z iY( FSrSSKJr SSKJr SSKrSSKJr SSK J r SSK J r SSK JrJrJrJrJrJrJrJrJrJrJr SS KJr SS KJr SS KJr SS KJ r \(aSS K!J"r" Sr#S//SQS/SS/SS/S/SS/SS/SS/SS//SQSS/S. r$\\\\\\\\\\\S. r%"SS5r&g)z4 Decompose a single-qubit unitary via Euler angles. ) annotations) TYPE_CHECKINGN)euler_one_qubit_decomposer)QuantumCircuit)Qubit) UGate PhaseGateU3GateU2GateU1GateRXGateRYGateRZGateRGateSXGateXGate) QiskitError)is_unitary_matrix)Gate)Operator) DAGCircuitg-q=u3)ru2u1upsxrrxrrzry)r rx) U3U321UPSXU1XRRZYZZXZXZXXYXZSXXZSX) rrrrrrr!r rrr"c~\rSrSrSrSSSjjrSSjrS\4SSjjrS\4Sjr \ S5r \ RS 5r SS jr SS jr\"\R"5r\"\R&5r\"\R*5r\"\R.5r\"\R25r\"\R65rS rg )OneQubitEulerDecomposerLa A class for decomposing 1-qubit unitaries into Euler angle rotations. The resulting decomposition is parameterized by 3 Euler rotation angle parameters :math:`(\theta, \phi, \lambda)`, and a phase parameter :math:`\gamma`. The value of the parameters for an input unitary depends on the decomposition basis. Allowed bases and the resulting circuits are shown in the following table. Note that for the non-Euler bases (:math:`U3`, :math:`U1X`, :math:`RR`), the :math:`ZYZ` Euler parameters are used. .. list-table:: Supported circuit bases :widths: auto :header-rows: 1 * - Basis - Euler Angle Basis - Decomposition Circuit * - 'ZYZ' - :math:`Z(\phi) Y(\theta) Z(\lambda)` - :math:`e^{i\gamma} R_Z(\phi).R_Y(\theta).R_Z(\lambda)` * - 'ZXZ' - :math:`Z(\phi) X(\theta) Z(\lambda)` - :math:`e^{i\gamma} R_Z(\phi).R_X(\theta).R_Z(\lambda)` * - 'XYX' - :math:`X(\phi) Y(\theta) X(\lambda)` - :math:`e^{i\gamma} R_X(\phi).R_Y(\theta).R_X(\lambda)` * - 'XZX' - :math:`X(\phi) Z(\theta) X(\lambda)` - :math:`e^{i\gamma} R_X(\phi).R_Z(\theta).R_X(\lambda)` * - 'U3' - :math:`Z(\phi) Y(\theta) Z(\lambda)` - :math:`e^{i\gamma} U_3(\theta,\phi,\lambda)` * - 'U321' - :math:`Z(\phi) Y(\theta) Z(\lambda)` - :math:`e^{i\gamma} U_3(\theta,\phi,\lambda)` * - 'U' - :math:`Z(\phi) Y(\theta) Z(\lambda)` - :math:`e^{i\gamma} U_3(\theta,\phi,\lambda)` * - 'PSX' - :math:`Z(\phi) Y(\theta) Z(\lambda)` - :math:`e^{i\gamma} U_1(\phi+\pi).R_X\left(\frac{\pi}{2}\right).` :math:`U_1(\theta+\pi).R_X\left(\frac{\pi}{2}\right).U_1(\lambda)` * - 'ZSX' - :math:`Z(\phi) Y(\theta) Z(\lambda)` - :math:`e^{i\gamma} R_Z(\phi+\pi).\sqrt{X}.` :math:`R_Z(\theta+\pi).\sqrt{X}.R_Z(\lambda)` * - 'ZSXX' - :math:`Z(\phi) Y(\theta) Z(\lambda)` - :math:`e^{i\gamma} R_Z(\phi+\pi).\sqrt{X}.R_Z(\theta+\pi).\sqrt{X}.R_Z(\lambda)` or :math:`e^{i\gamma} R_Z(\phi+\pi).X.R_Z(\lambda)` * - 'U1X' - :math:`Z(\phi) Y(\theta) Z(\lambda)` - :math:`e^{i\gamma} U_1(\phi+\pi).R_X\left(\frac{\pi}{2}\right).` :math:`U_1(\theta+\pi).R_X\left(\frac{\pi}{2}\right).U_1(\lambda)` * - 'RR' - :math:`Z(\phi) Y(\theta) Z(\lambda)` - :math:`e^{i\gamma} R\left(-\pi,\frac{\phi-\lambda+\pi}{2}\right).` :math:`R\left(\theta+\pi,\frac{\pi}{2}-\lambda\right)` .. automethod:: __call__ cXlX lg)aInitialize decomposer Supported bases are: ``'U'``, ``'PSX'``, ``'ZSXX'``, ``'ZSX'``, ``'U321'``, ``'U3'``, ``'U1X'``, ``'RR'``, ``'ZYZ'``, ``'ZXZ'``, ``'XYX'``, ``'XZX'``. Args: basis: the decomposition basis [Default: ``'U3'``] use_dag: If true the output from calls to the decomposer will be a :class:`~qiskit.dagcircuit.DAGCircuit` object instead of :class:`~qiskit.circuit.QuantumCircuit`. Raises: QiskitError: If input basis is not recognized. N)basisuse_dag)selfr3r4s h/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/synthesis/one_qubit/one_qubit_decompose.py__init__ OneQubitEulerDecomposer.