662).

\[Q = \text{Prep}_{H}(2|0\rangle\langle 0| - I)\text{Prep}_{H}^{\dagger} \text{Sel}_{H}.\]

Parameters:

• prep_op (ResourceOperator) – the operator that prepares the coefficients of the LCU

• select_op (ResourceOperator) – the operator that selectively applies the unitaries of the LCU

• wires (WiresLike | None) – the wires the operation acts on

Resources:

The resources are obtained from Equation 9 in Babbush et al. (2018). Specifically, the walk operator is defined as \(W = R \cdot S\), where \(R\) is a reflection about the state prepared by the Prepare operator, and \(S\) is the Select operator. The cost is therefore one Select and one Reflection.

Raises:

ValueError – if the wires provided don’t match the number of wires expected by the operator

Example

The resources for this operation are computed using:

>>> import pennylane.estimator as qre
>>> prep_op = qre.Hadamard(wires=0)
>>> select_op = qre.Z(wires=0)
>>> qw_op = qre.Qubitization(prep_op, select_op)
>>> print(qre.estimate(qw_op))
--- Resources: ---
 Total wires: 1
   algorithmic wires: 1
   allocated wires: 0
     zero state: 0
     any state: 0
 Total gates : 10
   'X': 4,
   'Z': 4,
   'Hadamard': 2

Attributes

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

resource_keys = {'prep_op', 'select_op'}

resource_params

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

Returns:

A dictionary containing the resource parameters:

• prep_op (CompressedResourceOp): a compressed representation for the operator that prepares the coefficients of the LCU

• select_op (CompressedResourceOp): a compressed representation for the operator that selectively applies the unitaries of the LCU

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.
resource_decomp(prep_op, select_op)	Returns a list representing the resources of the operator.
resource_rep(prep_op, select_op)	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:

Reflection operators are self-adjoint, and the Select operator is also self-adjoint. Thus the adjoint of this operator has the same resources, just applied in reverse order.

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

Resources:

The resources are obtained directly from Figure 1 in Babbush et al. (2018).

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(prep_op, select_op)

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

Parameters:

• prep_op (CompressedResourceOp) – A compressed representation for the operator that prepares the coefficients of the LCU.

• select_op (CompressedResourceOp) – A compressed representation for the operator that selectively applies the unitaries of the LCU.

Resources:

The resources are obtained from Equation 9 in Babbush et al. (2018). Specifically, the walk operator is defined as \(W = R \cdot S\), where \(R\) is a reflection about the state prepared by the Prepare operator, and \(S\) is the Select operator.

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(prep_op, select_op)

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

Parameters:

• prep_op (CompressedResourceOp) – A compressed representation for the operator that prepares the coefficients of the LCU.

• select_op (CompressedResourceOp) – A compressed representation for the operator that selectively applies the unitaries of the LCU.

Returns:

the operator in a compressed representation

Return type:

CompressedResourceOp

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