z i4 SrSSKrSSKJrJr SSKJr SSKrSSKr SSK J r SSK J r SSKJr SSKJrJr SS KJr SS KJr SS KJr S S KJrJr S SKJr S SKJ r \RBRDS1SS.Sjj5r#\RBRDS2Sj5r$\RBRDS3SSSSS S.Sjj5r%\RBRDS4SS.Sjj5r&\RBRDS1SS.Sjj5r'Sr(Sr)Sr*Sr+\RBRD\RXRDS5SS.Sjj55r-\RBRDS5r.Sr/S6Sjr0S7S \\ \4S!\1S"\2S#\24S$jjr3S8S%\\4S&\5S#\\24S'jjr6S9S(\\4S)\5S*\2S&\5S#\24 S+jjr7"S,S-5r8S6S.jr9S/r:S0r;g):z- Visualization functions for quantum states. N)ListUnion)reduce) user_config) Statevector)Operator) PauliList SparsePauliOp) DensityMatrix) optionals)pi_check) _num_to_latexarray_to_latex)matplotlib_close_if_inline)VisualizationError)filenamec  SSKJn [U5nURnUc [ S5eS[ R "[ R"[R"UR5R555-n [R"UR5n [R"UR5n UcSnU(dU(dURSSUS9un upO,U(aUR5n OUR5n Un Un[!SU-5Vs/sH n[#U5SSR%U5PM" nn[!SU-5Vs/sH n[#U5SSR%U5PM" snSSS 2nU R&unnU (GaU R(R+S 5 U R-S S 5 U R.R1UR355 U R4R1UR355 [R6"U 5HuunnnUUU- S- nnUS:aS OSn[R8"[R"U5U - 5nUR;SU-US- - SU-US- - /UUUUS9nU R=U5 M U R?S[R@"U5-5 U RCS[R@"U5-5 U RESU/5 U RGSU/5 U RIUSS9 U RKUSSS9 U RMSSS9 U(GaUR(R+S 5 UR-S S 5 UR.R1UR355 UR4R1UR355 [R6"U 5HuunnnUUU- S- nnUS:aS OSn[R8"[R"U5U - 5nUR;SU-US- - SU-US- - /UUUUS9nUR=U5 M UR?S[R@"U5-5 URCS[R@"U5-5 URESU/5 URGSU/5 URIUSS9 URKUSSS9 URMSSS9 U RO5 U(aU RQUSS9 UcUc [SU 5 UcU $U RUU5$s snfs snf)aPlot a hinton diagram for the density matrix of a quantum state. The hinton diagram represents the values of a matrix using squares, whose size indicate the magnitude of their corresponding value and their color, its sign. A white square means the value is positive and a black one means negative. Args: state (Statevector or DensityMatrix or ndarray): An N-qubit quantum state. title (str): a string that represents the plot title figsize (tuple): Figure size in inches. filename (str): file path to save image to. ax_real (matplotlib.axes.Axes): An optional Axes object to be used for the visualization output. If none is specified a new matplotlib Figure will be created and used. If this is specified without an ax_imag only the real component plot will be generated. Additionally, if specified there will be no returned Figure since it is redundant. ax_imag (matplotlib.axes.Axes): An optional Axes object to be used for the visualization output. If none is specified a new matplotlib Figure will be created and used. If this is specified without an ax_imag only the real component plot will be generated. Additionally, if specified there will be no returned Figure since it is redundant. Returns: :class:`matplotlib:matplotlib.figure.Figure` : The matplotlib.Figure of the visualization if neither ax_real or ax_imag is set. Raises: MissingOptionalLibraryError: Requires matplotlib. VisualizationError: Input is not a valid N-qubit state. Examples: .. plot:: :alt: Output from the previous code. :include-source: import numpy as np from qiskit import QuantumCircuit from qiskit.quantum_info import DensityMatrix from qiskit.visualization import plot_state_hinton qc = QuantumCircuit(2) qc.h([0, 1]) qc.cz(0,1) qc.ry(np.pi/3 , 0) qc.rx(np.pi/5, 1) state = DensityMatrix(qc) plot_state_hinton(state, title="New Hinton Plot") rpyplotN)Input is not a multi-qubit quantum state.)rfigsizegrayequalboxwhiteblack?) facecolor edgecolorfontsizeZr(rotationz Re[$\rho$]z Im[$\rho$])+ matplotlibrr num_qubitsrmathceillog2npabsdatamaxrealimagsubplots get_figurerangebinzfillshapepatch set_facecolor set_aspectxaxisset_major_locator NullLocatoryaxis ndenumeratesqrt Rectangle add_patch set_xticksarange set_yticksset_xlimset_ylimset_yticklabelsset_xticklabels set_title tight_layoutsuptitlersavefig)statetitlerax_realax_imagrpltrhonum max_weightdatarealdataimagfigax1ax2i column_names row_nameslylxxywplot_xplot_ycolorsizerects b/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/visualization/state_visualization.pyplot_state_hintonro'sp)  C ..C { !LMMdii "&&*:*>*>*@ ABBJwwsxx Hwwsxx H 7,,q!W,=Zc3 $$&C$$&C38C=A=aCF12J$$S)=LA05af > 1Q!!