qml.estimator.templates.GQSPTimeEvolution

class GQSPTimeEvolution(walk_op, time, one_norm, poly_approx_precision=None, wires=None)

Bases: ResourceOperator

Resource class for performing Hamiltonian simulation using GQSP.

Parameters:

• walk_op (ResourceOperator) – the quantum walk operator

• time (float) – the simulation time

• one_norm (float) – one norm of the Hamiltonian

• poly_approx_precision (float) – the tolerance for error in the polynomial approximation

• 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 7 and Corollary 8 of Generalized Quantum Signal Processing (2024).

Raises:

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

• ValueError – if the time provided is not a positive real number greater than zero

• ValueError – if the one_norm provided is not a positive real number greater than zero

• ValueError – if the poly_approx_precision provided is not a positive real number greater than zero

Example

The resources for this operation are computed using:

>>> import pennylane.estimator as qre
>>> walk_op = qre.RX(0.1, wires=0)
>>> time = 1.0
>>> one_norm = 1.0
>>> approx_error = 0.01
>>> hamsim = qre.GQSPTimeEvolution(walk_op, time, one_norm, approx_error)
>>> print(qre.estimate(hamsim))
--- Resources: ---
 Total wires: 2
   algorithmic wires: 2
   allocated wires: 0
     zero state: 0
     any state: 0
 Total gates : 1.110E+3
   'T': 1.080E+3,
   'CNOT': 12,
   'X': 6,
   'Hadamard': 12

Attributes

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

resource_keys = {'one_norm', 'poly_approx_precision', 'time', 'walk_op'}

resource_params

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

Returns:

A dictionary containing the resource parameters:

• walk_op (CompressedResourceOp): the quantum walk operator

• time (float): the simulation time

• one_norm (float): one norm of the Hamiltonian

• poly_approx_precision (float): the tolerance for error in the polynomial approximation

Return type:

dict

Methods

poly_approx(time, one_norm, epsilon)	Obtain the maximum degree of the polynomial approximation required to approximate \(e^{(iHt \cos{\theta})}\) within some error epsilon.
resource_decomp(walk_op, time, one_norm[, ...])	Returns a list representing the resources of the operator.
resource_rep(walk_op, time, one_norm[, ...])	Returns a compressed representation containing only the parameters of the Operator that are needed to compute the resources.

static poly_approx(time, one_norm, epsilon)

Obtain the maximum degree of the polynomial approximation required to approximate \(e^{(iHt \cos{\theta})}\) within some error epsilon.

Parameters:

• time (float) – the simulation time

• one_norm (float) – one norm of the Hamiltonian

• epsilon (float) – the tolerance for error in the polynomial approximation

Returns:

the minimum degree of the polynomial approximation

Return type:

int

classmethod resource_decomp(walk_op, time, one_norm, poly_approx_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:

• walk_op (CompressedResourceOp) – the quantum walk operator

• time (float) – the simulation time

• one_norm (float) – one norm of the Hamiltonian

• poly_approx_precision (float | None) – the tolerance for error in the polynomial approximation

Resources:

The resources are obtained as described in Theorem 7 and Corollary 8 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(walk_op, time, one_norm, poly_approx_precision=None)

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

Parameters:

• walk_op (CompressedResourceOp) – the quantum walk operator

• time (float) – the simulation time

• one_norm (float) – one norm of the Hamiltonian

• poly_approx_precision (float | None) – the tolerance for error in the polynomial approximation

Returns:

the operator in a compressed representation

Return type:

CompressedResourceOp

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