pprop.pauli.op module

This module defines PauliOp, which represents a Pauli word as a pair of bitmasks encoding X, Y, Z, and I operators across an arbitrary number of qubits.

Bitmask convention

Each qubit k is represented by bit k (i.e. 1 << k) in two integers:

x	z	Operator
0	0	I
1	0	X
0	1	Z
1	1	Y

class pprop.pauli.op.PauliOp(x=0, z=0)

Bases: object

A Pauli word represented as two integer bitmasks.

Using bitmasks instead of lists or dicts allows PauliOp objects to be hashed cheaply and compared in O(1), which is important because Pauli propagation creates a very large number of them. __slots__ is used to minimise per-instance memory overhead.

The encoding maps each qubit k to bit k in two integers x and z according to the table below:

x	z	Operator
0	0	I
1	0	X
0	1	Z
1	1	Y

Parameters:

• x (int, optional) – Bitmask encoding the qubits that carry an X or Y factor. Defaults to 0 (all identity).

• z (int, optional) – Bitmask encoding the qubits that carry a Z or Y factor. Defaults to 0 (all identity).

Examples

>>> PauliOp(0b101, 0b110)
Y0 Z1 X2

>>> PauliOp(0b1001)
X0 X3

>>> PauliOp()
I

copy()

Return a shallow copy of this PauliOp.

Returns:

A new instance with identical x and z bitmasks.

Return type:

PauliOp

classmethod from_qml(qml_op)

Construct a PauliOp from a PennyLane operator.

Accepts either a single-qubit PennyLane operator or an iterable of them (e.g. the result of iterating over a tensor product).

Parameters:

qml_op (pennylane.operation.Operator or Iterable) – A PennyLane X, Y, Z, or Identity operator, or an iterable thereof.

Returns:

Bitmask representation of the input operator.

Return type:

PauliOp

Notes

Identity operators are skipped; their bits remain 0, which is the correct encoding for I.

qubits()

Return the set of qubits where this word acts non-trivially (not as I).

Returns:

Qubit indices where self[k] != "I".

Return type:

set[int]

set(qubit, op)

Set the Pauli operator on a specific qubit in-place.

Updates the x and z bitmasks at bit position qubit to reflect the requested operator according to the bitmask convention.

Parameters:

• qubit (int) – Zero-based qubit index to update.

• op (str) – Target operator; one of "I", "X", "Y", or "Z".

Raises:

ValueError – If op is not one of the four valid Pauli operators.

Return type:

None

to_qml(indices)

Convert this PauliOp to a PennyLane operator on a subset of qubits.

Only the qubits listed in indices are included; qubits acting as identity are skipped. If all qubits are identity an Identity on wire 0 is returned as a fallback.

Parameters:

indices (list[int]) – Qubit indices to include in the operator.

Returns:

Tensor product of single-qubit Pauli operators over indices.

Return type:

pennylane.operation.Operator

weight()

Return the Pauli weight, i.e. the number of non-identity single-qubit factors.

Computed as the popcount of x | z: a qubit is non-identity if and only if at least one of its x or z bits is set.

Returns:

Number of qubits where the operator is X, Y, or Z.

Return type:

int

x

z

zerobracket()

Return True if this Pauli word has zero expectation in all but the Z/I basis.

A Pauli word \(P\) satisfies \(\langle 0 | P | 0 \rangle \neq 0\) if and only if every single-qubit factor is either \(Z\) or \(I\). This is equivalent to checking that no X bit is set (x == 0).

Return type:

bool