#& >ttDI ^^FB  ' w& ##COO$56 ##COO$561IFQAQ FF 1uG'E77266!9z12D==vq(#,*AB !D MM$ 2 sRYYr]*+ sRYYr]*+ aW aW I3 L2C mb 1  ' w& ##COO$56 ##COO$561IFQAQ FF 1uG'E77266!9z12D==vq(#,*AB !D MM$ 2 sRYYr]*+ sRYYr]*+ aW aW I3 L2C mb 1  UR (7?"3' {{8$$GB>s +'V$'V cSSKJn UcSnU"X%S9nUS:XaUSUSUSpnU[R"U 5-[R"U 5-US'U[R"U 5-[R"U 5-US'U[R"U 5-US'UR U5 UR US 9 Uc1URn U RUSUS5 [U 5 U $g) aPlot the Bloch sphere. Plot a Bloch sphere with the specified coordinates, that can be given in both cartesian and spherical systems. Args: bloch (list[double]): array of three elements where [, , ] (Cartesian) or [, , ] (spherical in radians) is inclination angle from +z direction is azimuth from +x direction title (str): a string that represents the plot title ax (matplotlib.axes.Axes): An Axes to use for rendering the bloch sphere figsize (tuple): Figure size in inches. Has no effect is passing ``ax``. coord_type (str): a string that specifies coordinate type for bloch (Cartesian or spherical), default is Cartesian font_size (float): Font size. Returns: :class:`matplotlib:matplotlib.figure.Figure` : A matplotlib figure instance if ``ax = None``. Raises: MissingOptionalLibraryError: Requires matplotlib. Examples: .. plot:: :alt: Output from the previous code. :include-source: from qiskit.visualization import plot_bloch_vector plot_bloch_vector([0,1,0], title="New Bloch Sphere") .. plot:: :alt: Output from the previous code. :include-source: import numpy as np from qiskit.visualization import plot_bloch_vector # You can use spherical coordinates instead of cartesian. plot_bloch_vector([1, np.pi/2, np.pi/3], coord_type='spherical') r)BlochN)rr)axes font_size sphericalrr)rU) blochrqr2sincos add_vectorsrenderr^set_size_inchesr) rurUaxr coord_typersrqBrthetaphir^s rnplot_bloch_vectorrsb 2+A[ a%(E!H#rvve}$rvvc{2arvve}$rvvc{2arvve}$aMM%HH5H zee GAJ 3"3' F) reverse_bitsrrstitle_font_size title_padc fSSKJn U(a[U5SSS2O [U5n [U 5n Ub UupX-n OUR SU - 5up[U5S:a U SUS- -- n UbUOSn UbUOU nUR X4S9n[ U 5HBnU(aU S- U- OUnURSXS-S S 9n[XS [U5-UX%S 9 MD URXS S9 [U5 UcUR5 U$URU5$![a U$f=f)aPlot a Bloch sphere for each qubit. Each component :math:`(x,y,z)` of the Bloch sphere labeled as 'qubit i' represents the expected value of the corresponding Pauli operator acting only on that qubit, that is, the expected value of :math:`I_{N-1} \otimes\dotsb\otimes I_{i+1}\otimes P_i \otimes I_{i-1}\otimes\dotsb\otimes I_0`, where :math:`N` is the number of qubits, :math:`P\in \{X,Y,Z\}` and :math:`I` is the identity operator. Args: state (Statevector or DensityMatrix or ndarray): an N-qubit quantum state. title (str): a string that represents the plot title figsize (tuple): size of each individual Bloch sphere figure, in inches. reverse_bits (bool): If True, plots qubits following Qiskit's convention [Default:False]. font_size (float): Font size for the Bloch ball figures. title_font_size (float): Font size for the title. title_pad (float): Padding for the title (suptitle ``y`` position is ``0.98`` and the image height will be extended by ``1 + title_pad/100``). Returns: :class:`matplotlib:matplotlib.figure.Figure` : A matplotlib figure instance. Raises: MissingOptionalLibraryError: Requires matplotlib. VisualizationError: if input is not a valid N-qubit state. Examples: .. plot:: :alt: Output from the previous code. :include-source: from qiskit import QuantumCircuit from qiskit.quantum_info import Statevector from qiskit.visualization import plot_bloch_multivector qc = QuantumCircuit(2) qc.h(0) qc.x(1) state = Statevector(qc) plot_bloch_multivector(state) .. plot:: :alt: Output from the previous code. :include-source: from qiskit import QuantumCircuit from qiskit.quantum_info import Statevector from qiskit.visualization