gZ+dZddlmZddlmZddlmZmZddlm Z ddl m Z ddl m Z ddlmZmZdd lmZGd d e ZGd d e ZdS)zRotation around the Z axis.) annotations)exp)OptionalUnion)Gate)ControlledGate)QuantumRegister)ParameterValueTypeParameterExpression) StandardGatec|eZdZdZejZ dddddfd Zd Z ddfd Z d d!dZ d"dZ d d#dZ dZ xZS)$RZGateuSingle-qubit rotation about the Z axis. This is a diagonal gate. It can be implemented virtually in hardware via framechanges (i.e. at zero error and duration). Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.rz` method. **Circuit symbol:** .. code-block:: text ┌───────┐ q_0: ┤ Rz(φ) ├ └───────┘ **Matrix Representation:** .. math:: RZ(\phi) = \exp\left(-i\frac{\phi}{2}Z\right) = \begin{pmatrix} e^{-i\frac{\phi}{2}} & 0 \\ 0 & e^{i\frac{\phi}{2}} \end{pmatrix} .. seealso:: :class:`~qiskit.circuit.library.standard_gates.U1Gate` This gate is equivalent to U1 up to a phase factor. .. math:: U1(\theta=\phi) = e^{i{\phi}/2}RZ(\phi) Reference for virtual Z gate implementation: `1612.00858 `_ Ndt)durationunitphir label Optional[str]cXtdd|g|||dS)zCreate new RZ gate.rz)rrrN)super__init__)selfrrrr __class__s ^/granary/edev/quantum/lib/python3.11/site-packages/qiskit/circuit/library/standard_gates/rz.pyrzRZGate.__init__Ds2 q3%uxdSSSSScddlm}ddlm}t dd}|jd}|||j| dz }|||dggfg}|D]\}}} |||| ||_dS) z/ gate rz(phi) a { u1(phi) a; } rQuantumCircuitr)U1Gateq)name global_phaseN) qiskit.circuit.quantumcircuitr u1r!r paramsr$_append definition) rr r!r"thetaqcrulesinstrqargscargss r_definezRZGate._defineJs A@@@@@ As # # A ^ADIUFQJ G G G&--!A$,-#( , , E5% JJueU + + + +rrnum_ctrl_qubitsint str | None ctrl_statestr | int | None annotated bool | Nonec|s5|dkr/t|jd||}|j|j_nE|t d|jD}t ||||}|S)aReturn a (multi-)controlled-RZ gate. Args: num_ctrl_qubits: number of control qubits. label: An optional label for the gate [Default: ``None``] ctrl_state: control state expressed as integer, string (e.g.``'110'``), or ``None``. If ``None``, use all 1s. annotated: indicates whether the controlled gate should be implemented as an annotated gate. If ``None``, this is set to ``True`` if the gate contains free parameters and more than one control qubit, in which case it cannot yet be synthesized. Otherwise it is set to ``False``. Returns: ControlledGate: controlled version of this gate. rr)rr5Nc3@K|]}t|tVdSN) isinstancer ).0ps r z!RZGate.control..ys-XXq 1.A B BXXXXXXr)r2rr5r7)CRZGater(r base_gateanyrcontrol)rr2rr5r7gaters rrCzRZGate.control[s. _114;q>:NNND#':DN  XXDKXXXXX 77?? /%# #D  rFboolc8t|jd S)aReturn inverted RZ gate :math:`RZ(\lambda)^{\dagger} = RZ(-\lambda)` Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.RZGate` with an inverted parameter value. Returns: RZGate: inverse gate. r)rr(rr7s rinversezRZGate.inversest{1~o&&&rcddl}|durtddt|jdz}|t | dgdt |gg|S)z%Return a numpy.array for the RZ gate.rNF9unable to avoid copy while creating an array as requestedy?dtype)numpy ValueErrorfloatr(arrayr)rrLcopynpilam2s r __array__zRZGate.__array__sp 5==XYY YuT[^,,,xx#uf++q)As5zz?;5xIIIrexponentrOc8|j\}t||zSr;)r(r)rrUr7r+s rpowerz RZGate.powers;h&'''rcZt|tr||SdSNF)r<r_compare_parametersrothers r__eq__z RZGate.