qat.synthopline.interface.WeylOperator

class qat.synthopline.interface.WeylOperator

Class representing a Pauli operator in a Weyl basis.

Pauli operators are represented via a \(\mathbb{Z}_4\)-vector of length \(2n + 1\).

The first entry represents a global phase as a power of \(\omega=i\).

The \(n\) next entries correspond to powers of \(Z_i\) for each qubit \(i\).

The \(n\) last entries correspond to powers of \(X_i\) for each qubit \(i\).

The operator represented by the string \(1|11|23\) will be:

\[i^{-2 - 2 - 3}(Z_0^1 Z_1^1)(X_0^2 X_1^3)\]

More generally, \(\phi|a|b\) represents the operator:

\[i^{-2\phi - a\cdot b} Z^a X^b\]

where \(P^x = P_0^{x_0}...P_{n-1}^{x_{n-1}}\) and \(\cdot\) represent the scalar product between vectors over \(\mathbb{Z}_4\).

A detailed introduction can be found in [dB12].

from qat.synthopline.interface import WeylOperator

pauli_operator = "IZY"

weyl_operator = WeylOperator(pauli_operator)
print(weyl_operator)

( 0 | 0 1 3 |0 0 3 )

Conjugate the Weyl operator using an OperatorTableau.

The conjugation happens in place.

Converts the Weyl operator back to a Pauli operator and a global phase.

Returns:

a pair (phase, pauli_string). If phase is True, then the operator: picked up a global phase of \(\pi\)

Return type:

(bool, str)