z ixSrSSKJr SSKJr SSKJr SSKrSSK J r SSK J r SSK Jr SS KJrJrJrJr SS KJr SS KJr SS KJrJr \(aSS KJr "SS\5rg)z Stabilizer state class. ) annotations) Collection) TYPE_CHECKINGN QiskitError)OpShape)Operator)CliffordPauli PauliList SparsePauliOp) _append_x) QuantumState)QuantumCircuit Instruction)circuitc ^\rSrSrSrS#S$U4Sjjjr\S%S&Sjj5rSrSr \ S5r S'Sjr S r S rS(S jrS(S jrS)S jrSrS*SjrS*SjrS+S,SjjrS+S-SjjrS+S.SjjrS/SjrS'S0SjjrS'S1SjjrS'S2SjjrS+S3SjjrS+S4SjjrS+S5SjjrSr\ S5r!\ S5r"\ S5r#\ S5r$S+S6S jjr%S7S8S!jjr&S"r'U=r($)9StabilizerState$a>StabilizerState class. Stabilizer simulator using the convention from reference [1]. Based on the internal class :class:`~qiskit.quantum_info.Clifford`. .. plot:: :include-source: :nofigs: from qiskit import QuantumCircuit from qiskit.quantum_info import StabilizerState, Pauli # Bell state generation circuit qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) stab = StabilizerState(qc) # Print the StabilizerState print(stab) # Calculate the StabilizerState measurement probabilities dictionary print (stab.probabilities_dict()) # Calculate expectation value of the StabilizerState print (stab.expectation_value(Pauli('ZZ'))) .. code-block:: text StabilizerState(StabilizerTable: ['+XX', '+ZZ']) {'00': 0.5, '11': 0.5} 1 Given a list of stabilizers, :meth:`qiskit.quantum_info.StabilizerState.from_stabilizer_list` returns a state stabilized by the list .. plot:: :include-source: :nofigs: from qiskit.quantum_info import StabilizerState stabilizer_list = ["ZXX", "-XYX", "+ZYY"] stab = StabilizerState.from_stabilizer_list(stabilizer_list) References: 1. S. Aaronson, D. Gottesman, *Improved Simulation of Stabilizer Circuits*, Phys. Rev. A 70, 052328 (2004). `arXiv:quant-ph/0406196 `_ cD>[U[5(aURUlOD[U[5(a[ UR 55UlO[ X5Ul[ TU][R"URRSS9S9 g)zInitialize a StabilizerState object. Args: data: Data from which the stabilizer state can be constructed. validate: validate that the stabilizer state data is a valid Clifford. r) num_qubits_r num_qubits_l)op_shapeN) isinstancer_datar r to_instructionsuper__init__rauto num_qubits)selfdatavalidate __class__s d/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/quantum_info/states/stabilizerstate.pyrStabilizerState.__init__Xsu dO , ,DJ e $ $!$"5"5"78DJ"$1DJ ',,DJJs r%cliffordStabilizerState.cliffordszzr'c6URR5$)z'Return True if a valid StabilizerState.)r is_unitary)r!atolrtols r%is_validStabilizerState.is_validszz$$&&r'c0[[U5S35e)Nz does not support additionNotImplementedErrortyper5s r%_addStabilizerState._adds!T$ZL0J"KLLr'c0[[U5S35e)Nz' does not support scalar multiplicationrLr5s r% _multiplyStabilizerState._multiplys!T$ZL0W"XYYr'cDUR5(d [S5eg)zReturn the trace of the stabilizer state as a density matrix, which equals to 1, since it is always a pure state. Returns: float: the trace (should equal 1). Raises: QiskitError: if input is not a StabilizerState. -StabilizerState is not a valid quantum state.?rIrr>s r%traceStabilizerState.trace}}MN Nr'cDUR5(d [S5eg)zReturn the purity of the quantum state, which equals to 1, since it is always a pure state. Returns: float: the purity (should equal 1). Raises: QiskitError: if input is not a StabilizerState. rUrVrWr>s r%purityStabilizerState.purityrZr'cH[UR5R5$)z&Convert state to matrix operator class)r rC to_operatorr>s r%r_StabilizerState.to_operators &2244r'cdUR5nURR5UlU$)z%Return the conjugate of the operator.)copyr conjugate)r!rets r%rcStabilizerState.conjugates&iikII'')  r'c[U[5(d [U5nUR5nURR UR5UlU$)uReturn the tensor product stabilizer state self ⊗ other. Args: other (StabilizerState): a stabilizer state object. Returns: StabilizerState: the tensor product operator self ⊗ other. Raises: QiskitError: if other is not a StabilizerState. )rrrbrCtensorrr!r6rds r%rgStabilizerState.tensorE%11#E*EiikMM((8  r'c[U[5(d [U5nUR5nURR UR5UlU$)uReturn the tensor product stabilizer state other ⊗ self. Args: other (StabilizerState): a stabilizer state object. Returns: StabilizerState: the tensor product operator other ⊗ self. Raises: QiskitError: if other is not a StabilizerState. )rrrbrCexpandrrhs r%rlStabilizerState.expandrjr'c[U[5(d [U5nUR5nURR URUS9UlU$)aEvolve a stabilizer state by a Clifford operator. Args: other (Clifford or QuantumCircuit or qiskit.circuit.Instruction): The Clifford operator to evolve by. qargs (list): a list of stabilizer subsystem positions to apply the operator on. Returns: StabilizerState: the output stabilizer state. Raises: QiskitError: if other is not a StabilizerState. QiskitError: if the operator dimension does not match the specified StabilizerState subsystem dimensions. )qargs)rrrbrCcomposer)r!r6rords r%evolveStabilizerState.evolvesJ$%11#E*EiikMM))%..)F  r'cT^^[U[5(aTRUT5$[U[5(aS[ UU4Sj[ UR RUR RUR555$[S[U5S35e)a;Compute the expectation value of a Pauli or SparsePauliOp operator. Args: oper: A Pauli or SparsePauliOp operator to evaluate the expectation value. qargs: Subsystems to apply the operator on. Returns: The expectation value. Raises: QiskitError: if oper is not a Pauli or SparsePauliOp operator. c3h># UH'upnUTR[X45T5-v M) g7fr2)_expectation_value_paulir ).0zxcoeffror!s r% 4StabilizerState.expectation_value..s4#QKA%55eQFmUKK#Qs/2zMOperator for expectation value is not a Pauli or SparsePauliOp operator, but .) rr rur sumzippaulisrwrxcoeffsrrN)r!operros` `r%expectation_value!StabilizerState.expectation_values dE " "00u= = dM * *#&t{{}}dkkmmT[[#Q   :,a !  r'c[U[5(d [S5eURRnUc [ U5nOUn[US-5nSnUR (aSUR -OSn[U5H^upURUURU 'URUURU 'XeRU URU -- nM` [ U5Hn Sn U [R"URURRU -5- n U [R"URURRU -5- n U S-S:XdM g URR5n [ U5GHDn Sn U [R"URURRU -5- n U [R"URURR U -5- n U S-S:XaMUSURR"U -- nU[R"URRU URRU -5- nUS[R"XRRU -5-- nXRRU - n GMG US-S:waU*$U$)a8Compute the expectation value of a Pauli operator. Args: oper (Pauli): a Pauli operator to evaluate expval. qargs (None or list): subsystems to apply the operator on. Returns: complex: the expectation value (only 0 or 1 or -1 or i or -i). Raises: QiskitError: if oper is not a Pauli operator. z7Operator for expectation value is not a Pauli operator.Iry)rr rrCr rangephase enumeraterxrwnp count_nonzerostab_xstab_zrbdestab_xdestab_z stab_phase) r!rror qubitspaulir pauli_phaseposqubitpnum_antipauli_zs r%ru(StabilizerState._expectation_value_pauli!s$&&WX X]]-- =:&FFj3&'-1ZZstzz)Q #F+JC!VVC[EGGEN!VVC[EGGEN WWU^eggen4 4E,z"AH ((4==3G3G3J)JK KH ((4==3G3G3J)JK KH!|q  #77.."z"AH ((4==3I3I!3L)LM MH ((4==3I3I!3L)LM MH!|q  Q11!44 4E R%%dmm&:&:1&= @T@TUV@W&WX XE Q))'MM4H4H4K*KLL LE 4 4Q 77G# 19>< r'c[U[5(d [U5nURnURU:wag[R "UR RUR RSUR R-5n[R "UR RUR RSUR R-5n[R"UVs/sHoURU5PM sn5(dg[U5HnURXF5nUS:wdM g g![a gf=fs snf)zReturn True if the two generating sets generate the same stabilizer group. Args: other (StabilizerState): another StabilizerState. Returns: bool: True if other has a generating set that generates the same StabilizerState. FrrT)rrrr r from_symplecticrrrrrr4commutesrr)r!r6r pauli_orig pauli_otherriexp_vals r%equivStabilizerState.equivbs'%11 '.__   z ).. JJ  tzz00!djj6K6K2K  // KK   2 2A 8N8N4N vv K u~~k2 KLL z"A,,[^*JJqM%((q|!R\H\B]11(wG+ 5=MM'BV4W4\4\4^HOOG0 1"$((:"6HJJw "$((:"6HJJw )-HJJw  &&-NN7 #Nr'cX!-SSU--SU---X-SSU--SU---- S-nUS:aUS- nUS:Xa [S5eU$)zNExponent g of i such that Pauli(x1,z1) * Pauli(x2,z2) = i^g Pauli(x1+x2,z1+z2)rrrrz9Invalid rowsum phase exponent in measurement calculation.r)x1z1x2z2rs r%_phase_exponentStabilizerState._phase_exponentqsl ABJR/027a!b&j1r6>Q3RRVWW 19 QJE A:YZ Z r'c SU-SU--n[UR5HRnU[RURUUR UURUUR U5- nMT US-nUS:gUS:g-(a [ S5e[US:H5nU=RUR-slU=R UR -slX4$)z)Aaronson-Gottesman rowsum helper functionrrrz*Invalid rowsum in measurement calculation.)rr rrrxrwrr) accum_pauli accum_phase row_pauli row_phasenewrrs r%_rowsumStabilizerState._rowsum~s9}q;.9//0E O33 E"IKK$6 e8Lkmm\aNb D1   AI$!) $JK K$!)n  $  $ ''r'c8URUnURUnURnURn[XRXb45n[XQXa45n[R XXs5upX@RU'URXa'URXQ'g)zUpdating StabilizerState Clifford in the non-deterministic rowsum calculation. row and accum are rows in the StabilizerState Clifford.N)rrwrxr rr) rCaccumrowrrrwrxrrs r%r(StabilizerState._rowsum_nondeterministics NN3' nnU+ JJ JJ1616*+ QXqx01 #2#:#: i$  !,u====r'cURUnURnUn[URUURU45n[R XTXc5upTUnXAlU$)zyUpdating an auxiliary Pauli aux_pauli in the deterministic rowsum calculation. The StabilizerState itself is not updated.)rr rwrxrr)rCrrrrrrs r%r%StabilizerState._rowsum_deterministicsi NN3' oo  8::c?HJJsO<= #2#:#: i$   %r'cSnUR5n[[U55HnX(S:XdM U[U5U- S- n [URR SS2U 45(dHUR U S5n Ub[XX5U :Xa[U 5X('M[XX5X('SnMUnM US:XaSRU5n X4U 'gUc [SS5O [XV5/Hjn UR5n [U 5X'UR5n U R U[U5U- S- U 5 U RXSU-XE5 Ml g) aRecursive helper function for calculating the probabilities Args: qubits (range): range of qubits outcome (list[str]): outcome being built outcome_prob (float): probability of the outcome probs (dict[str, float]): holds the outcomes and probability results outcome_bitstring (str): target outcome to measure which reduces measurements, None if not targeting a specific target XrNrrrg?) rbrrrrCrrrrjoin_get_probabilities)r!rr outcome_probrrqubit_for_branchingrdrrsingle_qubit_outcome str_outcome new_outcomestab_cpys r%r"StabilizerState._get_probabilitiess$$&#yy{s6{#AzS F a! 353<<..q%x899585L5LUTU5V((0-015II &))=%> &)):)=%> '( *+')$, " $'''*K!-+  ") !QK'<=> ? ! ",,.K/23G/HK ,xxzH  ( (F &99A=?AU   ' 'cL&85  ?r'cUc [URR5nOUnS/[U5-nSn0nUR XEXgU5 Ub&UR 5Hup[ X5Xx'M U$)aHelper Function for calculating the subsystem measurement probability dictionary. When the targeted outcome_bitstring value is set, then only the single outcome_bitstring probability will be calculated. Args: outcome_bitstring (None or str): targeted outcome bitstring to perform a measurement calculation for, this will significantly reduce the number of calculation performed (Default: None) qargs (None or list): subsystems to return probabilities for, if None return for all subsystems (Default: None). decimals (None or int): the number of decimal places to round values. If None no rounding is done (Default: None). Returns: dict: The measurement probabilities in dict (key) form. rrV)rrCr rrrround) r!rrorrrrrrrs r%r'StabilizerState._get_probabilities_dictsz, =4==334FF%#f+% "$ FWX  #kkm "53 , r'rB)T)r"zUStabilizerState | Clifford | Pauli | QuantumCircuit | circuit.instruction.Instructionr#bool)FF)r.zCollection[str]r*rr+rreturnr)NN)rfloat)rr )r6rrrr2)r6z'Clifford | QuantumCircuit | Instructionro list | Nonerr)rzPauli | SparsePauliOpro None | listrcomplex)rr rorrr )r6rrr)rorr None | intr np.ndarray)rrrorrr rdict[str, float])rorrr rr )rorrr)rorrtuple)rrrorrr ) rrrz list[str]rrrr rr)NNN)rz None | strrorrr rr ))__name__ __module__ __qualname____firstlineno____doc__r classmethodr/r7r?propertyrCrIrOrRrXr\r_rcrgrlrqrrurrrrrrrr staticmethodrrrrrr__static_attributes__ __classcell__)r$s@r%rr$s61ldcddd2!&', $!%   :;D'MZ  5 $&TX<EP 0 6?B'R:"# " " "  "  " JAEd d3=d d0#J<:.`  (($!!*8"& @@@ @  @  @H)-!# %%%% %  %%r'r)r __future__rcollections.abcrtypingrnumpyrqiskit.exceptionsr&qiskit.quantum_info.operators.op_shaper&qiskit.quantum_info.operators.operatorr (qiskit.quantum_info.operators.symplecticr r r r :qiskit.quantum_info.operators.symplectic.clifford_circuitsr(qiskit.quantum_info.states.quantum_staterqiskit.circuitrrqiskitrrr'r%r%sD#& ):;^^PA6A lA r'