z i/SrSSKrSSKJrJrJrJr SSKrSSK J r SSK J r S Sjr "SS5r\ "S S S 9SS j5rg)z^ Visualization function for animation of state transitions by applying gates to single qubit. N)sincosacossqrt)MissingOptionalLibraryError)deprecate_funcc^[SU55n[US- 5U:a [U5m[U4SjU55n[R "U5$)z_normalize..s a1uasg?c3,># UH oT- v M g7fr r )r rmags rrrs%1ac'1s)sumabsrtuplenparray)v tolerancemag2rs @r _normalizersL  a D 4#:"4j %1% % 88A;ct\rSrSrSrSr\S5r\S5rSr Sr Sr S r S r S rS rS rSrSrg) _Quaternion"z&For calculating vectors on unit spherecSUlgr _valselfs r__init___Quaternion.__init__%s  rcR[U5n[5nURX5 U$)zCreate quaternion from axis)rr_axisangle_to_q)thetarnew_quaternions rfrom_axisangle_Quaternion.from_axisangle(s( qM$&&u0rc&[5nXlU$)zCreate quaternion from vector)rr#)valuer+s r from_value_Quaternion.from_value1s%#rcUSnUSnUSn[US- 5nU[US- 5-nU[US- 5-nU[US- 5-n[R"XcXE/5Ulg)z$Convert axis and angle to quaternionr@N)rrrrr#)r%r*rxyzws rr)_Quaternion._axisangle_to_q8sx aD aD aD   ECK  ECK  ECK HHaA\* rc[U[5(aURU5$[U[[[ R 45(a7[U5S:wa[S[U535eURU5$[$)z6Multiplication of quaternion with quaternion or vectorz Input vector has invalid length ) isinstancer_multiply_with_quaternionlistrrndarraylen ValueError_multiply_with_vectorNotImplemented)r%bs r__mul___Quaternion.__mul__Ess a % %11!4 4 D%4 5 51v{ #CCF8!LMM--a0 0! !rc0URup#pEURupgpX&-X7-- XH-- XY-- n X'-X6--XI--XX-- n X(-XF--XW--X9-- n X)-XV--X8--XG-- n [R[R"XX455nU$)z,Multiplication of quaternion with quaternionr#rr0rr)r%q_2w_1x_1y_1z_1w_2x_2y_2z_2r9r6r7r8results rr>%_Quaternion._multiply_with_quaternionQs!YY# XX# I !CI - 9 I !CI - 9 I !CI - 9 I !CI - 9''!(>? rc[R[R"SU55nX-UR 5-R SS$)z(Multiplication of quaternion with vectorgr3N)rr0rappend get_conjugater#)r%rrJs rrC!_Quaternion._multiply_with_vector]s@$$RYYa%89 T//1177;;rcURupp4[R[R"X*U*U*455nU$)zConjugation of quaternionrI)r%r9r6r7r8rSs rrW_Quaternion.get_conjugatebs9YY a''!R!aR(AB rc VUR5upSUSUSSUSSUSS3 $)Nz((z; rz, r3r4z))) get_axisangle)r%r*rs r__repr___Quaternion.__repr__hs?%%'E7"QqTF"QqTF"QqTF"55rcrURSURSSp![U5S-nU[U54$)z&Returns angle and vector of quaternionrr3Nr5)r#rr)r%r9rr*s rr\_Quaternion.get_axisanglels7yy|TYYqr]1Q# jm##rc6URR5$)zConverts quaternion to a list)r#tolistr$s rrb_Quaternion.tolistssyy!!rcdUR5up[RRU5$)zCalculates norm of quaternion)r\rlinalgnorm)r%_rs r vector_norm_Quaternion.vector_normws%!!#yy~~a  rr"N)__name__ __module__ __qualname____firstlineno____doc__r& staticmethodr,r0r)rFr>rCrWr]r\rbrh__static_attributes__r rrrr"s_0 + " <  6$"!rrz1.2.0zin the 2.0 release)sinceremoval_timelinec  ^^^^^^SSKJn SnSSKnSSKJn SSKJn SSKJn S S KJ n S S K J n Sn SnS [R;aS [R;aSnU (d [SSSS9eU(dUSLa [SSSS9e[UR 5S :waW "S5eUmUS-U- n0nS["R%[&R(T- /SQ5S4US'S["R%[&R(T- /SQ5S4US'S["R%[&R(T- /SQ5S4US'S["R%[&R(S - T- /SQ5S!4US'S"["R%[&R(*S - T- /SQ5S#4US"'S$["R%[&R(T- [+/S%Q55S&4US$'S'["R%[&R(S(- T- /SQ5S)4US''S*["R%[&R(*S(- T- /SQ5S+4US*'/mUR,GHun nUR.S,:XaMUR.U;a TR1UUR.5 MJUR.S-:XaPUR2Sn["R%UT- /SQ5nTR1UR.S.US/3US045 MUR.S1:XaQUR2Sn["R%UT- /SQ5nTR1UR.S.US/3US245 GM UR.S3:XaQUR2Sn["R%UT- /SQ5nTR1UR.S.US/3US445 GMlUR.S5:XaQUR2Sn["R%UT- /SQ5nTR1UR.S.US/3US645 GMW "S7UR.S835e [T5S:XaW "S95e[+[&R4"/SQ55nWR7S:S;9n[9S<WR:R=S=555S>:aW "USS?9mUR?T5 OW "U5mTRAS@SA5 TRCS@SA5 W "TSB9m"SCSD5nU"5mUTl"UUUUUU4SEjnUU4SFjnW RGUU[IT[T5-S -5USSUSG9nU(aURKUSHSI9 U(a6SJURLSK'UROU5 W"URQ55$URS5 UROU5 g![a SnGNf=f![a Sn GNf=f)La Creates animation showing transitions between states of a single qubit by applying quantum gates. Args: circuit (QuantumCircuit): Qiskit single-qubit QuantumCircuit. Gates supported are h,x, y, z, rx, ry, rz, s, sdg, t, tdg and u1. trace (bool): Controls whether to display tracing vectors - history of 10 past vectors at each step of the animation. saveas (str): User can choose to save the animation as a video to their filesystem. This argument is a string of path with filename and extension (e.g. "movie.mp4" to save the video in current working directory). fpg (int): Frames per gate. Finer control over animation smoothness and computational needs to render the animation. Works well for tkinter GUI as it is, for jupyter GUI it might be preferable to choose fpg between 5-30. spg (int): Seconds per gate. How many seconds should animation of individual gate transitions take. Returns: IPython.core.display.HTML: If arg jupyter is set to True. Otherwise opens tkinter GUI and returns after the GUI is closed. Raises: MissingOptionalLibraryError: Must have Matplotlib (and/or IPython) installed. 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