import plot_bloch_multivector qc = QuantumCircuit(2) qc.h(0) qc.x(1) # You can reverse the order of the qubits. from qiskit.quantum_info import DensityMatrix qc = QuantumCircuit(2) qc.h([0, 1]) qc.t(1) qc.s(0) qc.cx(0,1) matrix = DensityMatrix(qc) plot_bloch_multivector(matrix, title='My Bloch Spheres', reverse_bits=True) rrNrrdr,r3d projectionzqubit )r{rrsg\(\?)r(rg)r-r_bloch_multivector_datalen figaspectfigurer: add_subplotrstrrRrrQAttributeErrorrS)rTrUrrrrsrrrX bloch_datarZwidthheightdefault_title_font_sizer^raposr{s rnplot_bloch_multivectorrs\`)1=&tt,BYZ_B` j/C   a#g.  5zA~!i#o%%+4+@ib)8)DoJaO **e_* -C 3Z)cAgkq __QUt_ < M8c#h.2w  LLDL9s#      {{8$$     s?D"" D0/D0c DSSKJn SSKJn SSKJn [ U5n U Rn U c [S5e[R"U R5n [R"U R5n[SU -5Vs/sH n[U5SSRU 5PM" nn[SU -5Vs/sH n[U5SSRU 5PM" nnU R SSunn[R""SUS5n[R""SUS5n[R$"US-US-5unnUR'5nUR'5n[R("UU-5nS [R*"U5-nUR-5nU R'5nUR'5nUcS unnO4[/U5S:wa [1S 5eUScS OUSnUScS OUSnUc?Uc<UcS nU R3USS9nUR5SSSSSS9nUR5SSSSSS9nO,UbUR75nUnUnOUR75nSnUnUR95 [R:"U5n [R:"U5n!UR=5un"n#[?U"S- U#5n$[ASU$-5n%SS[RB"U$5-- n&UUUS4UUUS44GHun'n(n)n*U'cM[R:"U(5n+[R>"U(5n,[EU)[F5(a'U)RIS5(aURKU)5n)U(S:n-[RL"U-5(a\[OUU-UU-UU-UU-UU-U(U-U)5n.U'RQUU-UU-UU-UU-UU-U(U-USS9n/U/RSU.5 U,Ss=:aU+:aoO OlSU/SU/n1n0[U[WU0U0SSS2-[RX"U1S5S/S-55/n2U "U2SSSS9n3U3R[S5 U'R]U35 U(S:n4[RL"U45(a\[OUU4UU4UU4UU4UU4U(U4U)5n.U'RQUU4UU4UU4UU4UU4U(U4US S9n5U5RSU.5 U'R_U*S!3U%S"9 U'Ra[R""S US -S55 U'Rc[R""S US -S55 U+U,:wa*U'RdRgU,[;U S#-U!55 OIU,S:Xa*U'RdRgU,[;U S#-U!55 OU'RdRgS$S%9 U'Ri5 U'RjRmUU%S&S'S(S)9 U'RnRmUU%S*S+S,S)9 U'RpRs5HTn6U6RtRwU%5 U6RtRyS+5 U6RtR{S-5 MV U'R}S.U&S/9 U'RS5 U'RS5 GM URUU%S0-S"9 URS1SSSSSS29 UcUc [U5 UcU$URU5$s snfs snf)3a Plot the cityscape of quantum state. Plot two 3d bar graphs (two dimensional) of the real and imaginary part of the density matrix rho. Args: state (Statevector or DensityMatrix or ndarray): an N-qubit quantum state. title (str): a string that represents the plot title figsize (tuple): Figure size in inches. color (list): A list of len=2 giving colors for real and imaginary components of matrix elements. alpha (float): Transparency value for bars ax_real (matplotlib.axes.Axes): An optional Axes object to be used for the visualization output. If none is specified a new matplotlib Figure will be created and used. If this is specified without an ax_imag only the real component plot will be generated. Additionally, if specified there will be no returned Figure since it is redundant. ax_imag (matplotlib.axes.Axes): An optional Axes object to be used for the visualization output. If none is specified a new matplotlib Figure will be created and used. If this is specified without an ax_real only the imaginary component plot will be generated. Additionally, if specified there will be no returned Figure since it is redundant. Returns: :class:`matplotlib:matplotlib.figure.Figure` : The matplotlib.Figure of the visualization if the ``ax_real`` and ``ax_imag`` kwargs are not set Raises: MissingOptionalLibraryError: Requires matplotlib. ValueError: When 'color' is not a list of len=2. VisualizationError: if input is not a valid N-qubit state. Examples: .. plot:: :alt: Output from the previous code. :include-source: # You can choose different colors for the real and imaginary parts of the density matrix. from qiskit import QuantumCircuit from qiskit.quantum_info import DensityMatrix from qiskit.visualization import plot_state_city qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) state = DensityMatrix(qc) plot_state_city(state, color=['midnightblue', 'crimson'], title="New State City") .. plot:: :alt: Output from the previous code. :include-source: # You can make the bars more transparent to better see the ones that are behind # if they overlap. import numpy as np from qiskit.quantum_info import Statevector from qiskit.visualization import plot_state_city from qiskit import QuantumCircuit qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) qc = QuantumCircuit(2) qc.h([0, 1]) qc.cz(0,1) qc.ry(np.pi/3, 0) qc.rx(np.pi/5, 1) state = Statevector(qc) plot_state_city(state, alpha=0.6) rNr)Poly3DCollectionrrrg?r#)#648fffrz 'color' must be a list of len=2.r)r,rrh)rr$rF)rcomputed_zorderg@ Real Imaginary#g?)alphazorderrk)rr$ linewidths?g?u Amplitude (ρ)r'g& .>T)auto-righttop)r(r+havag6leftcenterbottom)rrr)aspectzoomg?g?)rrrrhspacewspace)Ematplotlib.colorscolorsr-rmpl_toolkits.mplot3d.art3drr r.rr2r6r4r7r:r;r<r=rJmeshgridflattenzeros ones_likecopyr ValueErrorrrr9rQr5get_size_inchesminintrF isinstancer startswith to_rgba_arrayanygenerate_facecolorsbar3dr?listziprepeat set_zorderadd_collection3drPrIrKrr set_zlim3dget_autoscalez_onrAset_ticklabelsrDzaxisget_major_tickslabel1 set_fontsizeset_horizontalalignmentset_verticalalignmentset_box_aspect set_xmargin set_ymarginrRsubplots_adjustrrS)7rTrUrrkrrVrWrmcolorsrXrrYrZr\r]rarbrcrdrexposyposzposdxdydzrdzi real_color imag_colorr^r_r`max_dzrmax_dzi fig_width fig_height max_plot_size max_font_sizemax_zoomr{dzcolzlabelmax_dzmin_dzdznfc negative_barsxlimylimvertsplanedzp positive_barsticks7 rnplot_state_cityrtsx((;  C ..C { !LMMwwsxx Hwwsxx H49C=A=aCF12J$$S)=LA05af > 1Q!!#& I> ^^BQ FB 99QA D 99QA DTD[$+6JD$ <<>D <<>D 88BG D r||D! !B B    C    C }!5 J u:??@ @"'("2Ya "'("2Ya 7? ?GjjCj8ooaA$oNooaA$oN    "  "ffSkGffSkG //1Iz D(*5MM)*MR"''-001H c:v& c:{+ BV :  c3  CNN3$7$7'',C1f 66#;;$S 49d3iC"S'2c7CBHHS S S 333% M  ' ' + A  R1b'$D#dT$B$Z/41CaS1WMNOE$U$#RSTE   T "    &Ag 66#;;$S 49d3iC"S'2c7CBHHS S S 333% M  ' ' + x/- H biiR#Xq12 biiR#Xq12 V  GG  vs7T>7'C D{""63w~w+GH"""-    w5    =5VPX  HH,,.D KK $ $] 3 KK / / 7 KK - -h 7/ : q qe hLL!5L6C1QO7?"3' {{8$$aB>s '\'\cSSKJn [U5upx[U5n UcSnUcSn[R "U 5n Sn UcSn UR US9upOSn UR5n URSS S S 9 URXXS S 9 URS SS9 URSSS9 URU 5 UR/SQ5 URUSSS9 URSSS9 UR!SS /5 UR#S5 UR$R'5UR(R'5-HnUR*R-S5 M UR/USS9 U (a [1U 5 UcU R35 U $U R7U5$![4a U $f=f)a Plot the Pauli-vector representation of a quantum state as bar graph. The Pauli-vector of a density matrix :math:`\rho` is defined by the expectation of each possible tensor product of single-qubit Pauli operators (including the identity), that is .. math :: \rho = \frac{1}{2^n} \sum_{\sigma \in \{I, X, Y, Z\}^{\otimes n}} \mathrm{Tr}(\sigma \rho) \sigma. This function plots the coefficients :math:`\mathrm{Tr}(\sigma\rho)` as bar graph. Args: state (Statevector or DensityMatrix or ndarray): an N-qubit quantum state. title (str): a string that represents the plot title figsize (tuple): Figure size in inches. color (list or str): Color of the coefficient value bars. ax (matplotlib.axes.Axes): An optional Axes object to be used for the visualization output. If none is specified a new matplotlib Figure will be created and used. Additionally, if specified there will be no returned Figure since it is redundant. Returns: :class:`matplotlib:matplotlib.figure.Figure` : The matplotlib.Figure of the visualization if the ``ax`` kwarg is not set Raises: MissingOptionalLibraryError: Requires matplotlib. VisualizationError: if input is not a valid N-qubit state. Examples: .. plot:: :alt: Output from the previous code. :include-source: # You can set a color for all the bars. from qiskit import QuantumCircuit from qiskit.quantum_info import Statevector from qiskit.visualization import plot_state_paulivec qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) state = Statevector(qc) plot_state_paulivec(state, color='midnightblue', title="New PauliVec plot") .. plot:: :alt: Output from the previous code. :include-source: # If you introduce a list with less colors than bars, the color of the bars will # alternate following the sequence from the list. import numpy as np from qiskit.quantum_info import DensityMatrix from qiskit import QuantumCircuit from qiskit.visualization import plot_state_paulivec qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) qc = QuantumCircuit(2) qc.h([0, 1]) qc.cz(0, 1) qc.ry(np.pi/3, 0) qc.rx(np.pi/5, 1) matrix = DensityMatrix(qc) plot_state_paulivec(matrix, color=['crimson', 'midnightblue', 'seagreen']) rr)rrr#TrFrz--)r linewidth linestylerrkrr)rrk Coefficientsr&r')rgrr#rFr*Paulirz#eeeeeer,)r-r_paulivec_datarr2rJr8r9gridbaraxhline set_ylabelrIrKrO set_xlabelrMr?rArrDrrrPrrQrrS)rTrUrrkr{rrXlabelsvaluesnumelemindr return_figr^rs rnplot_state_paulivecr qsX)#E*NF&kG } ))G C E z ,,w,/R mmoGG1TG2FF31F5JJ#J&MM.2M.MM#MM'(vR8MM'BM'KKQY((*RXX-E-E-GG   $HLLL$"3'      {{8$$     sF55 GGc ~US:Xag[S[[X- S-US-5[SUS-55S5$)zReturn the number of combinations for n choose k. Args: n (int): the total number of options . k (int): The number of elements. Returns: int: returns the binomial coefficient rcXS-US- $)Nrr)rfrgs rnn_choose_k..sqQ4x!A$rr)rrr:)nrs rn n_choose_krsE Av .E!%!)QU4KUSTVWZ[V[_0]_` aarc^^[U5T:wa [S5eUVs/sH o0S- U- PM snm[UU4Sj[T555n[ U5$s snf)a Return the lex index of a combination.. Args: n (int): the total number of options . k (int): The number of elements. lst (list): list Returns: int: returns int index for lex order Raises: VisualizationError: if length of list is not equal to k zlist should have length krc3T># UHn[TTS- U- US-5v M g7f)rN)r).0racombrs rn lex_index.. s+EHq 4A ?AE22Hs%()rrsumr:r)rrlstrfdualmrs ` @rn lex_indexrsY 3x1} !<==" #s!EAIs #D EE!HE EE u: $sAc[U5nURS5nURS5X- :wa [S5e[U5VVs/sHup4US:XdM UPM nnn[ XU5$s snnf)z*Return the index of a string of 0s and 1s.10zs must be a string of 0 and 1)rcountr enumerater)srrrcharoness rnbit_string_indexr& sh AA  Awws|qu !@AA!*1 =ICCD = Q4   >s A2A2c[R"U5[RS-S- -[RS--n[R"U[RS-- SS5nU$)zMap a phase of a complexnumber to a color in (r,g,b). complex_number is phase is first mapped to angle in the range [0, 2pi] and then to the HSL color wheel rrrr#)r2anglepicolorsys hls_to_rgb)complex_numberanglesrgbs rn phase_to_rgbr/sV hh~&"%%!)a-8RUUQY GF   f 2C =C Jrc SSKJn SSKJn SSKJn SSKn SSKJn SSKJ n [U5n U RnUc [S 5eU RU R5unnUcS nUcS nURUS 9nOS nUR!5nUR#SSS9nUR%USS2SS24SS9nUR&R)SS5 UR&R+SS5 UR&R-SS5 UR&R/S 5 UR1SSS9 [3UR&S5(aUR&R5S5 [6R8"SS[6R:-S5n[6R8"S[6R:S5n[6R<"[6R>"U5[6R@"U55n[6R<"[6R@"U5[6R@"U55n[6R<"[6RB"[6RD"U55[6R>"U55nURGUUUSSURHSSSS9 URJRMS5 URNRMS5 URPRMS5 URJRRRUS5 URNRRRUS5 URPRRRUS5 URW/5 URY/5 UR[/5 []UR^SS- SS5GHnUUS :GaUSS2U4n[6R`"U5Rc5n[6Rd"UU5S[6R:--S[6R:--nf"S!U-5nUU-nUn[]SU-5GHtn[iU5SSRkU5nURmS"5n S#U -U- S-n![oUU 5n"[qU5n#[sU 5U- [6R:S--U#S-[6R:U"- --n$U US- :dU US- :Xa3U#U"S- :a*[6R:U$- S[6R:-U"- - n$[6Rt"SU!S-- 5[6R>"U$5-n%[6Rt"SU!S-- 5[6R@"U$5-n&[6Rv"[6Rx"UUUUR{555n'[}U'S5n'[UU5n(Sn)U&S$:aSU&- n)[6R"U'S5(GdbU(GaZS%n*[6R"[6Rt"SU!S-- 5U!5n+U*[6R@"U+5-[6R>"U$5-n,U*[6R@"U+5-[6R@"U$5-n-U*[6R>"U+5-n.S&U-S'-n/U(a[6Rd"UU5[6R:S(--[6R:S--n0U(aU/S)U0S*-[6R:- S+S,3- n/O#[U0SS-9RS.S/5n0U/S)U0S03- n/URU,U-U.U/S1S1S2S39 URU%/U&/U!/U(U(S4[6Rt"U'5S5-U)S69 U "SU%/SU&/SU!/S7U'S8U(SS99n1URU15 GMw []US-5Hn [6R8"S#[6R:-S[6R:-S:5n2S#U -U- S-n[6Rt"SUS-- 5n3U3[6R>"U25-nU3[6R@"U25-nURUUUS;SS9 M URS/S/S/S;S;S4SSS69 GM O S?n4[6RB"U45n2U RU45n5UR%USS2SS245n6U6RU2U5SU4-S@-SU5SSU4-S@--SASB9 U6RU "SCS=SDSSE95 SFn7U(a/SGQn8O/SHQn8U6RSSU8SS1S1SISJ9 U6RU7SU8SS1S1SISJ9 U6RSU7U8SS1S1SISJ9 U6RU7*SU8SS1S1SISJ9 U6RSU7*U8S(S1S1SISJ9 U(a [U5 UcU$URU5$)KaPlot the qsphere representation of a quantum state. Here, the size of the points is proportional to the probability of the corresponding term in the state and the color represents the phase. Args: state (Statevector or DensityMatrix or ndarray): an N-qubit quantum state. figsize (tuple): Figure size in inches. ax (matplotlib.axes.Axes): An optional Axes object to be used for the visualization output. If none is specified a new matplotlib Figure will be created and used. Additionally, if specified there will be no returned Figure since it is redundant. show_state_labels (bool): An optional boolean indicating whether to show labels for each basis state. show_state_phases (bool): An optional boolean indicating whether to show the phase for each basis state. use_degrees (bool): An optional boolean indicating whether to use radians or degrees for the phase values in the plot. Returns: :class:`matplotlib:matplotlib.figure.Figure` : A matplotlib figure instance if the ``ax`` kwarg is not set Raises: MissingOptionalLibraryError: Requires matplotlib. VisualizationError: Input is not a valid N-qubit state. QiskitError: Input statevector does not have valid dimensions. Examples: .. plot:: :alt: Output from the previous code. :include-source: from qiskit import QuantumCircuit from qiskit.quantum_info import Statevector from qiskit.visualization import plot_state_qsphere qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) state = Statevector(qc) plot_state_qsphere(state) .. plot:: :alt: Output from the previous code. :include-source: # You can show the phase of each state and use # degrees instead of radians from qiskit.quantum_info import DensityMatrix import numpy as np from qiskit import QuantumCircuit from qiskit.visualization import plot_state_qsphere qc = QuantumCircuit(2) qc.h([0, 1]) qc.cz(0,1) qc.ry(np.pi/3, 0) qc.rx(np.pi/5, 1) qc.z(1) matrix = DensityMatrix(qc) plot_state_qsphere(matrix, show_state_phases = True, use_degrees = True) r)gridspecr)CircleN)linalgr)Arrow3Dr)rrTrFr)nrowsncolsrrg?ri)elevazimrrrrrz grid.colorg?)rstridecstriderkrr)r7r7r7grgMbP?yrg?g?z$\vertz\rangle$rz $z.1fz^\circ$)ndigitsr)z\pi$r )rrrlo)markerfacecolormarkeredgecolormarker markersizer-)mutation_scaler arrowstylerklwr)r#r#r#:r#)rkrMlsr@rr)rradius)rrr!rgffffff?)z Phase (Deg)r 90z180 270)Phasez$0$z$\pi/2$z$\pi$z$3\pi/2$r&)horizontalalignmentverticalalignmentr()Kr-r1rmatplotlib.patchesr2seabornscipyr3rur4r r.reighr4rr9GridSpecrrr set_xlim3d set_ylim3drr view_inithasattrrr2linspacer)outerrwrvr%rl plot_surfacercParamsrAset_pane_colorrDrline set_colorrIrK set_zticksr:r=absoluteargmaxr(expr;r<r!rr&floatrFr6dotconjrr/isclosearctan2r replacetextplot add_artist hls_palettepierrS)9rTrr{show_state_labelsshow_state_phases use_degreesrr1rXr2snsr3r4rYrZeigvalseigvecsr r^gsuvrfrgzidxlocr-anglesetdraelementweightzvaluenumber_of_divisions weight_orderr(xvalueyvalueprob colorstatealfarprime angle_theta xvalue_text yvalue_text zvalue_text element_text element_anglearr~rrr`offsetrs9 rnplot_state_qspherer"s`$()  C ..C { !LMM{{388,GW z jjj) mmo   !  ,B AaC1H$ 7BGGtS!GGtS!GGtS!GGLLLLacL"rww()) y) Aq255y"%A Aruub!A BFF1I&A BFF1I&A $bffQi0AOO 1aAS\\,-Gs^_ HH01HH01HH01HHMM01HHMM01HHMM01MM"MM"MM"W]]1%)2r2 3<% AsFOE++e$++-ChhuSz*QY61ruu9EFvvcFl+Hu$EA1c6]a&***3/ s+fq1,&0F&;#/8 v*ruuqy9 1$0C(CDQUNq1u_<;NQR;R+REEEMQY9L-LMEVQY/"&&-?VQY/"&&-?wwrvveAha @A4|)%(3 S=">"NK"(266++>">"NK"(266++>">K#,w#6#DL()+%();ruuqy)IbeeVWi(X &(c-#2E2Mc1RRZ,[[L,4]A,N,V,VW[]c,dM(c-,BBLGG###$##HHH$.$.!wwt}r1 KKK#%"$  a S#X A, BJBEE 3?K!Oa'GGA1H%u %u %1a1CP ' GG / /   W3Z A GGAJE __Q F //"QRV* %CGGE&Q!. !a%1*1EEdGSNN6&#WQ?@ F=DHHQ6!9(hacHdHH6!9(hac HH 66!9(hac HH F1I8xbd HH F7F1I8xbd "3' {{8$$rcSSKJn [R"/SQ5n[R"UR UR -5n SX4SX4SX%44H_upn U S[R [R 4n U S[R [R 4n XUSU 4--U SU 4'Ma U RSU R SS-5n /n [U5[U5:XaUHnU RU/S-5 M OC[URU55n [U 5[U5:aU S[U5--n [U 5n[X5$) aGenerates shaded facecolors for shaded bars. This is here to work around a Matplotlib bug where alpha does not work in Bar3D. Args: x (array_like): The x- coordinates of the anchor point of the bars. y (array_like): The y- coordinates of the anchor point of the bars. z (array_like): The z- coordinates of the anchor point of the bars. dx (array_like): Width of bars. dy (array_like): Depth of bars. dz (array_like): Height of bars. color (array_like): sequence of valid color specifications, optional Returns: list: Shaded colors for bars. Raises: MissingOptionalLibraryError: If matplotlib is not installed rN))rrrrrrrrrrrr)rrrrrrr:rrr)rrrr)rrr:r)rrrr)rrr:rrr.)r)rrr2arrayemptyr=newaxisreshaperextendrr_generate_normals _shade_colors)rfrgrrrrrkrcuboidpolysrapdp facecolorscnormalss rnrrDsH(( XX+ -F` HHQWWv||+ ,EZ!QaZ8b c2::rzz) * RZZ+ ,Q//c1f 9 MM%%++ab/1 2EJ 5zSVA   qcAg &'//67 z?SV # !c!f* $J&G  --rc6[U[R5(aHURSnSUS-SU-S-pCnUSUSS24USUSS24- nUSUSS24USUSS24- nO[R"[ U5S45n[R"[ U5S45n[ U5HLupx[ U5nSUS-SU-S-pCnXSS24XSS24- XWSS24'XSS24XSS24- XgSS24'MN [R"XV5$)a Takes a list of polygons and return an array of their normals. Normals point towards the viewer for a face with its vertices in counterclockwise order, following the right hand rule. Uses three points equally spaced around the polygon. This normal of course might not make sense for polygons with more than three points not lying in a plane, but it's a plausible and fast approximation. Args: polygons (list): list of (M_i, 3) array_like, or (..., M, 3) array_like A sequence of polygons to compute normals for, which can have varying numbers of vertices. If the polygons all have the same number of vertices and array is passed, then the operation will be vectorized. Returns: normals: (..., 3) array_like A normal vector estimated for the polygon. r>rrr.N)rr2ndarrayr=rrr"cross) polygonsri1i2i3v1v2poly_ipss rnrrs&((BJJ'' NN2 QA  c2qj !HS"aZ$8 8 c2qj !HS"aZ$8 8XXs8}a( ) XXs8}a( )#H-JFBAAFAEQJBB1uIq5 1BqyM1uIq5 1BqyM . 88B rc SSKJnJn SSKJn UcU"SSS9nSn[R "UVs/sHHov"U5(a)[R "Xv"U5- UR5O[RPMJ sn5n[R"U5)n U R5(ayU"[X5[X55n [X5X)'URU5nUSS2S4n S U "U5SS2[R4S --U-n XSS2S4'U $[R"U5R!5n U $s snf) zv Shade *color* using normal vectors given by *normals*. *color* can also be an array of the same length as *normals*. r) Normalize LightSourceNg -x3@)azdegaltdegc^[R"USS-USS--USS--5$)Nrrr)r2rF)r~s rnmod_shade_colors..mods3wwqtqy1Q419,qtqy899rrr#)rrrrr2rrl directionnanisnanrrr5rr asanyarrayr) rkr lightsourcerrrrrshademasknormrrs rnrrs0 9'!G< : HHRYZRYQc!ffCF K11 2"&& HRYZ E HHUO D xxzzU[)3u{+;<5;'e %%e,ad U ArzzM2S88EAq!t  Mu%**, M# [sAErTdims conventionreturnc Uc#[UR55S1:XaSnOSnSnSnU(a"SnURR5nSUS3nURn[ UR 55S:H=(a [UR55S1:HnUS :XaU(a[ UR40UD6n O[UR4S S0UD6n XI-U-$) aReturn a Latex representation of a state. Wrapper function for `qiskit.visualization.array_to_latex` for convention 'vector'. Adds dims if necessary. Intended for use within `state_drawer`. Args: state: State to be drawn dims (bool): Whether to display the state's `dims` convention (str): Either 'vector' or 'ket'. For 'ket' plot the state in the ket-notation. Otherwise plot as a vector **args: Arguments to be passed directly to `array_to_latex` for convention 'ket' Returns: Latex representation of the state MissingOptionalLibrary: If SymPy isn't installed and ``'latex'`` or ``'latex_source'`` is selected for ``output``. rFTz\begin{align} z\\ \text{dims=z } \end{align}rketsource) setr _op_shapedims_lrdims_r_state_to_latex_ket_datar) rTrrargsprefixsuffixdims_stroperator_shapeis_qubit_statevector latex_strs rnstate_to_latexrs* | uzz|  #DD F F #??))+&xj0BC__N~44671<d^EZEZE\A]bcadAdU3' >[U5SSRT5$)Nr)r;r<)rarZs rnket_name%_state_to_latex_ket..ket_nameAs1vabz$$rrNrrrz + \ldots z |z\rangle) rr/r1rr2aroundwheretolistrr") r4rrrrnonzero_indices latex_termsrrket_idxrrrZs @rnrr0s diiD " #C% 99T $Dhhtqy)!,335O ?h& Oh!m ,s 2_YRS^VWEWEY5Z Z .d.CXN )-A &-d.CXN I!/2  ?  &I#D7#C 6C51 1I 3  rc.