g> dZddlmZddlZddlZddlmZmZddl m Z ddl m Z ddl mZddlmZdd lmZmZdd lmZdd lmZdd lmZejeZ d(d)dZ d*d+dZ d*d,dZ d-d.d#Z!d$Z"d%Z#d&Z$d'Z%dS)/zE A collection of useful quantum information functions for operators. ) annotationsN) QiskitErrorMissingOptionalLibraryError)Gate) BaseOperator)Operator)QuantumChannel)ChoiSuperOp) DensityMatrix)state_fidelity) optionalsTchannelOperator | QuantumChanneltarget Operator | QuantumChannel | None require_cpbool require_tpreturnfloatc t|tdd}t|tdd}|r0|j|jkr t d|jd|jdd|fd|ffD]\}}|U|rSt |}|d |jzk}tj|r"t d ||||{|ryt|}tj tj |d |j|j } tj| r"t d||| t|tr)||}d }|j\} } |t|tr2tjtj|j| z dz} n,tjt|j| dzz } t+tj| St/t1|j| z } t/t1|j| z }t3| |dS)aReturn the process fidelity of a noisy quantum channel. The process fidelity :math:`F_{\text{pro}}(\mathcal{E}, \mathcal{F})` between two quantum channels :math:`\mathcal{E}, \mathcal{F}` is given by .. math:: F_{\text{pro}}(\mathcal{E}, \mathcal{F}) = F(\rho_{\mathcal{E}}, \rho_{\mathcal{F}}) where :math:`F` is the :func:`~qiskit.quantum_info.state_fidelity`, :math:`\rho_{\mathcal{E}} = \Lambda_{\mathcal{E}} / d` is the normalized :class:`~qiskit.quantum_info.Choi` matrix for the channel :math:`\mathcal{E}`, and :math:`d` is the input dimension of :math:`\mathcal{E}`. When the target channel is unitary this is equivalent to .. math:: F_{\text{pro}}(\mathcal{E}, U) = \frac{Tr[S_U^\dagger S_{\mathcal{E}}]}{d^2} where :math:`S_{\mathcal{E}}, S_{U}` are the :class:`~qiskit.quantum_info.SuperOp` matrices for the *input* quantum channel :math:`\mathcal{E}` and *target* unitary :math:`U` respectively, and :math:`d` is the input dimension of the channel. Args: channel (Operator or QuantumChannel): input quantum channel. target (Operator or QuantumChannel or None): target quantum channel. If `None` target is the identity operator [Default: None]. require_cp (bool): check if input and target channels are completely-positive and if non-CP log warning containing negative eigenvalues of Choi-matrix [Default: True]. require_tp (bool): check if input and target channels are trace-preserving and if non-TP log warning containing negative eigenvalues of partial Choi-matrix :math:`Tr_{\text{out}}[\mathcal{E}] - I` [Default: True]. Returns: float: The process fidelity :math:`F_{\text{pro}}`. Raises: QiskitError: if the channel and target do not have the same dimensions. process_fidelityrrzHInput quantum channel and target unitary must have the same dimensions (z != z).InputTargetNz>%s channel is not CP. Choi-matrix has negative eigenvalues: %sr)atolrtolzA%s channel is not TP. Tr_2[Choi] - I has non-zero eigenvalues: %sF)validate)_input_formatterr rdimr _cp_conditionrnpanyloggerwarning _tp_condition logical_notiscloser isinstancecomposeadjointabstracedatarrealr r r )rrrrlabelchancp_condnegtp_condnon_zero input_dim_fidstate1state2s \/granary/edev/quantum/lib/python3.11/site-packages/qiskit/quantum_info/operators/measures.pyrr"s~lw1CYOOG fh0BH M MF  ;&* $ $?&{??06 ???  !'*Xv,>? t   #D))GBN*Cvc{{ TCL   #D))G~bj!$)RVR[&\&\&\]]Hvh WH% &(##//&.."2"233;LIq ~ gx ( ( C&',//);<<ACC(77++011Y\BCRWS\\""" 4==- 9 : :F 4<<,y8 9 9F &&5 9 9 99FQuantumChannel | OperatorOperator | Nonect|tdd}t|tdd}|3 t|}n"#t$r}td|d}~wwxYw|j\}}t ||||}||zdz|dzz S)aReturn the average gate fidelity of a noisy quantum channel. The average gate fidelity :math:`F_{\text{ave}}` is given by .. math:: \begin{aligned} F_{\text{ave}}(\mathcal{E}, U) &= \int d\psi \langle\psi|U^\dagger \mathcal{E}(|\psi\rangle\!\langle\psi|)U|\psi\rangle \\ &= \frac{d F_{\text{pro}}(\mathcal{E}, U) + 1}{d + 1} \end{aligned} where :math:`F_{\text{pro}}(\mathcal{E}, U)` is the :meth:`~qiskit.quantum_info.process_fidelity` of the input quantum *channel* :math:`\mathcal{E}` with a *target* unitary :math:`U`, and :math:`d` is the dimension of the *channel*. Args: channel (QuantumChannel or Operator): noisy quantum channel. target (Operator or None): target unitary operator. If `None` target is the identity operator [Default: None]. require_cp (bool): check if input and target channels are completely-positive and if non-CP log warning containing negative eigenvalues of Choi-matrix [Default: True]. require_tp (bool): check if input and target channels are trace-preserving and if non-TP log warning containing negative eigenvalues of partial Choi-matrix :math:`Tr_{\text{out}}[\mathcal{E}] - I` [Default: True]. Returns: float: The average gate fidelity :math:`F_{\text{ave}}`. Raises: QiskitError: if the channel and target do not have the same dimensions, or have different input and output dimensions. average_gate_fidelityrrNzTarget channel is not a unitary channel. To compare two non-unitary channels use the `qiskit.quantum_info.process_fidelity` function instead.rrr)r!r rrr"r)rrrrexr"r9f_pros r=rBrBsZw1H)TTG fh0G R RF  f%%FF   K    [FC WV Wa b b bE %K!Oa ((sA A! AA!r ct|tdd}t|tdd}dt||||z S)aReturn the gate error of a noisy quantum channel. The gate error :math:`E` is given by the average gate infidelity .. math:: E(\mathcal{E}, U) = 1 - F_{\text{ave}}(\mathcal{E}, U) where :math:`F_{\text{ave}}(\mathcal{E}, U)` is the :meth:`~qiskit.quantum_info.average_gate_fidelity` of the input quantum *channel* :math:`\mathcal{E}` with a *target* unitary :math:`U`. Args: channel (QuantumChannel): noisy quantum channel. target (Operator or None): target unitary operator. If `None` target is the identity operator [Default: None]. require_cp (bool): check if input and target channels are completely-positive and if non-CP log warning containing negative eigenvalues of Choi-matrix [Default: True]. require_tp (bool): check if input and target channels are trace-preserving and if non-TP log warning containing negative eigenvalues of partial Choi-matrix :math:`Tr_{\text{out}}[\mathcal{E}] - I` [Default: True]. Returns: float: The average gate error :math:`E`. Raises: QiskitError: if the channel and target do not have the same dimensions, or have different input and output dimensions. gate_errorrrrDrC)r!r rrB)rrrrs r=rHrHsSPwyIIG fh h G GF $:* r>SCSchoiChoi | QuantumChannelsolverstrc ddlm}tdtt |tdd}fd}|j}|j}||z}||f}||f} ||| } ||f} ||f} || | } ||f}||f}||}  |||g|j  || gg}  || |g|j  || gg}|||}tj tj|j||||fd|jj}|j}|j}| dz ||j k| | j k|dk| dz | | j k| | j k| dk|dz g }||z||zz}||}|jd d |i|}|S) aHReturn the diamond norm of the input quantum channel object. This function computes the completely-bounded trace-norm (often referred to as the diamond-norm) of the