qml.estimator.templates.SelectPauli

class SelectPauli(pauli_ham, wires=None)

Bases: ResourceOperator

Resource class for the Select opreation used with a Hamiltonian expressed as a linear combination of unitaries (LCU) where each unitary is a Pauli word.

Parameters:

• pauli_ham (PauliHamiltonian) – A Hamiltonian expressed as a linear combination of Pauli words, over which Select is applied.

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

Resources:

The resources are based on the analysis in Babbush et al. (2018), Section III.A, ‘Unary Iteration and Indexed Operations’, and Figures 4, 6, and 7.

Note: This implementation assumes we have access to \(n - 1\) additional auxiliary qubits, where \(n = \left\lceil log_{2}(N) \right\rceil\) and \(N\) is the number of batches of unitaries to select.

Raises:

• TypeError – If the input pauli_ham isn’t an instance of PauliHamiltonian.

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

See also

Select

Example

The resources for this operation are computed using:

>>> import pennylane.estimator as qre
>>> pauli_ham = qre.PauliHamiltonian(num_qubits=4, pauli_terms={"XY": 1, "Z": 2})
>>> select_pauli = qre.SelectPauli(pauli_ham)
>>> print(qre.estimate(select_pauli))
--- Resources: ---
 Total wires: 7
   algorithmic wires: 6
   allocated wires: 1
     zero state: 1
     any state: 0
 Total gates : 27
   'Toffoli': 2,
   'CNOT': 8,
   'X': 4,
   'Z': 1,
   'S': 2,
   'Hadamard': 10

Attributes

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

resource_keys = {'pauli_ham'}

resource_params

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

Returns:

A dictionary containing the resource parameters:

• pauli_ham (PauliHamiltonian): A Hamiltonian expressed as a linear combination of Pauli words, over which Select is applied.

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(pauli_ham)	The resources for a select implementation taking advantage of the unary iterator trick.
resource_rep(pauli_ham)	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:

Because each target operation is self-adjoint, the resources of the adjoint operation are the same as the original operation (up to some re-ordering of the application of the gates).

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 based on the analysis in Babbush et al. (2018), Section III.A, ‘Unary Iteration and Indexed Operations’. See Figures 4, 6, and 7. This presents the cost of a single qubit controlled Select operator. In the case of multiple control wires, we use one additional auxiliary qubit and two multi-controlled X gates.

Note: This implementation assumes we have access to \(n\) additional auxiliary qubits, where \(n = \left\lceil log_{2}(N) \right\rceil\) and \(N\) is the number of batches of unitaries to select.

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(pauli_ham)

The resources for a select implementation taking advantage of the unary iterator trick.

Parameters:

pauli_ham (PauliHamiltonian) – A Hamiltonian expressed as a linear combination of Pauli words, over which Select is applied.

Resources:

The resources are based on the analysis in Babbush et al. (2018), Section III.A, ‘Unary Iteration and Indexed Operations’, and Figures 4, 6, and 7.

Note: This implementation assumes we have access to \(n - 1\) additional auxiliary qubits, where \(n = \left\lceil log_{2}(N) \right\rceil\) and \(N\) is the number of batches of unitaries to select.

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(pauli_ham)

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

Parameters:

pauli_ham (PauliHamiltonian) – A Hamiltonian expressed as a linear combination of Pauli words, over which Select is applied.

Returns:

the operator in a compressed representation

Return type:

CompressedResourceOp

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