z i.rSrSSKJr SSKrSSKJrJr SSKJ r SSK J r SSK J r SSKJr "S S \5rg) zLinear Function.) annotationsN)QuantumCircuitGate) CircuitError)PermutationGate)deprecate_func)Cliffordc^\rSrSrSrSSU4Sjjjr\SSj5r\S5r\S5r Sr Sr S r \ "S S S S 9S5r\S5r\S5rSSjrSrSSjrSrSrSrU=r$)LinearFunctionuNA linear reversible circuit on n qubits. Internally, a linear function acting on n qubits is represented as a n x n matrix of 0s and 1s in numpy array format. A linear function can be synthesized into CX and SWAP gates using the Patel–Markov–Hayes algorithm, as implemented in :func:`~qiskit.synthesis.synth_cnot_count_full_pmh` based on reference [1]. For efficiency, the internal n x n matrix is stored in the format expected by cnot_synth, which is the big-endian (and not the little-endian) bit-ordering convention. Example: The circuit .. code-block:: text q_0: ──■── ┌─┴─┐ q_1: ┤ X ├ └───┘ q_2: ───── is represented by a 3x3 linear matrix .. math:: \begin{pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} References: [1] Ketan N. Patel, Igor L. Markov, and John P. Hayes, Optimal synthesis of linear reversible circuits, Quantum Inf. Comput. 8(3) (2008). `Online at umich.edu. `_ c@>Sn[U[[R45(a[R"U[ SS9n[UR5S:wd URSURS:wa [S5eU(aSSK J n U"U5(d [S 5eO[U[5(aUn[RU5nO[U[5(aURR!5nOa[U["5(a[R%U5nO6[U[&5(a[R)U5nO [S 5e[*TU]YS [U5X/S 9 g![ a [S5Sef=f) av Args: linear: data from which a linear function can be constructed. It can be either a nxn matrix (describing the linear transformation), a permutation (which is a special case of a linear function), another linear function, a clifford (when it corresponds to a linear function), or a quantum circuit composed of linear gates (CX and SWAP) and other objects described above, including nested subcircuits. validate_input: if True, performs more expensive input validation checks, such as checking that a given n x n matrix is invertible. Raises: CircuitError: if the input is invalid: either the input matrix is not square or not invertible, or the input quantum circuit contains non-linear objects (for example, a Hadamard gate, or a Clifford that does not correspond to a linear function). NT)dtypecopyz9A linear function must be represented by a square matrix.r)check_invertible_binary_matrixz>A linear function must be represented by an invertible matrix.z5A linear function cannot be successfully constructed.linear_function)name num_qubitsparams) isinstancelistnpndarrayarraybool ValueErrorrlenshapeqiskit.synthesis.linearrrr _circuit_to_matlinearrr_permutation_to_matr _clifford_to_matsuper__init__)selfr"validate_inputoriginal_circuitr __class__s r/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/generalized_gates/linear_function.pyr&LinearFunction.__init__Fsf@  ftRZZ0 1 1 &4@6<< A%aFLLO)K"#^__R5f==&X / /% #33F;F  / /]]'')F  0 0#77?F  ) )$44VURR5(dURR5(a [ S5e[ R "UR5$)a>This creates a nxn matrix corresponding to the given Clifford, when Clifford can be converted to a linear function. This is possible when the clifford has tableau of the form [[A, B], [C, D]], with B = C = 0 and D = A^{-1}^t, and zero phase vector. In this case, the required matrix is A^t. Raises an error otherwise. zSSKJn U"UR5Ulg)zTXY>Y7Z rRcUR5(d [S5eURn[R"US:H5nUS$)zThis method first checks if a linear function is a permutation and raises a `qiskit.circuit.exceptions.CircuitError` if not. In the case that this linear function is a permutation, returns the permutation pattern. z(The linear function is not a permutationr)rxrr"rwhere)r'r"locss r+permutation_pattern"LinearFunction.permutation_patternsC ""$$IJ Jxx! $AwrRc[R"U[S9n[U5HupEURSS2U4X2U4'M [ U5$)aAExtend linear function to a linear function over nq qubits, with identities on other subsystems. Args: num_qubits: number of qubits of the extended function. positions: describes the positions of original qubits in the extended function's qubits. Returns: LinearFunction: extended linear function. r.N)rr4rrVr"r )r'rrG extended_matrXposs r+r;#LinearFunction.extend_with_identitysKvvj5  *FA+/;;q!t+rms r+mat_strLinearFunction.mat_str(s4;;%%c*++rRc*SnURn[UR5HfnSn[UR5H/nX#U4(dMU(dUS- nUS[U5-- nSnM1 X0RS- :wdMaUS- nMh US- nU$) zWReturn string representation of the linear function viewed as a linear transformation. (Tz + x_Frz, z) )r"rangerr)r'outrArow first_entrycols r+ function_strLinearFunction.function_str.skk)CKT__-Cx==&u 4#c(?*C"'K . oo))t * u  rRrl)F)r"zblist[list[bool]] | np.ndarray[bool] | QuantumCircuit | LinearFunction | PermutationGate | Cliffordr(rreturnNone)r?r)rr)rr>rGz list[int]rr )__name__ __module__ __qualname____firstlineno____doc__r& staticmethodr!r$r#r]rbrfrrnpropertyr"r)rxr}r;rr__static_attributes__ __classcell__)r*s@r+r r s)j %Q  Q Q  Q Q f##J , ,3 A X(     ,(, rRr )r __future__rnumpyrqiskit.circuit.quantumcircuitrrqiskit.circuit.exceptionsr4qiskit.circuit.library.generalized_gates.permutationrqiskit.utils.deprecationrqiskit.quantum_infor r r`rRr+rs/">2P3)eTerR