qml.labs.resource_estimation.ResourceTrotterVibronic¶

class ResourceTrotterVibronic(compact_ham, num_steps, order, phase_grad_precision=1e-06, coeff_precision=0.001, wires=None)[source]¶

Bases: ResourceOperator

An operation representing the Suzuki-Trotter product approximation for the complex matrix exponential of real-space vibronic Hamiltonian.

The Suzuki-Trotter product formula provides a method to approximate the matrix exponential of Hamiltonian expressed as a linear combination of terms which in general do not commute. Consider the Hamiltonian \(H = \Sigma^{N}_{j=0} O_{j}\), the product formula is constructed using symmetrized products of the terms in the Hamiltonian. The symmetrized products of order \(m \in [1, 2, 4, ..., 2k]\) with \(k \in \mathbb{N}\) are given by:

\[\begin{split}\begin{align} S_{1}(t) &= \Pi_{j=0}^{N} \ e^{i t O_{j}} \\ S_{2}(t) &= \Pi_{j=0}^{N} \ e^{i \frac{t}{2} O_{j}} \cdot \Pi_{j=N}^{0} \ e^{i \frac{t}{2} O_{j}} \\ &\vdots \\ S_{m}(t) &= S_{m-2}(p_{m}t)^{2} \cdot S_{m-2}((1-4p_{m})t) \cdot S_{m-2}(p_{m}t)^{2}, \end{align}\end{split}\]

where the coefficient is \(p_{m} = 1 / (4 - \sqrt[m - 1]{4})\). The \(m^{\text{th}}\) order, \(n\)-step Suzuki-Trotter approximation is then defined as:

\[e^{iHt} \approx \left [S_{m}(t / n) \right ]^{n}.\]

For more details see J. Math. Phys. 32, 400 (1991).

Parameters:

compact_ham (CompactHamiltonian) – a real-space vibronic Hamiltonian to be approximately exponentiated
num_steps (int) – number of Trotter steps to perform
order (int) – order of the approximation (must be 1 or even)
phase_grad_precision (float) – precision for the phase gradient calculation, default value is 1e-6
coeff_precision (float) – precision for the loading of coefficients, default value is 1e-3
wires (list[int] or optional) – the wires on which the operator acts.

Resources:

The resources are defined according to the recursive formula presented above. Specifically, each operator in a single step expansion of the exponentiation is called a number of times given by the formula:

\[C_{O_{j}} = 2n \cdot 5^{\frac{m}{2} - 1}\]

Furthermore, the first and last terms of the Hamiltonian appear in pairs due to the symmetric form of the recursive formula. Those counts are further simplified by grouping like terms as:

\[\begin{split}\begin{align} C_{O_{0}} &= n \cdot 5^{\frac{m}{2} - 1} + 1, \\ C_{O_{N}} &= n \cdot 5^{\frac{m}{2} - 1}. \end{align}\end{split}\]

The resources for a single step expansion of real-space vibronic Hamiltonian are calculated based on arXiv:2411.13669.

The resources can be computed as:

Example

>>> import pennylane.labs.resource_estimation as plre
>>> compact_ham = plre.CompactHamiltonian.vibronic(num_modes=2, num_states=4, grid_size=4, taylor_degree=2)
>>> num_steps = 10
>>> order = 2
>>> res = plre.estimate_resources(plre.ResourceTrotterVibronic(compact_ham, num_steps, order))
>>> print(res)
--- Resources: ---
 Total qubits: 85.0
 Total gates : 1.332E+5
 Qubit breakdown:
  clean qubits: 75.0, dirty qubits: 0.0, algorithmic qubits: 10
 Gate breakdown:
  {'Z': 1, 'S': 1, 'T': 749.0, 'X': 1.456E+3, 'Hadamard': 6.638E+4, 'Toffoli': 2.320E+4, 'CNOT': 4.144E+4}

Attributes

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

num_wires = 0¶

resource_keys = {'coeff_precision', 'compact_ham', 'num_steps', 'order', 'phase_grad_precision'}¶

resource_params¶

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

Returns:

