z i SrSSKJr SSKrSSKrSSKrSSKJr SSK J r SSK r SSK Jr SSKJr SSKJrJrJrJrJrJrJr SS KJr SS KJr SS KJr SS KJ r SS K!J"r" SSK#J$r$ SSK%J&r&J'r' \ (aSSK(J)r) "SS\"5r*\$"\*5 g)z Matrix Operator class. ) annotationsN)Number) TYPE_CHECKING) _numpy_compat) Instruction)HGateIGateSGateTGateXGateYGateZGate) Operation)QuantumCircuit) QiskitError) BaseOperator)LinearOp)generate_apidocs)is_unitary_matrix matrix_equal)Layoutc^\rSrSrSrS%S&U4SjjjrS\R4SjrSr U4Sjr \ S5r \ S 5r S'S jrS r\S(S j5rS)S*Sjjr\S+S,Sjj5rS%SjrS-SjrSrSrSrS.S/Sjjr\R6S-S 4S0SjjrS1SjrS1Sjr\S5rS'Sjr Sr!S%S2Sjjr"S-Sjr#Sr$\S3S j5r%\S!5r&\S"5r'S'S#jr(S$r)U=r*$)4Operator*aMatrix operator class This represents a matrix operator :math:`M` that will :meth:`~Statevector.evolve` a :class:`Statevector` :math:`|\psi\rangle` by matrix-vector multiplication .. math:: |\psi\rangle \mapsto M|\psi\rangle, and will :meth:`~DensityMatrix.evolve` a :class:`DensityMatrix` :math:`\rho` by left and right multiplication .. math:: \rho \mapsto M \rho M^\dagger. For example, the following operator :math:`M = X` applied to the zero state :math:`|\psi\rangle=|0\rangle (\rho = |0\rangle\langle 0|)` changes it to the one state :math:`|\psi\rangle=|1\rangle (\rho = |1\rangle\langle 1|)`: .. plot:: :include-source: :nofigs: >>> import numpy as np >>> from qiskit.quantum_info import Operator >>> op = Operator(np.array([[0.0, 1.0], [1.0, 0.0]])) # Represents Pauli X operator >>> from qiskit.quantum_info import Statevector >>> sv = Statevector(np.array([1.0, 0.0])) >>> sv.evolve(op) Statevector([0.+0.j, 1.+0.j], dims=(2,)) >>> from qiskit.quantum_info import DensityMatrix >>> dm = DensityMatrix(np.array([[1.0, 0.0], [0.0, 0.0]])) >>> dm.evolve(op) DensityMatrix([[0.+0.j, 0.+0.j], [0.+0.j, 1.+0.j]], dims=(2,)) Ncb>Sn[U[[R45(a[R"U[ S9UlO[U[[45(a!URU5RUlO[US5(a.UR5nURUlURnOI[US5(a-[R"UR5[ S9UlO [S5e[ TU]EUUUUR R$S9 g)aInitialize an operator object. Args: data (QuantumCircuit or Operation or BaseOperator or matrix): data to initialize operator. input_dims (tuple): the input subsystem dimensions. [Default: None] output_dims (tuple): the output subsystem dimensions. [Default: None] Raises: QiskitError: if input data cannot be initialized as an operator. Additional Information: If the input or output dimensions are None, they will be automatically determined from the input data. If the input data is a Numpy array of shape (2**N, 2**N) qubit systems will be used. If the input operator is not an N-qubit operator, it will assign a single subsystem with dimension specified by the shape of the input. Note that two operators initialized via this method are only considered equivalent if they match up to their canonical qubit order (or: permutation). See :meth:`.Operator.from_circuit` to specify a different qubit permutation. Ndtype to_operator to_matrixz&Invalid input data format for Operator)op_shape input_dims output_dimsshape) isinstancelistnpndarrayasarraycomplex_datarr_init_instructiondatahasattrr _op_shaperrsuper__init__r#)selfr,r!r"r __class__s `/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/quantum_info/operators/operator.pyr0Operator.