__eq__s- eV $ $ 3++E22 2urr;)rr rr)rNNN)r2r3rr4r5r6r7r8Fr7rENN)rUrOr7rE)__name__ __module__ __qualname____doc__r r_standard_gaterr1rCrHrTrWr] __classcell__rs@rrrs%%N"(N?CTPT[_TTTTTTTT & ! '+!% &&&&&&&P''''' JJJJ(((((rrc`eZdZdZejZ ddddddfd Zd ZdddZ ddZ dZ xZ S)r@uControlled-RZ gate. This is a diagonal but non-symmetric gate that induces a phase on the state of the target qubit, depending on the control state. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.crz` method. **Circuit symbol:** .. code-block:: text q_0: ────■──── ┌───┴───┐ q_1: ┤ Rz(θ) ├ └───────┘ **Matrix representation:** .. math:: CRZ(\theta)\ q_0, q_1 = I \otimes |0\rangle\langle 0| + RZ(\phi=\theta) \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & e^{-i\frac{\theta}{2}} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\frac{\theta}{2}} \end{pmatrix} .. note:: In Qiskit's convention, higher qubit indices are more significant (little endian convention). In many textbooks, controlled gates are presented with the assumption of more significant qubits as control, which in our case would be q_1. Thus a textbook matrix for this gate will be: .. code-block:: text ┌───────┐ q_0: ┤ Rz(θ) ├ └───┬───┘ q_1: ────■──── .. math:: CRZ(\theta)\ q_1, q_0 = |0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes RZ(\theta) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & e^{-i\frac{\theta}{2}} & 0 \\ 0 & 0 & 0 & e^{i\frac{\theta}{2}} \end{pmatrix} .. seealso:: :class:`~qiskit.circuit.library.standard_gates.CU1Gate`: Due to the global phase difference in the matrix definitions of U1 and RZ, CU1 and CRZ are different gates with a relative phase difference. Nr)rr _base_labelr+r rrr5Optional[Union[str, int]]c |tdd|gd||t|||| dS)zCreate new CRZ gate.crzr#r)r)r2rr5rArrN)rrr)rr+rr5rrrirs rrzCRZGate.__init__sZ   G!U+666  rcddlm}ddlm}t dd}|||j}t |jddz |dggf||d|dggft |jd dz |dggf||d|dggfg}|D]\}}}||||||_ dS) zu gate crz(lambda) a,b { rz(lambda/2) b; cx a,b; rz(-lambda/2) b; cx a,b; } rrr)CXGater#r")r$N) r&r xrnr r$rr(r)r*) rr rnr"r,r-r.r/r0s rr1zCRZGate._defines A@@@@@ As # # ^ADI . . . DKNQ& ' '!A$ 4 VXX!ad|R ( T[^Oa' ( (1Q4&" 5 VXX!ad|R (   $) , , E5% JJueU + + + +rFr7rEcFt|jd |jS)aReturn inverse CRZ gate (i.e. with the negative rotation angle). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.CRZGate` with an inverted parameter value. Returns: CRZGate: inverse gate. r)r5)r@r(r5rGs rrHzCRZGate.inverses! A4?CCCCrc ddl}|durtddt|jdzdz }|jrB|gddt | ddggddddt |gg| S|t | dddggd ddt |dggd g| S) z&Return a numpy.array for the CRZ gate.rNFrJy?r#)rrrr)rrrrrK)rrrr)rrrr)rMrNrOr(r5rPr)rrLrQrMargs rrTzCRZGate.__array__*s 5==XYY Y5Q(((1, ? ;;3t99a3\\\Aq!SQTXXCVW  ;;sd))Q1%|||aCHHa5H,,,W rczt|tr%||o|j|jkSdSrY)r<r@rZr5r[s rr]zCRZGate.__eq__<s= eW % % [++E22Zt%JZ7Z Zurr`)r+r rrr5rjr^r_) rarbrcrdr r@rerr1rHrTr]rfrgs@rr@r@s>>@")N $04           .8 D D D D D$rr@N)rd __future__rcmathrtypingrrqiskit.circuit.gaterqiskit.circuit.controlledgaterqiskit.circuit.quantumregisterr "qiskit.circuit.parameterexpressionr r qiskit._accelerate.circuitr rr@rrr}s"!""""""""""""""$$$$$$888888::::::VVVVVVVV333333IIIIITIIIXYYYYYnYYYYYr