{ i?SrSSKrSSKrSSKJrJrJrJr SSKr SSK J r SSK J r JrJrJrJrJrJr SSKJr SSKJr SSKJrJrJr SS KJr SS KJr S S K J!r! S S K"J#r# S SK$J%r% \RL"\'5r(S\#S\S\#4Sjr)S\!S\!4Sjr*S\#S\#4Sjr+SSSS.Sjr,SSSS.Sjr-\ "5S/4/\"5S/4/\"5S/4/\"5S/4//r.\ "5S/4/\"5S/4/\"5S/4/\"5S/4//r/\.VVs/sHn\/HoU-PM M snnr0\ "5S/4/r1\ "5S/4\"5S/4/r2\ "5S/4/\1\2/r3\ "5S/4/r4\ "5S/4\"5S/4/r5\ "5S/4/\4\5/r6\3VVs/sHn\6HoU-PM M snnr7\ "54\"54\"54\"54\"54\"5\"54\"5\"54\"5\"54\"5\"54\"5\"54\"5\"54\"5\"5\"54\"5\"5\"54\"5\"5\"54\"5\"5\"54\"5\"5\"54\"5\"5\"54\"5\"5\"54\"5\"5\"54\"5\"5\"54\"54\"54\"5\"54\"5\"54/r8\.SS\0SSS.\3SS\7SSS.S\9"SS5VVs/sHn\8UVs/sHo3S/4PM snPM snn0S.r:S\\\\!4S\\\!4S\\;4Sjrgs snnfs snnfs snfs snnf)"a Noise transformation module The goal of this module is to transform one 1-qubit noise channel (given by the QuantumError class) into another, built from specified "building blocks" (given as Kraus matrices) such that the new channel is as close as possible to the original one in the Hilber-Schmidt metric. For a typical use case, consider a simulator for circuits built from the Clifford group. Computations on such circuits can be simulated at polynomial time and space, but not all noise channels can be used in such a simulation. To enable noisy Clifford simulation one can transform the given noise channel into the closest one, Hilbert-Schmidt wise, that can be used in a Clifford simulator. N)SequenceListUnionCallable)Reset)IGateXGateYGateZGateHGateSGateSdgGate) transpile)MissingOptionalLibraryError)KrausSuperOpChi)QuantumChannel)TranspilerError) QuantumError) NoiseModel) NoiseError noise_modelfuncreturncJ[R"U5nURR5Hup4U"U5URU'M URR5H6upVUR5HuptU"U5URUU'M M8 U$)aRReturn a new noise model by applyign a function to all quantum errors. This returns a new noise model containing the resulting errors from applying the supplied function to all QuantumErrors in the noise model. This function should have singature `func(error: QuantumError) -> QuantumError` where the returned quantum error is defined on the same number of qubits as the original error. Args: noise_model: the noise model to be transformed. func: function for transforming QuantumErrors. Returns: The transpiled noise model. Raises: NoiseError: if the transformation failed. )copydeepcopy_default_quantum_errorsitems_local_quantum_errors)rr new_noisekeyerror inst_name noise_dicqubitss _/home/james-whalen/.local/lib/python3.13/site-packages/qiskit_aer/utils/noise_transformation.pytransform_noise_modelr*:s( k*I77==? 15e ))#.@!* ? ? E E G &__.MFAEeI + +I 6v >/!H r%c [UR40UD6n[ [ X R 55$![an[SUSU35UeSnAff=f)aReturn a new quantum error containin transpiled circuits. This returns a new QuantumError containing the circuits resulting from transpiling all error circuits using :func:`qiskit.transpile` with the passed keyword agruments. Args: error: the quantum error to be transformed. transpile_kwargs: kwargs for passing to qiskit transpile function. Returns: The transformed quantum error. Raises: NoiseError: if the transformation failed. z Failed to transpile circuits in z with kwargs N)rcircuitsrrrzip probabilities)r%transpile_kwargstranspiled_circserrs r)transpile_quantum_errorr3Zsi"$U^^H7GH ,.A.AB CC .ug]CSBT U  s6 AAAc &^U4Sjn[X5$)aReturn a new noise model with transpiled QuantumErrors. This returns a new noise model containing the resulting errors from transpiling all QuantumErrors in the noise model using :func:`transpile_quantum_error` function with the passed keyword agruments. Args: noise_model: the noise model to be transformed. transpile_kwargs: kwargs for passing to qiskit transpile function. Returns: The transpiled noise model. Raises: NoiseError: if the transformation failed. c>[U40TD6$N)r3)r%r0s r)r#transpile_noise_model..funcs&uA0@AAr+r*)rr0rs ` r)transpile_noise_modelr9ts&B ! 