z i9SrSSKJr SSKrSSKJrJr SSKJ r SSK J r J r "SS \5r "S S \5rS rS rg)zHA class implementing a (piecewise-) linear function on qubit amplitudes.) annotationsN)QuantumCircuitGate)deprecate_func)PiecewiseLinearPauliRotations!PiecewiseLinearPauliRotationsGatec|^\rSrSrSr\"SSSS9S S U4Sjjj5rS SjrS rU=r $) LinearAmplitudeFunctionagA circuit implementing a (piecewise) linear function on qubit amplitudes. An amplitude function :math:`F` of a function :math:`f` is a mapping .. math:: F|x\rangle|0\rangle = \sqrt{1 - \hat{f}(x)} |x\rangle|0\rangle + \sqrt{\hat{f}(x)} |x\rangle|1\rangle. for a function :math:`\hat{f}: \{ 0, ..., 2^n - 1 \} \rightarrow [0, 1]`, where :math:`|x\rangle` is a :math:`n` qubit state. This circuit implements :math:`F` for piecewise linear functions :math:`\hat{f}`. In this case, the mapping :math:`F` can be approximately implemented using a Taylor expansion and linearly controlled Pauli-Y rotations, see [1, 2] for more detail. This approximation uses a ``rescaling_factor`` to determine the accuracy of the Taylor expansion. In general, the function of interest :math:`f` is defined from some interval :math:`[a,b]`, the ``domain`` to :math:`[c,d]`, the ``image``, instead of :math:`\{ 1, ..., N \}` to :math:`[0, 1]`. Using an affine transformation we can rescale :math:`f` to :math:`\hat{f}`: .. math:: \hat{f}(x) = \frac{f(\phi(x)) - c}{d - c} with .. math:: \phi(x) = a + \frac{b - a}{2^n - 1} x. If :math:`f` is a piecewise linear function on :math:`m` intervals :math:`[p_{i-1}, p_i], i \in \{1, ..., m\}` with slopes :math:`\alpha_i` and offsets :math:`\beta_i` it can be written as .. math:: f(x) = \sum_{i=1}^m 1_{[p_{i-1}, p_i]}(x) (\alpha_i x + \beta_i) where :math:`1_{[a, b]}` is an indication function that is 1 if the argument is in the interval :math:`[a, b]` and otherwise 0. The breakpoints :math:`p_i` can be specified by the ``breakpoints`` argument. References: [1] Woerner, S., & Egger, D. J. (2018). Quantum Risk Analysis. `arXiv:1806.06893 `_ [2] Gacon, J., Zoufal, C., & Woerner, S. (2020). Quantum-Enhanced Simulation-Based Optimization. `arXiv:2005.10780 `_ z2.2zIUse the class qiskit.circuit.library.LinearAmplitudeFunctionGate instead.z in Qiskit 3.0)sinceadditional_msgremoval_timelinec >[US5(dU/n[US5(dU/nUcUS/nO+[R"USUS5(d US/U-n[X#U5 [ Xt5 X@lXPlX`lUupUup/n /n/n[U5H=unnUU - X- - SU-S- -nU U/- n XUX- -SU-S- - /- nXU/- nM? [R"[U55n[RS- SU- -[R"[U55-n[[U55HVn[RU-UU-S- X- - UU'UU==[RU-UUU - -S- X- - - ss'MX [XSU-SU-US9n[TU]@"UR"SU06 UR%UR'5UR(5 g) a Args: num_state_qubits: The number of qubits used to encode the variable :math:`x`. slope: The slope of the linear function. Can be a list of slopes if it is a piecewise linear function. offset: The offset of the linear function. Can be a list of offsets if it is a piecewise linear function. domain: The domain of the function as tuple :math:`(x_\min{}, x_\max{})`. image: The image of the