z i6"SrSSKJr SSKrSSKrSSKJr SSKJ r SSK J r SSK J r SSKJr SS jrSSS jjrS rSS jrS rg)z3 Quantum information utility functions for states. ) annotationsN) QiskitError) Statevector) DensityMatrix)SuperOp) ATOL_DEFAULTcB[USS9nURRUS9nURUlUR UlURS:XaUR5$[U[5(a[URR55S- [R"U5- nURR!URR"5n[R$"XDR'5X34S9n[R "XRR(5n[+XRRS9$U(dUR-5$UR/U5n[1[R2"US5R!SUSS-5US/S/S 9nUR5XqS/5n[7USS USS 5HKup[1[R2"U 5R!SU S-5U /S/S 9nUR5Xy/5nMM X(lU$) aReturn reduced density matrix by tracing out part of quantum state. If all subsystems are traced over this returns the :meth:`~qiskit.quantum_info.DensityMatrix.trace` of the input state. Args: state (Statevector or DensityMatrix): the input state. qargs (list): The subsystems to trace over. Returns: DensityMatrix: The reduced density matrix. Raises: QiskitError: if input state is invalid. Fvalidate)qargsr)axesdims) input_dims output_dimsN) _format_state _op_shaperemove_dims_l_dims_r _num_qargs_l _num_qargs_rsizetrace isinstancerlendims_lnparray_datareshape tensor_shape tensordotconjshapercopyrreyeevolvezip) stater traced_shape trace_systemsarrrhortr_opretqargdims Z/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/quantum_info/states/utils.py partial_tracer6s" %% 0E??)))6L'//L , 9 9LA{{}%%%EOO22459BHHUOK kk!!%//">">?ll3 -1OPjj001S';';<< zz| ::e D BFF47O++AtAw!|<$q'ab`c dE ,,uQxj )CqrDH- s ++AsAv6C5WXVYZjj'.!M Jc^US:XaSnO4U[R:XaSnO[R"U5mU4SjnSnUH nSUs=:aS:dMO MX2"U5- nM" U$)aCompute the Shannon entropy of a probability vector. The shannon entropy of a probability vector :math:`\vec{p} = [p_0, ..., p_{n-1}]` is defined as .. math:: H(\vec{p}) = \sum_{i=0}^{n-1} p_i \log_b(p_i) where :math:`b` is the log base and (default 2), and :math:`0 \log_b(0) \equiv 0`. Args: pvec (array_like): a probability vector. base (int): the base of the logarithm [Default: 2]. Returns: float: The Shannon entropy H(pvec). rc6U*[R"U5-$N)mathlog2xs r5logfnshannon_entropy..logfnis2 ! $ $r7c6U*[R"U5-$r:r;logr=s r5r?r@ns2 # #r7c>>U*[R"U5-T- $r:rB)r>log_bases r5r?r@ts2 #h. .r7grr )r er;rC)pvecbaser?h_valr>rEs @r5shannon_entropyrJSsj( qy %  $88D> / E  q9199 U1X E Lr7c f[USS9n[U[5(aUR5nUR 5nUR R USSS25nURn[[U55n[U[[R45(d [S5e[U5nU[U5:XdURU5(d [S5e[U5nUVs/sH owU;dM UPM nnUR U5n UR U5n [R"U 5n [R"U 5n Xh-Vs/sHouSSS2R!U5PM snSSS2n UR#U 5nUR X/5n[R$R'USS9unnn[)UUR*U5VVVs/sH(unnnU[,:dMU[/UU S9[/UU S94PM* nnnnU$s snfs snfs snnnf) aReturn the Schmidt Decomposition of a pure quantum state. For an arbitrary bipartite state: .. math:: |\psi\rangle_{AB} = \sum_{i,j} c_{ij} |x_i\rangle_A \otimes |y_j\rangle_B, its Schmidt Decomposition is given by the single-index sum over k: .. math:: |\psi\rangle_{AB} = \sum_{k} \lambda_{k} |u_k\rangle_A \otimes |v_k\rangle_B where :math:`|u_k\rangle_A` and :math:`|v_k\rangle_B` are an orthonormal set of vectors in their respective spaces :math:`A` and :math:`B`, and the Schmidt coefficients :math:`\lambda_k` are positive real values. Args: state (Statevector or DensityMatrix): the input state. qargs (list): the list of Input state positions corresponding to subsystem :math:`B`. Returns: list: list of tuples ``(s, u, v)``, where ``s`` (float) are the Schmidt coefficients :math:`\lambda_k`, and ``u`` (Statevector), ``v`` (Statevector) are the Schmidt vectors :math:`|u_k\rangle_A`, :math:`|u_k\rangle_B`, respectively. Raises: QiskitError: if Input qargs is not a list of positions of the Input state. QiskitError: if Input qargs is not a proper subset of Input state. .. note:: In Qiskit, qubits are ordered using little-endian notation, with the least significant qubits having smaller indices. For example, a four-qubit system is represented as :math:`|q_3q_2q_1q_0\rangle`. Using this convention, setting ``qargs=[0]`` will partition the state as :math:`|q_3q_2q_1\rangle_A\otimes|q_0\rangle_B`. Furthermore, qubits will be organized in this notation regardless of the order they are passed. For instance, passing either ``qargs=[1,2]`` or ``qargs=[2,1]`` will result in partitioning the state as :math:`|q_3q_0\rangle_A\otimes|q_2q_1\rangle_B`. Fr Nz9Input qargs is not a list of positions of the Input statez1Input qargs is not a proper subset of Input state) full_matricesr)rrrto_statevectorrr"r#ndimlistranger ndarrayrsetissubsetprodindex transposelinalgsvdr+Trr)r,r r state_tensrOquditsqargs_biqargs_adims_bdims_andim_bndim_a qargs_axes state_matu_mats_arrvh_matsuvschmidt_componentss r5schmidt_decompositionrm~sR %% 0E%''$$& ::> #9MNN5kG 5&QW$4q&G5 ZZ F ZZ F WWV_F WWV_F291BC1BA2,$$Q'1BCDbDIJ%%j1J""F#34I99==%=HE5&5%''622GAq! |  FK 'QV)DE2 )6Ds; H"H"$ H'-H,H,c[U[5(a[R"U[S9n[U[R 5(aTUR nUS:Xa [U5nO6US:Xa0URup4US:Xa [U5nOX4:Xa [U5n[U[[45(d [S5eU(a UR5(d [S5eU$)z$Format input state into class object)dtyper rzInput is not a quantum statez"Input quantum state is not a valid) rrPr r!complexrRrOrr'rris_valid)r,r rOdim1dim2s r5rrs%g.%$$zz 19&E QYJDqy#E*%e, ek=9 : :899((>?? Lr7cSSKJn URU5up4n[R"U"U55nUR U5R U5$)aFApply real scalar function to singular values of a matrix. Args: matrix (array_like): (N, N) Matrix at which to evaluate the function. func (callable): Callable object that evaluates a scalar function f. Returns: ndarray: funm (N, N) Value of the matrix function specified by func evaluated at `A`. rN) scipy.linalgrXrYr diagdot)matrixfunclaunitary1singular_valuesunitary2diag_func_singulars r5 _funm_svdrsH*,&&.'Hxo!67 <<* + / / 99r7)r,zStatevector | DensityMatrixr rPreturnr)r)rGzlist | np.ndarrayrHintrfloat)T)__doc__ __future__rr;numpyr qiskit.exceptionsr&qiskit.quantum_info.states.statevectorr(qiskit.quantum_info.states.densitymatrixr%qiskit.quantum_info.operators.channelr(qiskit.quantum_info.operators.predicatesrr6rJrmrrr7r5rsA# )>B9A3l(VRj*:r7