__init__Ws: dT2::. / /D8DJ ~y9 : ://5::DJ T= ) )##%DDJ~~H T; ' 'DNN$4GDDJFG G !#**""  cvUcURROUn[R"URXS9$)N)rcopy)r,rr&array)r1rr7s r3 __array__Operator.__array__s*#(= exx ::r5c Sn[U5S-nU[R"URSUS9SUSUR 5SUR 5S3 $) Nz Operator( z, ) separatorprefixz, z input_dims=z, output_dims=))lenr& array2stringr,r!r")r1r>pads r3__repr__Operator.__repr__sd&kChrtyyDPQQTe;t01@P@P@R?SST V r5c>[TU]U5(dg[R"URURUR UR S9$)z Test if two Operators are equal.Frtolatol)r/__eq__r&allcloser,rGrH)r1otherr2s r3rIOperator.__eq__s:w~e$${{499ejjtyytyyQQr5cUR$)zThe underlying Numpy array.r*r1s r3r, Operator.dataszzr5cZURUR5UR5S.$)zReturn operator settings.)r,r!r")r*r!r"rOs r3settingsOperator.settingss+JJ//+++-  r5c SSKJn SnUcUnUS:XaUR5$US:XaSSKJn U"U40UD6$US:Xa U"U40UD6$US:Xa U"U4SS 0UD6$[ S US [ U5RS 35e) a Return a visualization of the Operator. **repr**: String of the state's ``__repr__``. **text**: ASCII TextMatrix that can be printed in the console. **latex**: An IPython Latex object for displaying in Jupyter Notebooks. **latex_source**: Raw, uncompiled ASCII source to generate array using LaTeX. Args: output (str): Select the output method to use for drawing the state. Valid choices are `repr`, `text`, `latex`, `latex_source`, Default is `repr`. drawer_args: Arguments to be passed directly to the relevant drawing function or constructor (`TextMatrix()`, `array_to_latex()`). See the relevant function under `qiskit.visualization` for that function's documentation. Returns: :class:`str` or :class:`TextMatrix` or :class:`IPython.display.Latex`: Drawing of the Operator. Raises: ValueError: when an invalid output method is selected. MissingOptionalLibrary: If SymPy isn't installed and ``'latex'`` or ``'latex_source'`` is selected for ``output``. r)array_to_latexreprtext) TextMatrixlatex latex_sourcesourceT'z$' is not a valid option for drawing zM objects. Please choose from: 'text', 'latex', or 'latex_source'.)qiskit.visualizationrUrC(qiskit.visualization.state_visualizationrX ValueErrortype__name__)r1output drawer_argsrUdefault_outputrXs r3draw Operator.draws> 8 >#F V ==? " v  Kd2k2 2 w !$6+6 6 ~ %!$CtC{C CfXA$t*BUBUAVWDG r5cUR5n[U[5(a [U5 gSSKJn U"U5 g)Nr)display)rer$strprintIPython.displayrh)r1outrhs r3_ipython_display_Operator._ipython_display_s+iik c3   #J / CLr5c[5R5[5R5[5R5[ 5R5[ 5R5[ 5R5[5R5[R"SS/SS//[S9[R"SS/SS//[S9[R"SS/SS//[S9[R"SS/SS//[S9[R"SS/SS//[S9[R"SS/SS//[S9S. n[R"S U5c [S 5e[U5n[[R "S U-[S95n[#[%U55H upVUS :wdM UR'X&U/S 9nM" U$)a=Return a tensor product of single-qubit operators. Args: label (string): single-qubit operator string. Returns: Operator: The N-qubit operator. Raises: QiskitError: if the label contains invalid characters, or the length of the label is larger than an explicitly specified num_qubits. Additional Information: The labels correspond to the single-qubit matrices: 'I': [[1, 0], [0, 1]] 'X': [[0, 1], [1, 0]] 'Y': [[0, -1j], [1j, 0]] 'Z': [[1, 0], [0, -1]] 'H': [[1, 1], [1, -1]] / sqrt(2) 'S': [[1, 0], [0 , 1j]] 'T': [[1, 0], [0, (1+1j) / sqrt(2)]] '0': [[1, 0], [0, 0]] '1': [[0, 0], [0, 1]] '+': [[0.5, 0.5], [0.5 , 0.5]] '-': [[0.5, -0.5], [-0.5 , 0.5]] 'r': [[0.5, -0.5j], [0.5j , 0.5]] 'l': [[0.5, 0.5j], [-0.5j , 0.5]] rrg?gyy?) IXYZHST01+-rlz^[IXYZHST01rl\-+]+$z"Label contains invalid characters.rqqargs)r rr r rrr r r&r8r)rematchrr@reye enumeratereversedcompose)clslabel label_mats num_qubitsopqubitchars r3 from_labelOperator.from_labelsB""$""$""$""$""$""$""$Aq6Aq6*':Aq6Aq6*':C:Sz2'BC;s 4GDC<$5WEC; 5WE  88*E 2 :BC CZ bffQ ]': ;$Xe_5KEs{ZZ 0Z@6 r5Fc P^^^^^[R"U5nTRR5m[ T5mTRR 5m[ T5mU(a[ U5T:wa [ S5eTRR5n[UU4Sj[U555n[S[TRR555n[U4Sj[R"USSS25SSS255nTRR5n[UU4Sj[U555n O[ U5T:wa [ S5e[UU4Sj[U555nTRR 5n[[R"USSS25SSS25n[U4S j[TRR555n[UU4S j[U555nTRR 5n XE-n Xg-n TRRU 5RU 5RTRR5n [!XUS 9n U $) aModifies operator's data by composing it with a permutation. Args: perm (list): permutation pattern, describing which qubits occupy the positions 0, 1, 2, etc. after applying the permutation. front (bool): When set to ``True`` the permutation is applied before the operator, when set to ``False`` the permutation is applied after the operator. Returns: Operator: The modified operator. Raises: QiskitError: if the size of the permutation pattern does not match the dimensions of the operator. zNThe size of the permutation pattern does not match dimensions of the operator.c3:># UHnTTU- S- v M g7frpN.0nn_dims_r raw_shape_rs r3 -Operator.apply_permutation..WsR>aK1 q(89>c3$# UHov M g7fNr)rxs r3rrZsI&H1&Hsc3V># UHnTRRU-v M g7frr. _num_qargs_lrrr1s r3rr[s"cDbq4>>66:Db&)Nc3:># UHnTTU- S- v M g7frrrs r3rr_s!ZGY! HqL1,< =GYrc3:># UHnTTU- S- v M g7frrrrn_dims_l raw_shape_ls r3rrks!VCUaK1 q(89CUrc3V># UHnTRRU-v M g7frrrs r3rrps$9[A++a/9[rc3:># UHnTTU- S- v M g7frrrs r3rrusV~! HqL1,< =~r)r!r")r&argsortr.dims_lr@dims_rrtuplerranger _num_qargs_rr*reshape transposer#r)r1permfrontinv_permshape_lshape_raxes_laxes_r new_shape_l new_shape_r split_shape axes_ordernew_matnew_oprrrrs` @@@@r3apply_permutationOperator.apply_permutation2s((::d#nn++- {#nn++- {# 4yH$!d nn++-GR8D>RRGIeDNN,G,G&HIIFcRZZPTUYWYUYPZE[]a_a]aDbccF..//1KZxPXGYZZK 4yH$!d V8HCUVVGnn++-GBJJx"~6"=>F9>t~~?Z?Z9[F  VxPT~VVK..//1K' _ JJ  { + 5 5j A I I$..J^J^ _ '{S r5c UcU(d [USS5nO5SSKJn U"U[UR5VVs0sHupgXv_M snnS9nUb UR OSnUcU(dUb [USS5nSSKJn [U5n UbS/[UR5-n URR5H upXU 'M URU 5nU "U5nU RUS5n Ub5URUR5nU "U5nU RUS 5n U RUS 5n U $Ub5URUR5nU "U5nU RUS 5n U $s snnf) aCreate a new Operator object from a :class:`.QuantumCircuit` While a :class:`~.QuantumCircuit` object can passed directly as ``data`` to the class constructor this provides no options on how the circuit is used to create an :class:`.Operator`. This constructor method lets you control how the :class:`.Operator` is created so it can be adjusted for a particular use case. By default this constructor method will permute the qubits based on a configured initial layout (i.e. after it was transpiled). It also provides an option to manually provide a :class:`.Layout` object directly. Args: circuit (QuantumCircuit): The :class:`.QuantumCircuit` to create an Operator object from. ignore_set_layout (bool): When set to ``True`` if the input ``circuit`` has a layout set it will be ignored layout (Layout): If specified this kwarg can be used to specify a particular layout to use to permute the qubits in the created :class:`.Operator`. If this is specified it will be used instead of a layout contained in the ``circuit`` input. If specified the virtual bits in the :class:`~.Layout` must be present in the ``circuit`` input. final_layout (Layout): If specified this kwarg can be used to represent the output permutation caused by swap insertions during the routing stage of the transpiler. Returns: Operator: An operator representing the input circuit N_layoutr)TranspileLayout)initial_layoutinput_qubit_mapping final_layout)_inverse_patternTF)getattrqiskit.transpiler.layoutrrqubitsr.qiskit.synthesis.permutation.permutation_utilsrrr@ritemsto_permutationr)rcircuitignore_set_layoutlayoutrrindexrrrr input_qubitsqpinitial_permutationinitial_permutation_inversefinal_permutationfinal_permutation_inverses r3 from_circuitOperator.from_circuitsN >$ )T: @$%FOPWP^P^F_$`F_leU\F_$`F 392D..$  $);&v~tD S g   % 6C(B(B$CCL2288:"#Q;#1"?"? "M *:;N*O '%%&94@B'$0$?$?$O!,<=N,O)))*CUK%%&A5IB   % , ; ;GNN K (89J(K %%%&?GB A%asE> cfUc URnUc URn[URX!S9$)z,Return True if operator is a unitary matrix.rF)rHrGrr*)r1rHrGs r3 is_unitaryOperator.is_unitarys/ <99D <99D $BBr5cU$)z)Convert operator to matrix operator classrrOs r3rOperator.to_operators r5c2SSKJn U"UR5$)z%Convert to a UnitaryGate instruction.r) UnitaryGate)0qiskit.circuit.library.generalized_gates.unitaryrr,)r1rs r3to_instructionOperator.to_instructions Q499%%r5c|[R"U5n[R"UR5UlU$r)_copyr7r&conjr*r1rets r3 conjugateOperator.conjugates)jjGGDJJ'  r5c[R"U5n[R"UR5UlUR R5UlU$r)rr7r&rr*r.rs r3rOperator.transposes=jjLL, 002  r5c :Uc [USS5n[U[5(d [U5nURR URX#5nUR 5nUR 5nUcrU(a,[R"URUR5nO+[R"URUR5n[XuU5nXHlU$URRupU(aU n U n Sn OU n Sn Sn [R"URURR5n[R"URURR5nUVs/sH nU S- U- PM nn[[R"U55[[R"U55/n[R"[R!XUX5U5n[XuU5nXHlU$s snf)NrTrFrp)rr$rr.rrrr&dotr*r, num_qargsr tensor_shapeintprod_einsum_matmul)r1rKrr new_shaper!r"r,r num_qargs_l num_qargs_r num_indicesshift right_multensormatrindices final_shapes r3rOperator.composes =E7D1E%**UOENN**5??EI %%' &&(  =vvdjj%**5vvejj$**54[9C%MJ$(>>#;#; %KEI%KEI DIIt~~'B'BCjjU__%A%AB8=>u;?U*>277;/0#bggj6I2JK zz  # #F% K[ t5!  ?sHg-q=cvUR5UR5:wa [S5e[R"U5n[ U[ 5(a1[RRURU5Ul U$SSK nU(aURR[R"SU*5UR-SS9upgUR!5nUV s/sHn [#X5PM n n U[R$"U 5-UR'5R(-n [R"SX!-5U -Ul U$[R"SX!-5URR+[R"SU*5UR-U5-Ul U$s sn f)aP Return the matrix power of the operator. Non-integer powers of operators with an eigenvalue whose complex phase is :math:`\pi` have a branch cut in the complex plane, which makes the calculation of the principal root around this cut subject to precision / differences in BLAS implementation. For example, the square root of Pauli Y can return the :math:`\pi/2` or :math:`-\pi/2` Y rotation depending on whether the -1 eigenvalue is