qml.labs.resource_estimation.ResourceTrotterCDF

class ResourceTrotterCDF(compact_ham, num_steps, order, wires=None)

Bases: ResourceOperator

An operation representing the Suzuki-Trotter product approximation for the complex matrix exponential of compressed double factorized 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 compressed double factorized 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.

• wires (list[int] or optional) – the wires on which the operator acts

Resources:

The resources are defined according to the recursive formula presented above. The number of times an operator, \(e^{itO_{j}}\), is applied depends on the number of Trotter steps (n) and the order of the approximation (m) and is given by:

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

Furthermore, because of the symmetric form of the recursive formula, the first and last terms get grouped. This reduces the counts for those terms to:

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

The resources for a single step expansion of compressed double factorized Hamiltonian are calculated based on arXiv:2506.15784.

See also

TrotterProduct

The resources can be computed as:

Example

>>> import pennylane.labs.resource_estimation as plre
>>> num_steps, order = (1, 2)
>>> compact_ham = plre.CompactHamiltonian.cdf(num_orbitals = 4, num_fragments = 4)
>>> res = plre.estimate(plre.ResourceTrotterCDF(compact_ham, num_steps, order))
>>> print(res)
--- Resources: ---
 Total qubits: 8
 Total gates : 2.238E+4
 Qubit breakdown:
  clean qubits: 0, dirty qubits: 0, algorithmic qubits: 8
 Gate breakdown:
  {'T': 2.075E+4, 'S': 504.0, 'Z': 336.0, 'Hadamard': 336.0, 'CNOT': 448.0}

Attributes

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

num_wires = 1

resource_keys = {'compact_ham', 'num_steps', 'order'}

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 compressed double factorized 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.

Return type:

dict

Methods

adjoint_resource_decomp(*args, **kwargs)	Returns a list representing the resources for the adjoint of the operator.
controlled_resource_decomp(compact_ham, ...)	Returns the controlled resource decomposition.
dequeue(op_to_remove[, context])	Remove the given resource operator(s) from the Operator queue.
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(compact_ham, num_steps, ...)	Returns a list representing 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
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 representing the resources for the adjoint of the operator.

classmethod controlled_resource_decomp(compact_ham, num_steps, order, ctrl_num_ctrl_wires, ctrl_num_ctrl_values, **kwargs)

Returns the controlled resource decomposition.

Parameters:

• compact_ham (CompactHamiltonian) – a compressed double factorized 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.

• ctrl_num_ctrl_wires (int) – the number of control wires for the controlled operations

• ctrl_num_ctrl_values (int) – the number of control values for the controlled operations

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]

Resources:

The original resources are controlled only on the Z rotation gates.

static dequeue(op_to_remove, context=<class 'pennylane.queuing.QueuingManager'>)

Remove the given resource operator(s) from the Operator queue.

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(compact_ham, num_steps, order, **kwargs)

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 compressed double factorized 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.

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(compact_ham, num_steps, order)

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

Parameters:

• compact_ham (CompactHamiltonian) – a compressed double factorized 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.

Returns:

the operator in a compressed representation

Return type:

CompressedResourceOp

resource_rep_from_op()

Returns a compressed representation directly from the operator

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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