33r+operator_string operator_dict operator_listc@[U[[45(d"[SURR 35eUR S:a[SUR S35eUbP[R5nUR5nX;a[USU35e[UUR nUb[UR56upcUb[U[5(d[S U35eUVs/sH(n[U[5(aUO [US 4/5PM* nn[X5S Sn [R "S [#U 5- S 5n U S:dU S :a[SS U - 35e[%5S/4U 4/n [X95HupU R'X45 M [U 5$[S5e![a"n[SUSUR S 35UeSnAff=fs snf![an[S U35UeSnAff=f)a Return a ``QuantumError`` object that approximates an error as a mixture of specified operators (channels). The approximation is done by minimizing the Hilbert-Schmidt distance between the process matrix of the target error channel (:math:`T`) and the process matrix of the output channel (:math:`S = \sum_i{p_i S_i}`), i.e. :math:`Tr[(T-S)^\dagger (T-S)]`, where :math:`[p_1, p_2, ..., p_n]` denote probabilities and :math:`[S_1, S_2, ..., S_n]` denote basis operators (channels). See `arXiv:1207.0046 `_ for the details. Args: error (QuantumError or QuantumChannel): the error to be approximated. The number of qubits must be 1 or 2. operator_string (string): a name for a pre-made set of building blocks for the output channel (Default: None). Possible values are ``'pauli'``, ``'reset'``, ``'clifford'``. operator_dict (dict): a dictionary whose values are the building blocks for the output channel (Default: None). E.g. {"x": XGate(), "y": YGate()}, keys "x" and "y" are not used in transformation. operator_list (list): list of building block operators for the output channel (Default: None). E.g. [XGate(), YGate()] Returns: QuantumError: the approximate quantum error. Raises: NoiseError: if any invalid argument is specified or approximation failed. MissingOptionalLibraryError: if cvxpy is not installed. Note: The operator input precedence is: ``list`` < ``dict`` < ``string``. If a ``string`` is given, ``dict`` is overwritten; if a ``dict`` is given, ``list`` is overwritten. The ``string`` supports only 1- or 2-qubit errors and its possible values are ``'pauli'``, ``'reset'``, ``'clifford'``. The ``'clifford'`` does not support 2-qubit errors. zInvalid input error type: rz2Only 1-qubit and 2-qubit noises can be converted, z-qubit noise found in modelNz3 is not a valid operator_string. It must be one of zPreset 'z<' operators do not support the approximation of errors with z qubitsz!operator_list is not a sequence: z%Invalid type found in operator list: rzChannel probabilities sum to zHQuantum error approximation failed - no approximating operators detected) isinstancerrr __class____name__ num_qubits_PRESET_OPERATOR_TABLEkeyslowerKeyErrorr.r!r_transform_by_operator_listnproundsumrappend)r%r;r<r=valid_operator_stringsr2_op channel_listr/ identity_prob noise_opsoperator probabilitys r)approximate_quantum_errorrVsoZ elN; < <5eoo6N6N5OPQQ ! @ ; =  "!7!)//1  8"#$%%;$<>  2?CEDTDTUM   3 3 56 -22@PQ Q _('B!^44,Qy:QQ' 4LHL S%7!7; 1   1[UTTTS9$)Nr:)rV)noiser<r=r;s r) approximate,approximate_noise_model..approximate s( +''   r+r8)modelr;r<r=rZs ``` r)approximate_noise_modelr]sD  ! 