\rSrSrSrSSjrSrSrSrg) TextMatrixiZzaText representation of an array, with `__str__` method so it displays nicely in Jupyter notebooksNcpXlX lUc[U[[45(a[ UR 55S1:Xd[U[5(av[UR55[UR55:XaB[ UR55[ UR55s=:XaS1:XaO OSnOSnX0lX@l XPl [U[5(aX lg[U[5(a[U5S-UlgUSUlg)NrFTr)rTrrrr rrrr input_dims output_dimsrrrr)selfrTrrrrs rn__init__TextMatrix.__init__^s  <5; ">??C DUZ[Y\D\5(++((*+s53D3D3F/GG((*+s53D3D3F/GNA3N   h $ $$M } - - MQ.DM$QKDMrcJURn[R"URRUR USS9nSnUR (aUS- nUS[UR 5-- n[UR[[45(a+USURRR53- nOAUSURR5S3- nUS URR53- nUR U-U-UR-$) N,)r threshold separatorrz,  zdims=z input_dims=z, z output_dims=)rr2 array2stringrTrrrrrrr rrrrr)rrr4dimstrs rn__str__TextMatrix.__str__vsMM  JJ  T[[IQT  99 EMD cC ,, ,F$**{M&BCCE$**"6"6"="="?!@AAK (=(=(?'@CCL)?)?)A(BCC{{T!F*T[[88rc"UR5$N)r)rs rn__repr__TextMatrix.__repr__s||~r)rrrrTr)rNrr) __name__ __module__ __qualname____firstlineno____doc__rrr__static_attributes__rrrnrrZs,(09"rrc [R"5nSnUcU(aURSS5nUnUR5n[[ [ [[[[S.nUS:Xa=[RRS5 SSKJn USnU"S U"U40UD6S 35$US:XaUR!5$XQnU"U40UD6$!["a+n[%S US ['U5R(S 35UeSnAff=f) aReturns a visualization of the state. **repr**: ASCII TextMatrix 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. **qsphere**: Matplotlib figure, rendering of statevector using `plot_state_qsphere()`. **hinton**: Matplotlib figure, rendering of statevector using `plot_state_hinton()`. **bloch**: Matplotlib figure, rendering of statevector using `plot_bloch_multivector()`. **city**: Matplotlib figure, rendering of statevector using `plot_state_city()`. **paulivec**: Matplotlib figure, rendering of statevector using `plot_state_paulivec()`. Args: output (str): Select the output method to use for drawing the circuit. Valid choices are ``text``, ``latex``, ``latex_source``, ``qsphere``, ``hinton``, ``bloch``, ``city`` or ``paulivec``. Default is `'text`'. drawer_args: Arguments to be passed to the relevant drawer. For 'latex' and 'latex_source' see ``array_to_latex`` Returns: :class:`matplotlib.figure` or :class:`str` or :class:`TextMatrix` or :class:`IPython.display.Latex`: Drawing of the state. Raises: MissingOptionalLibraryError: when `output` is `latex` and IPython is not installed. or if SymPy isn't installed and ``'latex'`` or ``'latex_source'`` is selected for ``output``. ValueError: when `output` is not a valid selection. reprN state_drawer)rq latex_sourceqspherehintonrucitypauliveclatexr)Latexrz$$'z$' is not a valid option for drawing z objects. Please choose from: 'text', 'latex', 'latex_source', 'qsphere', 'hinton', 'bloch', 'city' or 'paulivec'.)r get_configgetlowerrrrrorrr  _optionals HAS_IPYTHON require_nowIPython.displayrrKeyErrorrtyper ) rToutput drawer_argsconfigdefault_outputdrawersr draw_funcerrs rnrrsR # # %FN ~ #ZZ?N \\^F&%#''G**>:)N+ r)E9[9:"=>> ~~ O .+.. &=d5k>R>R=ST+ .   s C D&DDc V[U5nURnUc [S5e[/SQ5n/n[ U5HnUS:a^[R "[ R"SUS- 4[S9[ R"SUS- 4[S95RXSSS9nOUnUR5Vs/sHKn[ R"[ R"[ R"XqR555PMM nnURU5 M U$s snf)zReturn list of Bloch vectors for each qubit Args: state (DensityMatrix or Statevector): an N-qubit state. Returns: list: list of Bloch vectors (x, y, z) for each qubit. Raises: VisualizationError: if input is not an N-qubit state. r)XYZrr)dtypeT)qubit)r r.rr r:from_symplecticr2rboolinsert matrix_iterr6tracerlr4r) rTrYrZ pauli_singlesrrapaulismat bloch_states rnrrs  C ..C { !LMMo.MJ 3Z 7..!cAgt4bhhC!G~UY6ZfQTf2 #FKQK]K]K_`K_CrwwrxxsHH(=>?K_ `+& as;AD&c[R"[U55nURc [ S5eUR R 5[R"URSUR--54$)zReturn paulivec data for plotting. Args: state (DensityMatrix or Statevector): an N-qubit state. Returns: tuple: (labels, values) for Pauli vector. Raises: VisualizationError: if input is not an N-qubit state. rr) r from_operatorr r.rr7 to_labelsr2r6coeffs)rTrYs rnrrsb  % %mE&: ;C ~~ !LMM ::   !2773::3>>8I+I#J JJr)rNNN)rNN cartesianN)rN)rNNrNN)NNTFFr)Nr)r)rBrr)rOs  >;MB020-* **Q%]aQ%+Q%h **NRA+AH ** o%  o%+o%d **    y%y%+y%x **t%X\t%+t%n b*! ** ''   ]%]%(+]%@  **[.+[.|%P!JTY*' m+ ,*'48*'MP*'*'ZT']c4PS9*PR' w-'#&'58'IL''T..bOd<Kr