Using PennyLane

Release news

Development

API

Internals

  1. Docs
  2. qml.estimator
  3. qml.estimator.compact_hamiltonian.PauliHamiltonian

qml.estimator.compact_hamiltonian.PauliHamiltonian

class PauliHamiltonian(num_qubits, pauli_terms, one_norm=None)[source]

Bases: object

Stores the minimum necessary information required to estimate resources for a Hamiltonian expressed as a linear combination of tensor products of Pauli operators.

Parameters:

  • num_qubits (int) – total number of qubits the Hamiltonian acts on

  • pauli_terms (dict[str, int] | Iterable[dict]) – A dictionary representing the Hamiltonian terms where the keys are Pauli strings, e.g "XY", and the values are integers denoting how frequently a Pauli string appears in the Hamiltonian. When a list of dictionaries is provided, each dictionary is interpreted as a commuting group of terms. See the Usage Details section for more information.

  • one_norm (float | int | None) – the one-norm of the Hamiltonian

Raises:

  • TypeError – if pauli_terms is not a dictionary

  • ValueError – if one_norm is provided but is not a non-negative float or integer

  • ValueError – if pauli_terms contains invalid keys (not Pauli strings) or values (not integers)

See also

TrotterPauli, SelectPauli

Example

A PauliHamiltonian is a compact representation which can be used with compatible templates to obtain resource estimates. Consider for example the Hamiltonian:

\[\hat{H} = 0.1 \cdot \Sigma^{30}_{j=1} \hat{X}_{j} \hat{X}_{j+1} - 0.05 \cdot \Sigma^{30}_{k=1} \hat{Y}_{k} \hat{Y}_{k+1} + 0.25 \cdot \Sigma^{40}_{l=1} \hat{X}_{l}\]

This Hamiltonian is represented in a compact form using PauliHamiltonian:

>>> import pennylane.estimator as qre
>>> pauli_ham = qre.PauliHamiltonian(
...     num_qubits = 40,
...     pauli_terms = {"X":40, "XX":30, "YY":30},
...     one_norm = 14.5,  # (|0.1| * 30) + (|-0.05| * 30) + (|0.25| * 40)
... )
>>> pauli_ham
PauliHamiltonian(num_qubits=40, one_norm=14.5, pauli_terms={'X': 40, 'XX': 30, 'YY': 30})

The Hamiltonian can be used as input for other subroutines, like TrotterPauli:

>>> num_steps, order = (10, 2)
>>> res = qre.estimate(qre.TrotterPauli(pauli_ham, num_steps, order))
>>> print(res)
--- Resources: ---
 Total wires: 40
   algorithmic wires: 40
   allocated wires: 0
     zero state: 0
     any state: 0
 Total gates : 9.400E+4
   'T': 8.800E+4,
   'CNOT': 2.400E+3,
   'Z': 1.200E+3,
   'S': 2.400E+3

The terms of the Hamiltonian can also be separated into groups such that all operators in the group commute. Users can instantiate the PauliHamiltonian by specifying these groups of terms directly.

>>> import pennylane.estimator as qre
>>> commuting_groups = [
...     {"X": 40, "XX": 30}, # first commuting group
...     {"YY": 30}, # second commuting group
... ]
>>> pauli_ham = qre.PauliHamiltonian(
...     num_qubits = 40,
...     pauli_terms = commuting_groups,
...     one_norm = 14.5,  # (|0.1| * 30) + (|-0.05| * 30) + (|0.25| * 40)
... )
>>> pauli_ham
PauliHamiltonian(num_qubits=40, one_norm=14.5, pauli_terms=[{'X': 40, 'XX': 30}, {'YY': 30}])

Note that providing more information will generally lead to more accurate resource estimates.

>>> num_steps, order = (10, 2)
>>> res = qre.estimate(qre.TrotterPauli(pauli_ham, num_steps, order))
>>> print(res)
--- Resources: ---
 Total wires: 40
   algorithmic wires: 40
   allocated wires: 0
     zero state: 0
     any state: 0
 Total gates : 5.014E+4
   'T': 4.708E+4,
   'CNOT': 1.260E+3,
   'Z': 600,
   'S': 1.200E+3

num_qubits

The number of qubits the Hamiltonian acts on

num_terms

The total number of Pauli words in the Hamiltonian

one_norm

The one-norm of the Hamiltonian

pauli_terms

A dictionary representing the distribution of Pauli words in the Hamiltonian
num_qubits

The number of qubits the Hamiltonian acts on

num_terms

The total number of Pauli words in the Hamiltonian

one_norm

The one-norm of the Hamiltonian

pauli_terms

A dictionary representing the distribution of Pauli words in the Hamiltonian

Previous
Next