44r+r?)r?r)pauliresetclifford basis_opstargetc xSUSR-n[[R"U55/U-nUVs/sHn[ U5R PM nn[ U5R n[ U5n[R"Xf45n[U5HSup[U5H?upX:a[X5XxU 'MX:aXzUXxU 'M/[U 5XxU'MA MU S[R"UV s/sHn [XY5PM sn 5-n Sn [R"UVs/sH o="U5PM sn5nU "U5nSSK nUR#U5nUR%UR'UR)UU5U R*U--5UR-U5S :*US:UR*U-U:*/S 9nUR/5 UR0nU$s snfs sn fs snf![a'n[RS5 [!SSS S S 9UeSnAff=f)a Transform (or approximate) the target quantum channel into a mixture of basis operators (channels) and return the mixing probabilities. The approximate channel is found by minimizing the Hilbert-Schmidt distance between the process matrix of the target channel (:math:`T`) and the process matrix of the output channel (:math:`S = \sum_i{p_i S_i}`), i.e. :math:`Tr[(T-S)^\dagger (T-S)]`, where :math:`[p_1, p_2, ..., p_n]` denote probabilities and :math:`[S_1, S_2, ..., S_n]` denote basis operators (channels). Such an optimization can represented as a quadratic program: Minimize :math:`p^T A p + b^T p`, subject to :math:`p \ge 0`, `\sum_i{p_i} = 1`, `\sum_i{p_i} = 1`. The last constraint is for making the approximation conservative by forcing the output channel have more error than the target channel in the sense that a "fidelity" against identity channel should be worse. See `arXiv:1207.0046 `_ for the details. Args: target: Quantum channel to be transformed. basis_ops: a list of channel objects constructing the output channel. Returns: list: A list of amplitudes (probabilities) of basis that define the output channel. Raises: MissingOptionalLibraryError: if cvxpy is not installed. rrc z[[R"[R"[ U5555$r6)floatrJabstracer)channels r)fidelity-_transform_by_operator_list..fidelitys$RVVBHHWW%56788r+Nz7cvxpy module needs to be installed to use this feature.cvxpyz%Transformation/Approximation of noisezpip install cvxpyzTCVXPY is required to solve an optimization problem of approximating a noise channel.)libnamename pip_installmsgr?) constraints)rDrrJeyerdatalenzeros enumerate_hs_inner_prod_real_hs_normarrayrm ImportErrorloggerr%rVariableProblemMinimize quad_formTrLsolvevalue)rbrcNrPbasis_ops_matsrnAiS_ijS_jbrk source_fids target_fidrmr2xprobr/s r)rIrIQsH Yq\ $ $$Arvvay!"Y.I.77Yrc"gllYN7 F A NA !AN+/FAu-c7Q$q'Q"3-Q0, RXXnMns*12nM NNA9((9=9RHRL9=>K&!J  qA == uq!,qssQw67YYq\Q&Q 0AZ0OP  D  JJLGGM W8N>  NO)8+.    s)G9 G> >HH H9"H44H9c[R"[R"U5RU-5R$r6rJriconjrreal)rs r)ryrys( 88BGGAJLL1$ % * **r+c[R"[R"UR5U-5R$r6r)rBs r)rxrxs( 88BGGACCL1$ % * **r+)?__doc__rloggingtypingrrrrnumpyrJqiskit.circuitr%qiskit.circuit.library.standard_gatesrr r r r r rqiskit.compilerrqiskit.exceptionsr%qiskit.quantum_info.operators.channelrrr5qiskit.quantum_info.operators.channel.quantum_channelrqiskit.transpiler.exceptionsr noise.errorsrnoise.noise_modelrnoise.noiseerrorr getLoggerrCr|r*r3r9rVr] _PAULIS_Q0 _PAULIS_Q1 _PAULIS_Q0Q1_RESET_Q0_TO_0_RESET_Q0_TO_1 _RESET_Q0_RESET_Q1_TO_0_RESET_Q1_TO_1 _RESET_Q1 _RESET_Q0Q1_CLIFFORD_GATESrangerErgrIryrx)op_q0op_q1rgates0000r)rs" 22 &9EEP8'*)   8 $zj@D<D D44z4*44#$d[a|7;$^b*5\!~%'A3 0EGaS>2BegPQs^DT U !~%'A3 0EGaS>2BegPQs^DT U +5N:%:% : :N 7QC.!7QC.57QC.1wn ~~ > 7QC.!7QC.57QC.1wn ~~ > *3K)u}})K  WJ WJ YL WJ WJ Weg Weg Weg Weg Wgi Y Weguw Y! Weguw Wegwy! Y# Wegwy! Weguw Y! Weguw WJ WJ Weg Y5> ab>   QR= qr? %2, O,Q_Q%7 8%7TQC[%7 8, O Tnl:;<T .,. /T %[Tn+ +eOLR 9 Os$M <M? M MM M