A dictionary containing the resource parameters:

compact_ham (~pennylane.labs.resource_estimation.CompactHamiltonian): a real-space vibronic Hamiltonian to be approximately exponentiated
num_steps (int): number of Trotter steps to perform
order (int): order of the approximation, must be 1 or even
phase_grad_precision (float): precision for the phase gradient calculation, default value is 1e-6
coeff_precision (float): precision for the loading of coefficients, default value is 1e-3

Return type:

dict

Methods

`adjoint_resource_decomp`(args, *kwargs)	Returns a list of actions that define the resources of the operator.
`controlled_resource_decomp`(...)	Returns a list representing the resources for a controlled version of the operator.
`default_adjoint_resource_decomp`(args, *kwargs)	Returns a list representing the resources for the adjoint of the operator.
`default_controlled_resource_decomp`(...)	Returns a list representing the resources for a controlled version of the operator.
`default_pow_resource_decomp`(pow_z, *args, ...)	Returns a list representing the resources for an operator raised to a power.
`default_resource_decomp`(compact_ham, ...)	Returns a list representing the resources of the operator.
`pow_resource_decomp`(pow_z, args, *kwargs)	Returns a list representing the resources for an operator raised to a power.
`queue`([context])	Append the operator to the Operator queue.
`resource_decomp`(args, *kwargs)	Returns a list of actions that define the resources of the operator.
`resource_rep`(compact_ham, num_steps, order)	Returns a compressed representation containing only the parameters of the Operator that are needed to compute a resource estimation.
`resource_rep_from_op`()	Returns a compressed representation directly from the operator
`set_resources`(new_func[, override_type])	Set a custom function to override the default resource decomposition.
`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(*args, **kwargs)¶: Returns a list of actions that define the resources of the operator.

classmethod controlled_resource_decomp(ctrl_num_ctrl_wires, ctrl_num_ctrl_values, *args, **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

classmethod default_adjoint_resource_decomp(*args, **kwargs)¶: Returns a list representing the resources for the adjoint of the operator.

classmethod default_controlled_resource_decomp(ctrl_num_ctrl_wires, ctrl_num_ctrl_values, *args, **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

classmethod default_pow_resource_decomp(pow_z, *args, **kwargs)¶

Returns a list representing the resources for an operator raised to a power.

Parameters:: pow_z (int) – exponent that the operator is being raised to

classmethod default_resource_decomp(compact_ham, num_steps, order, phase_grad_precision, coeff_precision, **kwargs)[source]¶

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

Parameters:

compact_ham (CompactHamiltonian) – a real space vibronic Hamiltonian to be approximately exponentiated
num_steps (int) – number of Trotter steps to perform
order (int) – order of the approximation, must be 1 or even
phase_grad_precision (float) – precision for the phase gradient calculation, default value is 1e-6
coeff_precision (float) – precision for the loading of coefficients, default value is 1e-3

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 pow_resource_decomp(pow_z, *args, **kwargs)¶

Returns a list representing the resources for an operator raised to a power.

Parameters:: pow_z (int) – exponent that the operator is being raised to

queue(context=<class 'pennylane.queuing.QueuingManager'>)¶: Append the operator to the Operator queue.

classmethod resource_decomp(*args, **kwargs)¶: Returns a list of actions that define the resources of the operator.

classmethod resource_rep(compact_ham, num_steps, order, phase_grad_precision=1e-06, coeff_precision=0.001)[source]¶

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

Parameters:

compact_ham (CompactHamiltonian) – a real space vibronic Hamiltonian to be approximately exponentiated
num_steps (int) – number of Trotter steps to perform
order (int) – order of the approximation, must be 1 or even
phase_grad_precision (float) – precision for the phase gradient calculation, default value is 1e-6
coeff_precision (float) – precision for the loading of coefficients, default value is 1e-3

Returns:

the operator in a compressed representation

Return type:

CompressedResourceOp

resource_rep_from_op()¶: Returns a compressed representation directly from the operator

classmethod set_resources(new_func, override_type='base')¶

Set a custom function to override the default resource decomposition.

This method allows users to replace any of the resource_decomp, adjoint_resource_decomp, ctrl_resource_decomp, or pow_resource_decomp methods globally for every instance of the class.

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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qml.labs.resource_estimation.ResourceTrotterVibronic¶

Attributes

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