qrunch.quantum.operators.pauli.strings

Efficient representation of a Pauli string.

Classes

PauliString

Class for efficiently describing a hermitian Pauli string.

Stabilizer

Class for describing Stabilizer of Pauli strings.
class PauliString

Bases: object

Class for efficiently describing a hermitian Pauli string.

It is enforced that no indices can be overlapping for x, y, or z, i.e., expressions of the form:

\[X(1) Y(3) X(2) Z(5).\]
__init__(x_indices: tuple[int, ...] = (), y_indices: tuple[int, ...] = (), z_indices: tuple[int, ...] = ()) → None

Initialize a Pauli string.

Parameters:

  • x_indices (tuple[int, ...]) – Tuple holding which indices the X operators act on.. Defaults to ().

  • y_indices (tuple[int, ...]) – Tuple holding which indices the Y operators act on.. Defaults to ().

  • z_indices (tuple[int, ...]) – Tuple holding which indices the Z operators act on.. Defaults to ().

Return type:

None

property as_ints: tuple[int, int, int]

Get the x-mask, y-mask and z-mask defining the Pauli string as integers.

commutative_sign(other: PauliString) → int

Return the sign when commuting the Pauli string with and other.

Parameters:

other (PauliString)

Return type:

int

classmethod from_sorted_and_disjoint_sets(x_indices: tuple[int, ...], y_indices: tuple[int, ...], z_indices: tuple[int, ...]) → PauliString

Construct a PauliString assuming the indices are already valid.

  • Sorted: Each of x_indices, y_indices, and z_indices is in strictly ascending order (no need to sort internally).

  • Disjoint: No index appears in more than one of the three tuples.

  • No duplicates: No index is repeated within a tuple.

This constructor bypasses all duplicate/overlap/sortedness checks for speed, and should only be used in performance-critical code where the caller can guarantee these invariants (e.g., after generating indices in canonical order).

Parameters:

  • x_indices (tuple[int, ...]) – Sorted tuple of qubit indices acted on by X.

  • y_indices (tuple[int, ...]) – Sorted tuple of qubit indices acted on by Y.

  • z_indices (tuple[int, ...]) – Sorted tuple of qubit indices acted on by Z.

Return type:

PauliString

classmethod from_stabilizer(stabilizer: Stabilizer) → PauliString

Return the Pauli string corresponding to the given stabilizer.

Parameters:

stabilizer (Stabilizer)

Return type:

PauliString

classmethod from_z_indices(z_indices: tuple[int, ...]) → PauliString

Construct a PauliString assuming only sorted z_indices.

This constructor bypasses all duplicate/overlap/sortedness checks for speed, and should only be used in performance-critical code where the caller can guarantee these invariants (e.g., after generating indices in canonical order).

Parameters:

z_indices (tuple[int, ...]) – Sorted tuple of qubit indices acted on by Z.

Return type:

PauliString

is_commuting(other: PauliString) → bool

Check if the Pauli string commutes with another.

Parameters:

other (PauliString)

Return type:

bool

is_diagonal() → bool

Check if the Pauli string only contains diagonal (I and Z) operators.

Return type:

bool

is_identity() → bool

Check if the Pauli string does not contain any operators.

Returns: True if no operators are present, False otherwise.

Return type:

bool

property max_index: int | None

Return the largest index of the Pauli string.

property min_index: int | None

Return the largest index of the Pauli string.

multiply(other: PauliString) → tuple[PauliString, complex]

Multiply with other Pauli string.

Parameters:

other (PauliString)

Return type:

tuple[PauliString, complex]

to_stabilizer(num_qubits: int | None = None) → Stabilizer

Get the stabilizer of the Pauli string.

Parameters:

num_qubits (int | None) – Number of qubits in the stabilizer (must be larger than the Pauli operator working on the largest index)

Return type:

Stabilizer

property x_indices: tuple[int, ...]

Get the indices of the X operators.

property y_indices: tuple[int, ...]

Get the indices of the Y operators.

property z_indices: tuple[int, ...]

Get the indices of the Z operators.

class Stabilizer

Bases: object

Class for describing Stabilizer of Pauli strings.

These are used for stabilizer codes, https://en.wikipedia.org/wiki/Stabilizer_code

All fields are immutable (frozen=True) so an instance can be safely reused.

Parameters:

  • z – One-hot encoding of Z operators.

  • x – One-hot encoding of X operators.

__init__(z: list[int], x: list[int]) → None
Parameters:

  • z (list[int])

  • x (list[int])

Return type:

None

multiply(other: Stabilizer) → tuple[Stabilizer, complex]

Multiply with other stabilizer.

Parameters:

other (Stabilizer)

Return type:

tuple[Stabilizer, complex]

x: list[int]
z: list[int]