g6"dZddlmZddlZddlZddlmZddlm Z ddl m Z ddl m Z ddlmZddZdddZdZddZdZdS)z3 Quantum information utility functions for states. ) annotationsN) QiskitError) Statevector) DensityMatrix)SuperOp) ATOL_DEFAULTstateStatevector | DensityMatrixqargslistreturnrct|d}|j|}|j|_|j|_|jdkr|St|trt|j dz tj|z }|j|jj}tj||||f}tj||j}t+||jS|s|S||}t1tj|dd|ddz|dgdg }|||dg}t7|dd |dd D]Y\} } t1tj| d| dz| gdg }||| g}Z||_|S) 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)r r)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) r r traced_shape trace_systemsarrrhortr_opretqargdims V/granary/edev/quantum/lib/python3.11/site-packages/qiskit/quantum_info/states/utils.py partial_tracer9s" %% 0 0 0E?)))66L'/L , 9LA{{}}%%%=EO2244559BHUOOK k!!%/">??l3 -1OPPPjl011S|';<<<< zz|| ::e  D BF47OO++AtAw!|<<$q'ab`c d d dE ,,uuQxj ) )CqrrDH--(( cs ++AsAv66C5WXVYZZZjj'' CM Jrpveclist | np.ndarraybaseintfloatc|dkrd}n-|tjkrd}ntj|fd}d}|D] }d|cxkrdkrn|||z }!|S)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). rc2| tj|zSN)mathlog2xs r8logfnzshannon_entropy..logfnis2 ! $ $r:c2| tj|zSrBrClogrEs r8rGzshannon_entropy..logfnns2 # #r:c:| tj|zz SrBrI)rFlog_bases r8rGzshannon_entropy..logfnts2 #h. .r:grr)r$erCrJ)r;r=rGh_valrFrLs @r8shannon_entropyrOSs( qyy % % % %  $ $ $ $8D>> / / / / / E  q9999199999 UU1XX E Lr:ct|d}t|tr|}|}|j|ddd}|j}tt|t|ttj fstdt|}|tks|stdt|fdD}|||tj}tj}fd|zDddd}||}|||g} tj| d \} } } fd t'| | j| D} | S) asReturn 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`. FrNz9Input qargs is not a list of positions of the Input statez1Input qargs is not a proper subset of Input statecg|]}|v| SrS).0iqargs_bs r8 z)schmidt_decomposition..s#555QAW$4$4q$4$4$4r:cLg|] }ddd|!S)NrQ)index)rTrUquditss r8rWz)schmidt_decomposition..s1CCCA&2,$$Q''CCCr:) full_matricesctg|]4\}}}|tk|t|t|f5S)r)rr)rTsuvdims_adims_bs r8rWz)schmidt_decomposition..sU Aq! |   K ' ' 'QV)D)D)DE   r:)rr!rto_statevectorrr&r'ndimr ranger$ndarrayrsetissubsetprod transposelinalgsvdr/T)r r r state_tensrcqargs_andim_bndim_a qargs_axes state_matu_mats_arrvh_matschmidt_componentsr`rarVrZs @@@@r8schmidt_decompositionrw~s R %% 0 0 0E%'''$$&& ::<> #9MNNN5kkG5555&555G ZZ F ZZ F WV__F WV__FDCCC71BCCCDDbDIJ%%j11J""FF#344I9==%=HHE5&5%'622 r:Tct|trtj|t}t|tjrX|j}|dkrt|}n;|dkr5|j\}}|dkrt|}n||krt|}t|ttfstd|r#| std|S)z$Format input state into class object)dtyperrzInput is not a quantum statez"Input quantum state is not a valid) r!r r$r%complexrercrr+rris_valid)r rrcdim1dim2s r8rrs%/g...%$$ -z 199&&EE QYYJD$qyy#E**%e,, ek=9 : ::8999@((@>??? Lr:cddlm}||\}}}tj||}|||S)abApply real scalar function to singular values of a matrix. Args: matrix (array_like): (N, N) Matrix at which to evaluate the function. func (callable): Callable object that evaluates a scalar function f. Returns: ndarray: funm (N, N) Value of the matrix function specified by func evaluated at `A`. rN) scipy.linalgrjrkr$diagdot)matrixfunclaunitary1singular_valuesunitary2diag_func_singulars r8 _funm_svdrsg*,&&..'Hoxo!6!677 <<* + + / / 9 99r:)r r r r r r)r)r;r<r=r>r r?)T)__doc__ __future__rrCnumpyr$qiskit.exceptionsr&qiskit.quantum_info.states.statevectorr(qiskit.quantum_info.states.densitymatrixr%qiskit.quantum_info.operators.channelr(qiskit.quantum_info.operators.predicatesrr9rOrwrrrSr:r8rs#""""" ))))))>>>>>>BBBBBB999999AAAAAA3333l(((((VRRRj*:::::r: