qat.spd.pauli_tableau.TableauSimulation

class qat.spd.pauli_tableau.TableauSimulation(obs, **kwargs)

Implements sparse Pauli dynamics by evolving a PauliTableau representation of an observable through the Heisenberg picture

Several truncation methods are available:

  • threshold: discard Pauli rows with coefficients below this value (in absolute value)

  • max_weight: discard Pauli rows with Hamming weight above this value

  • max_size: truncate the tableau to this maximum size, keeping rows with the largest coefficients

  • max_x_weight: discard Pauli rows with more X or Y terms than this maximum

Parameters:

  • obs (qat.core.Observable) – Observable to be evolved as a PauliTableau.

  • threshold (float, optional) – Minimum absolute coefficient to retain a Pauli row (default is 1e-16).

  • max_weight (int, optional) – Maximum allowed Hamming weight for the Pauli rows.

  • max_size (int, optional) – Maximum allowed number of Pauli rows in the tableau.

  • max_x_weight (int, optional) – Maximum allowed number of X or Y terms in a Pauli row.

  • nprocs (int, optional) – Number of processes to use for parallel execution (default is 1).

nqbits

Number of qubits in the system.

Type:

int

observable

Heisenberg-evolved observable represented as a PauliTableau.

Type:

qat.core.Observable

threshold

Threshold for filtering Pauli rows based on coefficient magnitude.

Type:

float

max_weight

Maximum Hamming weight for retained Pauli rows.

Type:

int or None

max_size

Maximum number of Pauli rows allowed in the tableau.

Type:

int or None

max_x_weight

Maximum number of X or Y terms allowed in a Pauli row.

Type:

int or None

nprocs

Number of processes used in parallel computations.

Type:

int

apply_rotation(pauli_rota, angle)

Apply a unitary Pauli rotation to the observable.

The rotation applied is defined as:

\[e^{i \frac{\theta}{2} \sigma} \mathcal{O} e^{-i \frac{\theta}{2} \sigma}\]

Where \(\sigma\) is pauli_rota and \(\theta\) is angle.

The steps are:

  1. Identify the set of Pauli rows in self.observable that anticommute with pauli_rota.

  2. Compute new Pauli rows and update coefficients of existing Pauli rows.

  3. Discard existing Pauli rows from self.observable that do not fit the truncation criteria

  4. Insert new Pauli rows from new_paulis into self.observable if they fit the truncation criteria

  5. If max_size is exceeded, remove the smallest coefficients until the size of the Pauli tableau is below max_size

Parameters:

  • pauli_rota (PauliTableau) – The axis of the Pauli rotation

  • angle (float) – The angle of the rotation

expectation_value()

Compute expectation value of the observable at the end of the circuit