z i>TSrSSKJr SSKrSSKrSSKJrJr SSK J r SSK J r SSK Jr SSKJr SS KJrJr SS KJr SS KJr SS KJr \R6"\5rSSS jjrSSSjjrSSSjjr SSSjjr!Sr"Sr#Sr$Sr%g)zE A collection of useful quantum information functions for operators. ) annotationsN) QiskitErrorMissingOptionalLibraryError)Gate) BaseOperator)Operator)QuantumChannel)ChoiSuperOp) DensityMatrix)state_fidelity) optionalsc .[U[SS5n[U[SS5nU(a@URUR:wa&[ SURSURS35eSU4SU44HupEUbXU(aQ[ U5nUS UR -:n[R"U5(a[RS UXg5 UcMeU(dMn[U5n[R"[R"US UR URS 95n [R"U 5(dM[RSUX5 M [U[5(a!UR!UR#55nS nURupUc[U[5(a;[R$"[R&"UR(5U - 5S-n O/[R&"[U5R(5U S-- n [+[R,"U 55$[/[1U5R(U - 5n [/[1U5R(U - 5n[3XSS9$)asReturn 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_fidelitychanneltargetzHInput 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 isinstancecomposeadjointabstracedatafloatrealr r r )rr require_cp require_tplabelchancp_condnegtp_condnon_zero input_dim_fidstate1state2s `/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/quantum_info/operators/measures.pyrr"slw1CYOG fh0BH MF ;;&** $&{{m4 |2?  !'*Xv,>?    #D)GBN*Cvvc{{TL   #D)G~~bjj!$))RVR[R[&\]HvvhW%@(&(##//&.."23;;LI ~ gx ( (&&',,/);<AC((77+001Y\BCRWWS\"" 4=-- 9 :F 4<,,y8 9F &5 99c[U[SS5n[U[SS5nUb [U5nURupV[ XX#S9nXW-S-US-- $![an[S5UeSnAff=f)a-Return 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.rr,r-)rr rrrr)rrr,r-exrr5f_pros r9r<r<sZw1H)TG fh0G RF  f%F[[FC W bE K!Oa (( K   s A A4# A//A4cd[U[SS5n[U[SS5nS[XX#S9- $)a"Return 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_errorrrr>r=)rr rr<)rrr,r-s r9rBrBs?PwyIG fh h GF $: r:c L^SSKJn [S5m[[ U[SS55nU4SjnUR nUR nXV-nTRXU45nTRXU45n U"X5n TRXU45n TRXU45n U"X5n TRXw45nTRXw45nURU5nTRTRUU5U/URTRUU 5//5nTRTRUU 5U/UR*TRUU 5//5nU"UU5n[R"[R"URXVXV45S5RURR 5nUR"nUR$nU S- XR:HXR*:HTR'U5S:HU S- XR:HXR*:HTR'U 5S:HUS- / nTR)TR'UU-5TR'UU-5-5nTR+UU5nUR,"S S U0UD6nU$) aReturn the diamond norm of the input quantum channel object. This function computes the completely-bounded trace-norm (often referred to as the diamond-norm) of the input quantum channel object using the semidefinite-program from reference [1]. Args: choi(Choi or QuantumChannel): a quantum channel object or Choi-matrix array. solver (str): The solver to use. kwargs: optional arguments to pass to CVXPY solver. Returns: float: The completely-bounded trace norm :math:`\|\mathcal{E}\|_{\diamond}`. Raises: QiskitError: if CVXPY package cannot be found. Additional Information: The input to this function is typically *not* a CPTP quantum channel, but rather the *difference* between two quantum channels :math:`\|\Delta\mathcal{E}\|_\diamond` where :math:`\Delta\mathcal{E} = \mathcal{E}_1 - \mathcal{E}_2`. Reference: J. Watrous. "Simpler semidefinite programs for completely bounded norms", arXiv:1207.5726 [quant-ph] (2012). .. note:: This function requires the optional CVXPY package to be installed. Any additional kwargs will be passed to the ``cvxpy.solve`` function. See the CVXPY documentation for information on available SDP solvers. r)sparsez`diamond_norm` diamond_normchoic0>TRX*/X//5$)z2Block matrix for embedding complex matrix in reals)bmat)mat_rmat_icvxpys r9cvx_bmatdiamond_norm..cvx_bmat(szzE6?UN;<rr>solver)scipyrD _cvxpy_checkr r _input_dim _output_dimVariableeyerHkronTr transposereshaper)shaper+imagr(MaximizeProblemsolve)rFrOkwargsrDrLdim_indim_outsizer0_rr0_ir0r1_rr1_ir1x_rx_iidenc_rc_icchoi_rt choi_rt_r choi_rt_iconsobjprobsolrKs @r9rErEshH ) *E  t^VD ED= __FG  D >>6* +D >>6* +D $ B >>6* +D >>6* +D $ B ..$ &C ..$ &C ::g D **uzz$-s3ceeUZZd=S5TU VC **uzz$-s3suufejjt>T5UV WCcAll 499v@A< gdiioo  I I a   DQ a   DQ Q D ..Y_5 IPSO8TT UC ==d #D ** -F -f -C Jr:c[RRU5 SSKnURnUSS:wa[ SSSUS3S9eU$) z1Check that a supported CVXPY version is installedrN1z CVXPY >= 1.0rEzIncompatible CVXPY version z found.)msg) _optionals HAS_CVXPY require_nowrK __version__r)namerKversions r9rRrRasZ$$T*GqzS)  -gYg>  Lr:c UcU$[U[5(aU$[US5(aUR5$[US5(aUR 5$[U[ [ 45(a [U5$[US5(aUR5$[SUSUSURS35e)z(Formatting function for input conversionto_quantumchannel to_channel to_operatorzinvalid type supplied to z of z. A z is best.) r$r hasattrrrrrrr TypeError__name__)rtfallback_class func_namearg_names r9rrss { #~&& s'(($$&&sL!!~~#l+,,}sM""   #H:T)=%% &i 1 r:cN[U[5(aI[U[5(d [U5n[RR UR 5$[U5R n[R"XR5SS/SS/4S9R$)zaxes) r$r r rlinalgeigvalshr)r tensordotconjr+)runitarys r9rrsx'>**'4((7mGyy!!',,//w$$G <<1v1v6F G L LLr:cH[U[5(a[U[5(d [U5nURn[ [ R "UR5R[55nX"-n[ R"[ R"X5SSS9nO8[U5Rn[ R"XUR5SS9n[ RR!U[ R""[%U55- 5$)zGReturn partial tr Choi-matrix eigenvalues for checking if channel is TPr>rN)axis1axis2)rrr)r$r r r)tuplersqrtr[astypeintr(rZrrrrrrVlen)rrFdimsr[tr_choirs r9r!r!s'>**'4((7mG||RWWTZZ(//45 ((2::d2!1E7#((,,w VD 99  gs7|(<< ==r:)NTT) rzOperator | QuantumChannelrz Operator | QuantumChannel | Noner,boolr-rreturnr*)NTF) rzQuantumChannel | OperatorrOperator | Noner,rr-rrr*) rr rrr,rr-rrr*)SCS)rFzChoi | QuantumChannelrOstrrr*)&__doc__ __future__rloggingnumpyrqiskit.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.utilsrrz getLoggerrrrr<rBrErRrrr!rPr:r9rs#F$D;P?B>0   8 $ 04 l: &l: ,l:l: l:  l:b# ;) &;) ;);) ;)  ;)@# , , ,, ,  ,^`F$2M >r: