z iKSrSSKJr SSKrSSKJr SSKrSSKJ r SSK J r J r J r Jr SSKJr SSKJr S S KJrJr "S S \5r"S S\5rg)z=Piecewise polynomial Chebyshev approximation to a given f(x).) annotationsN)Callable) Chebyshev)QuantumCircuitQuantumRegisterAncillaRegisterGate)BlueprintCircuit) CircuitError)!PiecewisePolynomialPauliRotations%PiecewisePolynomialPauliRotationsGatec^\rSrSrSrSSU4SjjjrSSSjjr\SSj5r\RSSj5r\SSj5r \ RSSj5r \SS j5r \ RSS j5r \SS j5r \ RSS j5r \SS j5r \ RSSj5r SSjrU4SjrSrU=r$)PiecewiseChebyshevaPiecewise Chebyshev approximation to an input function. For a given function :math:`f(x)` and degree :math:`d`, this class implements a piecewise polynomial Chebyshev approximation on :math:`n` qubits to :math:`f(x)` on the given intervals. All the polynomials in the approximation are of degree :math:`d`. The values of the parameters are calculated according to [1] and see [2] for a more detailed explanation of the circuit construction and how it acts on the qubits. Examples: .. plot:: :alt: Circuit diagram output by the previous code. :include-source: import numpy as np from qiskit import QuantumCircuit from qiskit.circuit.library.arithmetic.piecewise_chebyshev import PiecewiseChebyshev f_x, degree, breakpoints, num_state_qubits = lambda x: np.arcsin(1 / x), 2, [2, 4], 2 pw_approximation = PiecewiseChebyshev(f_x, degree, breakpoints, num_state_qubits) pw_approximation._build() qc = QuantumCircuit(pw_approximation.num_qubits) qc.h(list(range(num_state_qubits))) qc.append(pw_approximation.to_instruction(), qc.qubits) qc.draw(output='mpl') References: [1] Haener, T., Roetteler, M., & Svore, K. M. (2018). Optimizing Quantum Circuits for Arithmetic. `arXiv:1805.12445 `_ [2] Carrera Vazquez, A., Hiptmair, H., & Woerner, S. (2022). Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation. `ACM Transactions on Quantum Computing 3, 1, Article 2 `_ c>[TU]US9 SUlXlUbUOSUlUbUOS/UlSUlX@lg)a Args: f_x: the function to be approximated. Constant functions should be specified as f_x = constant. degree: the degree of the polynomials. Defaults to ``1``. breakpoints: the breakpoints to define the piecewise-linear function. Defaults to the full interval. num_state_qubits: number of qubits representing the state. name: The name of the circuit object. nameNr r)super__init___num_state_qubits_f_x_degree _breakpoints _polynomialsnum_state_qubits)selff_xdegree breakpointsrr __class__s o/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/arithmetic/piecewise_chebyshev.pyrPiecewiseChebyshev.__init__EsS& d#"& !'!3v +6+BK6: 0cSnURcSnU(a [S5eURcSnU(a [S5eURcSnU(a [S5eURcSnU(a [S5eUR URS-:a%SnU(a[ SURS-S 35eU$) z,Check if the current configuration is valid.TFz1The function to be approximated has not been set.z/The degree of the polynomials has not been set.z"The breakpoints have not been set.z&The number of qubits has not been set.r z0Not enough qubits in the circuit, need at least .)rAttributeErrorrrr num_qubitsr )rraise_on_failurevalids r"_check_configuration'PiecewiseChebyshev._check_configurationfs 99 E$%XYY << E$%VWW    $E$%IJJ  (E$%MNN ??T22Q6 6E"F,,q014  r$cUR$)zPThe function to be approximated. Returns: The function to be approximated. )rrs r"rPiecewiseChebyshev.f_xsyyr$cURbXR:wa2UR5 XlURUR5 gg)zSet the function to be approximated. Note that this may change the underlying quantum register, if the number of state qubits changes. Args: f_x: The new function to be approximated. N)r _invalidate_reset_registersr)rrs r"rr/sA 99 yy 0    I  ! !$"7"7 8 !1r$cUR$)zLThe degree of the polynomials. Returns: The degree of the polynomials. )rr.s r"rPiecewiseChebyshev.degrees||r$cURbXR:wa2UR5 XlURUR5 gg)zSet the error tolerance. Note that this may change the underlying quantum register, if the number of state qubits changes. Args: degree: The new degree. N)rr1r2r)rrs r"rr4sA << 6\\#9    !L  ! !$"7"7 8 $:r$cURnURb,SUR-nUSU:aX/-nUSS:aS/U-nU$)zpThe breakpoints for the piecewise approximation. Returns: The breakpoints for the piecewise approximation. r)rr)rr num_statess r"r PiecewiseChebyshev.breakpointsse''   ,D111J2+)L8 1~! cK/ r$cURbXR:wa9UR5 UbUOS/UlURUR5 gg)zSet the breakpoints for the piecewise approximation. Note that this may change the underlying quantum register, if the number of state qubits changes. Args: breakpoints: The new breakpoints for the piecewise approximation. Nr)rr1r2r)rr s r"r r:sR    $ 7H7H(H    /:/F QCD   ! !$"7"7 8 )Ir$c URc//$URnUS/:XaSSUR-/n[U5n/n[SUS- 5Hn[ UR [ [45(aURUR /5 MG[R"UR URXXS-/S9nSUR[RRS9R -nURUR#55 M US SUR-:aUS[R,"S5-//-nUSS:aS[R,"S5-//U-nU$![$a;n['SUR R(R*S-S-S -5UeSnAff=f) The polynomials for the piecewise approximation. Returns: The polynomials for the piecewise approximation. Raises: TypeError: If the input function is not in the correct format. Nrr7r domainkind5 () missing 1 required positional argument: ''.< Constant functions should be specified as 'f_x = constant'.r8)rrlenrange isinstancerfloatintappendr interpolaterconvertnp polynomial Polynomialcoeftolist ValueError TypeError__code__ co_varnamesarcsin)rr num_intervals polynomialsipolyerrs r"rXPiecewiseChebyshev.polynomialss  (4K '' 1# a!6!667KK(  q-!+,A dhh 55&&z2$00$++{~{WXSXGY6ZDt||1I1I|JOOOD&&t{{}5-0 r?Q 5 55 5%!biil*:);(<A  ! ,-.UR(ag[TU] 5 [R"5 [R "S[ SS9 [URURURURS9nSSS5 URWR5UR5 g!,(df  N9=f)znBuild the circuit if not already build. The operation is considered successful when q_objective is :math:`|1>`Nignoreqiskit)categorymoduler) _is_builtr_buildwarningscatch_warningsfilterwarningsDeprecationWarningr rr rXrrJto_gatequbits)rpoly_rr!s r"rqPiecewiseChebyshev._buildVs >>   $ $ &  # #H7IRZ [6%%t'7'79I9IPTPYPYF' FNN$dkk2' &s AB99 C)rrrrrr rrd)NNNpw_cheb) rfloat | Callable[[int], float]r int | Noner list[int] | Nonerr|rstrreturnNone)T)r)boolrr)rr{)rz%float | Callable[[int], float] | Nonerr)rrI)rr|rr)rz list[int])r r}rr)rzlist[list[float]])rXzlist[list[float]] | Nonerr)rr|rr)__name__ __module__ __qualname____firstlineno____doc__rr+propertyrsetterrr rXrr2rq__static_attributes__ __classcell__r!s@r"rrsT#P"(,'+ 1 +11& 1 % 1  1 11B D ZZ 9 9 ]] 9 9, 9 977r 9 9&&44& .33r$rc\^\rSrSrSrSSU4SjjjrSrSrSrU=r $) PiecewiseChebyshevGateiiaPiecewise Chebyshev approximation to an input function. For a given function :math:`f(x)` and degree :math:`d`, this class implements a piecewise polynomial Chebyshev approximation on :math:`n` qubits to :math:`f(x)` on the given intervals. All the polynomials in the approximation are of degree :math:`d`. The values of the parameters are calculated according to [1] and see [2] for a more detailed explanation of the circuit construction and how it acts on the qubits. Examples: .. plot:: :alt: Example of generating a circuit with the piecewise Chebyshev gate. :include-source: import numpy as np from qiskit import QuantumCircuit from qiskit.circuit.library.arithmetic import PiecewiseChebyshevGate f_x, num_state_qubits, degree, breakpoints = lambda x: np.arcsin(1 / x), 2, 2, [2, 4] pw_approximation = PiecewiseChebyshevGate(f_x, num_state_qubits, degree, breakpoints) qc = QuantumCircuit(pw_approximation.num_qubits) qc.h(list(range(num_state_qubits))) qc.append(pw_approximation, qc.qubits) qc.draw(output="mpl") References: [1] Haener, T., Roetteler, M., & Svore, K. M. (2018). Optimizing Quantum Circuits for Arithmetic. `arXiv:1805.12445 `_ [2] Carrera Vazquez, A., Hiptmair, H., & Woerner, S. (2022). Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation. `ACM Transactions on Quantum Computing 3, 1, Article 2 `_ c>XlUbUOSUlX lUcS/nSU-nUSU:aXF/-nUSS:aS/U-nX@l[ [ U5S:5n[ TU]SX'-S-/U5 UR5Ul g)a Args: f_x: the function to be approximated. Constant functions should be specified as f_x = constant. num_state_qubits: number of qubits representing the state. degree: the degree of the polynomials. Defaults to ``1``. breakpoints: the breakpoints to define the piecewise-linear function. Defaults to the full interval. label: A label for the gate. Nr rr7r8r) rrrr rIrErr_build_polynomialsrX) rrrrr labelr9 num_comparer!s r"rPiecewiseChebyshevGate.__init__s( & 2f 0  #K(( r?Z '% 4K q>A # +K&#k*Q./  -/?/MPQ/QSUW\] 224r$c dURnURS- nUS/:XaSSU-/n[U5n/n[SUS- 5Hn[ UR [ [45(aURUR /5 MG[R"UR URXXS-/S9nSUR[RRS9R -nURUR#55 M US SU-:aUS[R,"S5-//-nUSS:aS[R,"S5-//U-nU$![$a;n['SUR R(R*S-S-S-5UeS nAff=f) r=r rr7r>r@rBrCrDNr8)r r(rErFrGrrHrIrJrrKrrLrMrNrOrPrQrRrSrTrUrV)rr rrWrXrYrZr[s r"r)PiecewiseChebyshevGate._build_polynomialss&&  ??Q. 1# a!112KK(  q-!+,A dhh 55&&z2$00$++{~{WXSXGY6ZDt||1I1I|JOOOD&&t{{}5-0 r?Q 00 0%!biil*:);(<A  ! ,-.rsID"0QQD2 G3)G3T S?TS?r$