found as ``complex(-1, tiny)`` or ``complex(-1, -tiny)``. Such eigenvalues are really common in quantum information, so this function first phase-rotates the input matrix to shift the branch cut to a far less common point. The underlying numerical precision issues around the branch-cut point remain, if an operator has an eigenvalue close to this phase. The magnitude of this rotation can be controlled with the ``branch_cut_rotation`` parameter. The choice of ``branch_cut_rotation`` affects the principal root that is found. For example, the square root of :class:`.ZGate` will be calculated as either :class:`.SGate` or :class:`.SdgGate` depending on which way the rotation is done:: from qiskit.circuit import library from qiskit.quantum_info import Operator z_op = Operator(library.ZGate()) assert z_op.power(0.5, branch_cut_rotation=1e-3) == Operator(library.SGate()) assert z_op.power(0.5, branch_cut_rotation=-1e-3) == Operator(library.SdgGate()) Args: n (float): the power to raise the matrix to. branch_cut_rotation (float): The rotation angle to apply to the branch cut in the complex plane. This shifts the branch cut away from the common point of :math:`-1`, but can cause a different root to be selected as the principal root. The rotation is anticlockwise, following the standard convention for complex phase. assume_unitary (bool): if ``True``, the operator is assumed to be unitary. In this case, for fractional powers we employ a faster implementation based on Schur's decomposition. Returns: Operator: the resulting operator ``O ** n``. Raises: QiskitError: if the input and output dimensions of the operator are not equal. .. note:: It is only safe to set the argument ``assume_unitary`` to ``True`` when the operator is unitary (or, more generally, normal). Otherwise, the function will return an incorrect output. z-Can only power with input_dims = output_dims.rNrpr))rb)r!r"rrr7r$rr&linalg matrix_powerr,r* scipy.linalgschurcmathrectdiagonalpowdiagrrwfractional_matrix_power) r1rbranch_cut_rotationassume_unitaryrscipy decompositionunitarydecomposition_diagonalelementdecomposition_power unitary_powers r3powerOperator.power$sy` ??  0 0 2 2MN Njj a   ..tyy!%((56 6jjJJ&  r5c[U[5(d [U5nURUR:wagUc URnUc UR n[ URURSX#S9$![a gf=f)a,Return True if operators are equivalent up to global phase. Args: other (Operator): an operator object. rtol (float): relative tolerance value for comparison. atol (float): absolute tolerance value for comparison. Returns: bool: True if operators are equivalent up to global phase. FT) ignore_phaserGrH)r$rrdimrHrGrr,)r1rKrGrHs r3equivOperator.equivs}%**   88uyy  <99D <99DDIIuzz4[[  s A;; BBc^[R"U5n[[URR S- SS55mT[U4SjT55-m[ R"[ R"[ R"URURR5T5URR5Ul URR5UlU$)acReturn an Operator with reversed subsystem ordering. For a tensor product operator this is equivalent to reversing the order of tensor product subsystems. For an operator :math:`A = A_{n-1} \otimes ... \otimes A_0` the returned operator will be :math:`A_0 \otimes ... \otimes A_{n-1}`. Returns: Operator: the