__init__s  cf[5/nSn[U5S:a[US[5(aSnSSKJn UR 5nX&lURU5 UHGnU(a[USR"US6nO URnURXS4SS9 MI U$)z6Return the circuit or dag object from a list of gates.FrT) dagcircuit)check) rlen isinstancetupleqiskit.dagcircuitr;r global_phase add_qubitsNAME_MAPnameapply_operation_back) r5gatesrBqr lookup_gater;dag gate_entrygates r6 build_circuit%OneQubitEulerDecomposer.build_circuitsgY u:>jq599K0##%' rJ 1 2 23Z]C!  $ $TqE85 $ A   r9TcZ[US5(aUR5RnO![US5(aUR5n[R "U[ S9nURS:wa [S5e[U5(d [S5eURXUS9$)aDecompose single qubit gate into a circuit. Args: unitary: 1-qubit unitary matrix simplify: reduce gate count in decomposition [Default: True]. atol: absolute tolerance for checking angles when simplifying returned circuit [Default: 1e-12]. Returns: QuantumCircuit: the decomposed single-qubit gate circuit Raises: QiskitError: if input is invalid or synthesis fails. to_operator to_matrixdtype)rTz2OneQubitEulerDecomposer: expected 2x2 input matrixz5OneQubitEulerDecomposer: input matrix is not unitary.)simplifyatol) hasattrrPdatarQnpasarraycomplexshaperr _decompose)r5unitaryrUrVs r6__call__ OneQubitEulerDecomposer.__call__s( 7M * *))+00G Wk * *'')G**WG4 ==F "RS S ))UV VwEEr9c UR(aA[R"XR/SSX#5nUR XDR 5nU$[ R"[R"XR/SSX#5SS9$)NrT) legacy_qubits) r4runitary_to_gate_sequencer3rMrBr_from_circuit_dataunitary_to_circuit)r5r^rUrVcircuit_sequencecircuits r6r]"OneQubitEulerDecomposer._decomposes| <<9RR**q$  (()9;X;XYGN00 & 9 9**q$    r9cUR$)zThe decomposition basis.)_basis)r5s r6r3OneQubitEulerDecomposer.basiss{{r9c VURURURURURURURURURURURUR S. nX;a[ SU35eXlX!Ulg)zSet the decomposition basis.) r$r#r%r&r.r-r'r(r)r*r,r+z+OneQubitEulerDecomposer: unsupported basis N) _params_u3 _params_u1x _params_zyz _params_zxz _params_xyx _params_xzxrrj_params)r5r3 basis_methodss r6r3rksOO//####$$##""########    % KE7ST T $+ r9cd[R"U[S9nURU5up#pEX#U4$)zReturn the Euler angles for input array. Args: unitary: :math:`2\times2` unitary matrix. Returns: tuple: ``(theta, phi, lambda)``. rRrYrZr[rs)r5r^thetaphilam_s r6anglesOneQubitEulerDecomposer.angless1**WG4!\\'2C3r9cV[R"U[S9nURU5$)zReturn the Euler angles and phase for input array. Args: unitary: :math:`2\times2` Returns: tuple: ``(theta, phi, lambda, phase)``. rRrv)r5r^s r6angles_and_phase(OneQubitEulerDecomposer.angles_and_phases#**WG4||G$$r9)rjrsr3r4N)r#F)r3strr4bool)returnQuantumCircuit | DAGCircuit)r^zOperator | Gate | np.ndarrayrUrrVfloatrr)r^z np.ndarrayrr@)__name__ __module__ __qualname____firstlineno____doc__r7rM DEFAULT_ATOLr_r]propertyr3setterr{r~ staticmethodr params_zyzro params_zxzrp params_xyxrq params_xzxrr params_u3rm params_u1xrn__static_attributes__r9r6r0r0Ls<|$0" %F-%F%F %F % %FN,0l   \\,,*  %9DDEK9DDEK9DDEK9DDEK8BBCJ9DDEKr9r0)'r __future__rtypingrnumpyrYqiskit._acceleraterqiskit.circuit.quantumcircuitrqiskit.circuitr%qiskit.circuit.library.standard_gatesrr r r r r rrrrrqiskit.exceptionsr(qiskit.quantum_info.operators.predicatesrqiskit.circuit.gater&qiskit.quantum_info.operators.operatorrrArrONE_QUBIT_EULER_BASIS_GATESrDr0rr9r6rs# 98     *F$;,  &   ; $< % $< $< $< $<  $<             TFTFr9