function as tuple :math:`(f_\min{}, f_\max{})`. rescaling_factor: The rescaling factor to adjust the accuracy in the Taylor approximation. breakpoints: The breakpoints if the function is piecewise linear. If None, the function is not piecewise. name: Name of the circuit. __len__Nrr)namer)hasattrnpisclose_check_sizes_match_check_sorted_and_in_range_domain_image_rescaling_factor enumeratezeroslenpionesrangersuper__init__qregsappendto_gatequbits)selfnum_state_qubitsslopeoffsetdomainimagerescaling_factor breakpointsrabcdmapped_breakpoints mapped_slope mapped_offsetipointmapped_breakpoint slope_angles offset_anglespwl_pauli_rotation __class__s u/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/arithmetic/linear_amplitude_function.pyr$ LinearAmplitudeFunction.__init__Os3@ui((GEvy))XF  !!9+K::k!nfQi88%aykK7 5+6";7  !1  !+.HAu!&qu 5> &..0$++>cUS- [RS- UR--nUS[R- UR- -nX RSURS- -nX RS- nU$aMap the function value of the approximated :math:`\hat{f}` to :math:`f`. Args: scaled_value: A function value from the Taylor expansion of :math:`\hat{f}(x)`. Returns: The ``scaled_value`` mapped back to the domain of :math:`f`, by first inverting the transformation used for the Taylor approximation and then mapping back from :math:`[0, 1]` to the original domain. g?rrrr)rr rrr) scaled_valuevalues r?post_processing'LinearAmplitudeFunction.post_processingswu$ruuqy43I3I'II RUUT3333 Q$++a.00 Q rA)rrrrNF)r*intr+float | list[float]r,rLr-tuple[float, float]r.rMr/floatr0list[float] | NonerstrreturnNonerErNrQrN) __name__ __module__ __qualname____firstlineno____doc__rr$rG__static_attributes__ __classcell__r>s@r?r r s2hb(#$*.L?L?#L?$ L? $ L? # L? L?(L?L? L?  L?\rAr cl^\rSrSrSrSSU4SjjjrSrS SjrSrU=r $) LinearAmplitudeFunctionGateagA circuit implementing a (piecewise) linear function on qubit amplitudes. An amplitude function :math:`F` of a function :math:`f` is a mapping .. math:: F|x\rangle|0\rangle = \sqrt{1 - \hat{f}(x)} |x\rangle|0\rangle + \sqrt{\hat{f}(x)} |x\rangle|1\rangle. for a function :math:`\hat{f}: \{ 0, ..., 2^n - 1 \} \rightarrow [0, 1]`, where :math:`|x\rangle` is a :math:`n` qubit state. This circuit implements :math:`F` for piecewise linear functions :math:`\hat{f}`. In this case, the mapping :math:`F` can be approximately implemented using a Taylor expansion and linearly controlled Pauli-Y rotations, see [1, 2] for more detail. This approximation uses a ``rescaling_factor`` to determine the accuracy of the Taylor expansion. In general, the function of interest :math:`f` is defined from some interval :math:`[a,b]`, the ``domain`` to :math:`[c,d]`, the ``image``, instead of :math:`\{ 1, ..., N \}` to :math:`[0, 1]`. Using an affine transformation we can rescale :math:`f` to :math:`\hat{f}`: .. math:: \hat{f}(x) = \frac{f(\phi(x)) - c}{d - c} with .. math:: \phi(x) = a + \frac{b - a}{2^n - 1} x. If :math:`f` is a piecewise linear function on :math:`m` intervals :math:`[p_{i-1}, p_i], i \in \{1, ..., m\}` with slopes :math:`\alpha_i` and offsets :math:`\beta_i` it can be written as .. math:: f(x) = \sum_{i=1}^m 1_{[p_{i-1}, p_i]}(x) (\alpha_i x + \beta_i) where :math:`1_{[a, b]}` is an indication function that is 1 if the argument is in the interval :math:`[a, b]` and otherwise 0. The breakpoints :math:`p_i` can be specified by the ``breakpoints`` argument. References: [1] Woerner, S., & Egger, D. J. (2018). Quantum Risk Analysis. `arXiv:1806.06893 `_ [2] Gacon, J., Zoufal, C., & Woerner, S. (2020). Quantum-Enhanced Simulation-Based Optimization. `arXiv:2005.10780 `_ c >[US5(dU/n[US5(dU/nUcUS/nO+[R"USUS5(d US/U-n[X#U5 [ Xt5 X lX0lX@lXPlX`l Xpl [[U5S:5n [T U]9SX-S-/US9 g)a Args: num_state_qubits: The number of qubits used to encode the variable :math:`x`. slope: The slope of the linear function. Can be a list of slopes if it is a piecewise linear function. offset: The offset of the linear function. Can be a list of offsets if it is a piecewise linear function. domain: The domain of the function as tuple :math:`(x_\min{}, x_\max{})`. image: The image of the function as tuple :math:`(f_\min{}, f_\max{})`. rescaling_factor: The rescaling factor to adjust the accuracy in the Taylor approximation. breakpoints: The breakpoints if the function is piecewise linear. If None, the function is not piecewise. label: A label for the gate. rNrr LinFunction)label)rrrrrr+r,r-r.r/r0rKrr#r$) r)r*r+r,r-r.r/r0ra num_comparer>s r?r$$LinearAmplitudeFunctionGate.__init__s4ui((GEvy))XF  !!9+K::k!nfQi88%aykK7 5+6";7    0&#k*Q./  (8(F(JBV[\rAc[[UR5S:5nURU- S- nURup4UR upV/n/n/n [ UR5HNupX- XC- - SU-S- -n X|/- nXRU XC- -SU-S- - /- nXRU /- n MP [R"[UR55n [RS- SUR- -[R"U 5-n[ [X55Hhun unn[RUR-U-S- Xe- - X'X==[RUR-UU- -S- Xe- - - ss'Mj [X'SU -SU-5n[!UR5UlUR"R%UUR"R&5 g)Nrrr)rKrr0 num_qubitsr-r.rr+r,rrr r/ ones_likezipr r definitionr&r()r)rbr*r1r2r3r4r5r6r7r8r9r:r;r<slope_ioffset_ir=s r?_define#LinearAmplitudeFunctionGate._define"s#d../!34 ??[81<{{zz  !$"2"23HA!&qu 5)>%>?",,|B\\ &/L0P&Q "A" eed&;&;;gEIQUSLO  (=(= =A NQR RVWV[ \ \ 'R ? !l2BA DU ));)F)FG 14??3I3IJrAcUS- [RS- UR--nUS[R- UR- -nX RSURS- -nX RS- nU$rC)rr r/r.rDs r?rG+LinearAmplitudeFunctionGate.post_processingFswu$ruuqy43H3H'HH RUUT2222 AA.. A rA)r0rhr-r.r,r/r+rI)r*rKr+rLr,rLr-rMr.rMr/rNr0rOrarPrQrRrS) rTrUrVrWrXr$rkrGrYrZr[s@r?r]r]s4z#$*.1]1]#1]$ 1] $ 1] # 1] 1](1]1] 1]1]f"KHrAr]cUcg[R"[R"U5S:5(d [S5eUSUS:d USUS:a [S5eg)Nrz&Breakpoints must be unique and sorted.rz'Breakpoints must be included in domain.)ralldiff ValueError)r0r-s r?rr\sg 66"''+&* + +ABB1~q ![_vay%@BCC&ArAc[U5n[U5U:wa[SUS[U5S35eUb+[U5U:wa[SUS[U5S35egg)NzSize mismatch of slope (z) and offset (z).z) and breakpoints ()rrs)r+r,r0sizes r?rrhs{ u:D 6{d3D6F }TVWXX { t #*4&0CC DTCUUWX  $rA)rX __future__rnumpyrqiskit.circuitrrqiskit.utils.deprecationr piecewise_linear_pauli_rotationsrr r r]rrrAr?r|sEO"/3 [n[|a$aH DrA