qml.estimator.templates.GQSP

class GQSP(signal_operator, d_plus, d_minus=0, rotation_precision=None, wires=None)

Bases: ResourceOperator

Resource class for the Generalized Quantum Signal Processing (GQSP) algorithm.

The GQSP operator is defined based on Theorem 6 of Generalized Quantum Signal Processing (2024):

\[GQSP = \left( \prod_{j=1}^{d^{-}} R(\theta_{j}, \phi_{j}, 0) \hat{A}^{\prime} \right) \left( \prod_{j=1}^{d^{+}} R(\theta_{j + d^{-}}, \phi_{j + d^{-}}, 0) \hat{A} \right) R(\theta_0, \phi_0, \lambda),\]

where \(R\) is the single-qubit rotation operator and \(\vec{\phi}\), \(\vec{\theta}\) and \(\lambda\) are the rotation angles that generate the polynomial transformation. The maximum positive and negative polynomial degrees are denoted by \(d^{+}\) and \(d^{-}\), respectively. Additionally, \(\hat{A}\) and \(\hat{A}^{\prime}\) are given by:

\[\begin{split}\begin{align} \hat{A} &= \ket{0}\bra{0}\otimes\hat{U} + \ket{1}\bra{1}\otimes\mathbf{I}, \\ \hat{A}^{\prime} &= \ket{0}\bra{0}\otimes\mathbf{I} + \ket{1}\bra{1}\otimes\hat{U}^{\dagger}, \\ \\ \end{align}\end{split}\]

where \(U\) is a signal operator which encodes a target Hamiltonian.

Parameters:

• signal_operator (ResourceOperator) – the signal operator which encodes a target Hamiltonian

• d_plus (int) – The largest positive degree \(d^{+}\) of the polynomial transformation.

• d_minus (int) – The largest (in absolute value) negative degree \(d^{-}\) of the polynomial transformation, representing powers of the adjoint of the signal operator.

• rotation_precision (float | None) – The precision with which the general rotation gates are applied.

• wires (WiresLike | None) – The wires the operation acts on. This includes both the wires of the signal operator and the control wire required for block-encoding.

Resources:

The resources are obtained as described in Theorem 6 of Generalized Quantum Signal Processing (2024).

Raises:

• ValueError – if d_plus is not a positive integer greater than zero

• ValueError – if d_minus is not an integer greater than or equal to zero

• ValueError – if rotation_precision is not a positive real number greater than zero

• 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
>>> signal_op = qre.RX(0.1, wires=0)
>>> d_plus = 5
>>> d_minus = 3
>>> gqsp = qre.GQSP(signal_op, d_plus, d_minus)
>>> print(qre.estimate(gqsp))
--- Resources: ---
 Total wires: 2
   algorithmic wires: 2
   allocated wires: 0
     zero state: 0
     any state: 0
 Total gates : 1.438E+3
   'T': 1.396E+3,
   'CNOT': 16,
   'X': 10,
   'Hadamard': 16

Attributes

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

resource_keys = {'cmpr_signal_op', 'd_minus', 'd_plus', 'rotation_precision'}

resource_params

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

Returns:

A dictionary containing the resource parameters:

• cmpr_signal_op (CompressedResourceOp): the compressed representation of the signal operator which encodes the target Hamiltonian

• d_plus (int): The largest positive degree \(d^{+}\) of the polynomial transformation.

• d_minus (int): The largest (in absolute value) negative degree \(d^{-}\) of the polynomial transformation, representing powers of the adjoint of the signal operator.

• rotation_precision (float | None): The precision with which the general rotation gates are applied.

Return type:

dict

Methods

resource_decomp(cmpr_signal_op, d_plus[, ...])	Returns a list representing the resources of the operator.
resource_rep(cmpr_signal_op, d_plus[, ...])	Returns a compressed representation containing only the parameters of the Operator that are needed to compute the resources.

classmethod resource_decomp(cmpr_signal_op, d_plus, d_minus=0, rotation_precision=None)

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:

• cmpr_signal_op (CompressedResourceOp) – the compressed representation of the signal operator which encodes the target Hamiltonian

• d_plus (int) – The largest positive degree \(d^{+}\) of the polynomial transformation.

• d_minus (int) – The largest (in absolute value) negative degree \(d^{-}\) of the polynomial transformation, representing powers of the adjoint of the signal operator.

• rotation_precision (float | None) – The precision with which the general rotation gates are applied.

Resources:

The resources are obtained as described in Theorem 6 of Generalized Quantum Signal Processing (2024).

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(cmpr_signal_op, d_plus, d_minus=0, rotation_precision=None)

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

Parameters:

• cmpr_signal_op (CompressedResourceOp) – the compressed representation of the signal operator which encodes the target Hamiltonian

• d_plus (int) – The largest positive degree \(d^{+}\) of the polynomial transformation.

• d_minus (int) – The largest (in absolute value) negative degree \(d^{-}\) of the polynomial transformation, representing powers of the adjoint of the signal operator.

• rotation_precision (float | None) – The precision with which the general rotation gates are applied.

Returns:

the operator in a compressed representation

Return type:

CompressedResourceOp

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