operator with reversed subsystem order. rprc3@># UHn[T5U-v M g7fr)r@)riaxess r3r)Operator.reverse_qargs..s84aCIM4s)rr7rrr.rr&rrr,rr#r*reverse)r1rr8s @r3 reverse_qargsOperator.reverse_qargssjjU4>>66:BCDe84888JJ LLDIIt~~/J/JKT R NN   ..0  r5cUR$)z!Convert operator to NumPy matrix.)r,rOs r3rOperator.to_matrixs yyr5c URnURnUS-S:wa [S5e[[U55n[ U5HupXi-XU-'M [[ [Xf[ U5-555n [ U5V s/sHoU-PM n n U(aX-n OX-n [R"XX-5$s sn f)a)Perform a contraction using Numpy.einsum Args: tensor (np.array): a vector or matrix reshaped to a rank-N tensor. mat (np.array): a matrix reshaped to a rank-2M tensor. indices (list): tensor indices to contract with mat. shift (int): shift for indices of tensor to contract [Default: 0]. right_mul (bool): if True right multiply tensor by mat (else left multiply) [Default: False]. Returns: Numpy.ndarray: the matrix multiplied rank-N tensor. Raises: QiskitError: if mat is not an even rank tensor. r~rz6Contracted matrix must have an even number of indices.) ndimrr%rrrr@r&einsum)rrrrrrrankrank_matindices_tensorjr mat_contractmat_free indices_mats r3rOperator._einsum_matmuls${{88 a<1 VW WeDk*!'*HA,0HN5= )+HU4G 1D%EFG /7/@A/@eEM/@A &1K"1KyyBB BsC c4[US5(a"[[R"U[S95$SUR -n[[R "U55n[U[5(aUR5nURU5 U$)z5Convert a QuantumCircuit or Operation to an Operator.r9rr~) r-rr&r8r)rrr$rr_append_instruction)r instruction dimensionrs r3r+Operator._init_instruction sx ; , ,BHH[@A A{--- bffY' ( k> 2 2%446K {+ r5cSSKJn SSKJn [ U[ X#45(d [ S5eSn[US5(aUR5nU$U$![ a U$f=f)z=Return Operator for instruction if defined or None otherwise.r)Clifford)AnnotatedOperationz=Input is neither Instruction, Clifford or AnnotatedOperation.Nr) qiskit.quantum_inforP"qiskit.circuit.annotated_operationrQr$rrr-r)robjrPrQrs r3_instruction_to_matrixOperator._instruction_to_matrixsn 1I# XJKK]^ ^ 3 $ $ mmo s    sA A%$A%c SSKJn SSKJn UR U5nUb!UR XRS9nUR Ulg[X5(agURc[SUR35e[UR[5(d/[SURS [UR5S 35eURR(akS UR-nUR U"U[ R""S [%URR5-55US9nUR UlURnUR&UR(4V V V s0sHn [+U 5HupX_M M n n n n UHn U R((a"[S U R,R35eUcU R&Vs/sHoUPM nnO U R&Vs/sH oXPM nnUR/U R,US9 M gs sn n n fs snfs snf)z4Update the current Operator by apply an instruction.r)Barrierrpr&NrzCannot apply Operation: z Operation "z" definition is z but expected QuantumCircuit.r~y?z,Cannot apply operation with classical bits: )qiskit.circuit.barrierrX scalar_opr'rUrr,r*r$ definitionrnamerr` global_phaserr&expfloatrclbitsr operationrK)r1rTrrXr'rrrM flat_instrbitsrbit bit_indicesrLtup new_qargss r3rKOperator._append_instruction0s2'))#. ?c/BDJ  % %  ~~%!$)>i(P * !Q Ws4!H2"H9H>rN)NN)r,z6QuantumCircuit | Operation | BaseOperator | np.ndarrayr! tuple | Noner"rir)rrireturnr)F)rr%rboolrjr)FNN) rrrrkr Layout | Nonerrlrjr)rjr)NF)rKrrz list | Nonerrkrjr)rr_rjr)rKrrjr)rKrrG float | NonerHrmrjrk)rF)+ra __module__ __qualname____firstlineno____doc__r0rCOPY_ONLY_IF_NEEDEDr9rCrIpropertyr,rRrerm classmethodrrrrrrrrrrpirrrrr+r.r3r;rrr+rUrK__static_attributes__ __classcell__)r2s@r3rr*s*^$($( > D> !> " > > @#)J)J; R   7r66pM^#( $&* NN N N $ N  NN`C& 0f-2HHu,rsf#    2aaa.8)D<AT/w Qxw Qvr5