z iSrSSKJr SSKrSSKJr SSKJr SSK J r SSK J r SS K Jr S SS jjrSSS jjrSSS jjrg)z& Random symplectic operator functions ) annotationsN) default_rng)random_clifford_tableau)Clifford)Pauli) PauliListcZUc[RR5nO7[U[RR5(aUnO [U5nUR SU[ S9nUR SU[ S9nU(aUR S5OSn[XEU45nU$)aReturn a random Pauli. Args: num_qubits (int): the number of qubits. group_phase (bool): Optional. If True generate random phase. Otherwise the phase will be set so that the Pauli coefficient is +1 (default: False). seed (int or np.random.Generator): Optional. Set a fixed seed or generator for RNG. Returns: Pauli: a random Pauli sizedtyper)nprandomr isinstance Generatorintegersboolr) num_qubits group_phaseseedrngzxphasepaulis i/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/quantum_info/operators/symplectic/random.py random_paulirs  |ii##% D"))-- . .$ QZt 4A QZt 4A*CLLOE 1- E LcUc[RR5nO7[U[RR5(aUnO [U5nUR SX4S9R [5nUR SX4S9R [5nU(a'UR SUS9n[R"XVU5$[R"XV5$)aReturn a random PauliList. Args: num_qubits (int): the number of qubits. size (int): Optional. The length of the Pauli list (Default: 1). seed (int or np.random.Generator): Optional. Set a fixed seed or generator for RNG. phase (bool): If True the Pauli phases are randomized, otherwise the phases are fixed to 0. [Default: True] Returns: PauliList: a random PauliList. r )r r) rrrrrrastyperr from_symplectic)rr rrrrr_phases rrandom_pauli_listr%9s$ |ii##% D"))-- . .$ Qd/ 077=A Qd/ 077=A ad+((v66  $ $Q **r cUc[RR5nO7[U[RR5(aUnO [U5nUR SS[R S9Sn[XS9n[USS9$)aReturn a random Clifford operator. The Clifford is sampled using the method of Reference [1]. Args: num_qubits (int): the number of qubits for the Clifford seed (int or np.random.Generator): Optional. Set a fixed seed or generator for RNG. Returns: Clifford: a random Clifford operator. Reference: 1. S. Bravyi and D. Maslov, *Hadamard-free circuits expose the structure of the Clifford group*. `arXiv:2003.09412 [quant-ph] `_ irr r)rF)validate) rrrrrruint64rr)rrrtableaus rrandom_cliffordr*Zsu$ |ii##% D"))-- . .$ <<Qbii< 8 ;D%jr5s#$I!Z^"&6V>-1 ++ + ++  +B-r