input quantum channel object using the semidefinite-program from reference [1]. Args: choi(Choi or QuantumChannel): a quantum channel object or Choi-matrix array. solver (str): The solver to use. kwargs: optional arguments to pass to CVXPY solver. Returns: float: The completely-bounded trace norm :math:`\|\mathcal{E}\|_{\diamond}`. Raises: QiskitError: if CVXPY package cannot be found. Additional Information: The input to this function is typically *not* a CPTP quantum channel, but rather the *difference* between two quantum channels :math:`\|\Delta\mathcal{E}\|_\diamond` where :math:`\Delta\mathcal{E} = \mathcal{E}_1 - \mathcal{E}_2`. Reference: J. Watrous. "Simpler semidefinite programs for completely bounded norms", arXiv:1207.5726 [quant-ph] (2012). .. note:: This function requires the optional CVXPY package to be installed. Any additional kwargs will be passed to the ``cvxpy.solve`` function. See the CVXPY documentation for information on available SDP solvers. r)sparsez`diamond_norm` diamond_normrJc<|| g||ggS)z2Block matrix for embedding complex matrix in reals)bmat)mat_rmat_icvxpys r=cvx_bmatzdiamond_norm..cvx_bmat(s$zzEE6?UEN;<<)rrDrrDrL)scipyrO _cvxpy_checkr r! _input_dim _output_dimVariableeyerRkronTr$ transposereshaper0shaper1imagr/MaximizeProblemsolve)rJrLkwargsrOrVdim_indim_outsizer0_rr0_ir0r1_rr1_ir1x_rx_iidenc_rc_icchoi_rt choi_rt_r choi_rt_iconsobjprobsolrUs @r=rPrPsH ) * *E  t^VDD E ED===== _FG G D >>66* + +D >>66* + +D $  B >>66* + +D >>66* + +D $  B ..$ & &C ..$ & &C ::g  D **uzz$--s3ceUZZd=S=S5TU V VC **uzz$--s3sufejjt>T>T5UV W WCcAl 49vw@AA< gdio  I I a   DQ a   DQ Q D ..Y_55 IPSO8T8TT U UC ==d # #D $* - -F -f - -C Jr>ctj|ddl}|j}|ddkrt ddd|d|S) z1Check that a supported CVXPY version is installedrN1z CVXPY >= 1.0rPzIncompatible CVXPY version z found.)msg) _optionals HAS_CVXPY require_nowrU __version__r)namerUversions r=rZrZaso$$T***LLLGqzS)  >g>>>    Lr>c ||St|tr|St|dr|St|dr|St|t t frt|St|dr|Std|d|d|j d) z(Formatting function for input conversionNto_quantumchannel to_channel to_operatorzinvalid type supplied to z of z. A z is best.) r+r hasattrrrrrrr TypeError__name__)r|fallback_class func_namearg_names r=r!r!ss { #~&& s'(('$$&&&sL!! ~~#l+,,}}sM""!    1H 1 1) 1 1% 1 1 1  r>cLt|trHt|tst|}tj|jSt|j}tj|| ddgddgfj S)z**0'4(( $7mmGy!!',///w$G <1v1v6F G G G LLr>cZt|trt|tst|}|j}t t j|jt}||z}t j t j ||dd}n=t|j}t j ||d}t j|t jt%|z S)zGReturn partial tr Choi-matrix eigenvalues for checking if channel is TPrDrW)axis1axis2)rrr)r+r r r0tupler$sqrtrcastypeintr/rbrrrrrr^len)rrJdimsrctr_choirs r=r(r(s'>** E'4(( $7mmG|RWTZ((//4455t (2:dE22!1EEE7##(,w VDDD 9  gs7||(<(<< = ==r>)NTT) rrrrrrrrrr)NTF) rr?rr@rrrrrr) rr rr@rrrrrr)rI)rJrKrLrMrr)&__doc__ __future__rloggingnumpyr$qiskit.exceptionsrrqiskit.circuit.gater+qiskit.quantum_info.operators.base_operatorr&qiskit.quantum_info.operators.operatorr5qiskit.quantum_info.operators.channel.quantum_channelr %qiskit.quantum_info.operators.channelr r (qiskit.quantum_info.states.densitymatrixr #qiskit.quantum_info.states.measuresr qiskit.utilsrr getLoggerrr&rrBrHrPrZr!r#r(rXr>r=rs#"""""FFFFFFFF$$$$$$DDDDDD;;;;;;PPPPPP????????BBBBBB>>>>>>000000  8 $ $ 04 l:l:l:l:l:b# ;););););)@# ,,,,,^`````F$2MMM > > > > >r>