gdZddlmZddlmZddlZddlmZddl m Z ddl m Z ddl mZmZerdd lmZGd d eZd Zd ZdS)z0A gate to implement time-evolution of operators.) annotations) TYPE_CHECKINGN)Gate)ParameterValueType)ParameterExpression)Pauli SparsePauliOp)EvolutionSynthesiscxeZdZdZ ddfd ZeddZejddZdZdfd Z xZ S)PauliEvolutionGateu$Time-evolution of an operator consisting of Paulis. For an operator :math:`H` consisting of Pauli terms and (real) evolution time :math:`t` this gate implements .. math:: U(t) = e^{-itH}. This gate serves as a high-level definition of the evolution and can be synthesized into a circuit using different algorithms. The evolution gates are related to the Pauli rotation gates by a factor of 2. For example the time evolution of the Pauli :math:`X` operator is connected to the Pauli :math:`X` rotation :math:`R_X` by .. math:: U(t) = e^{-itX} = R_X(2t). **Examples:** .. code-block:: python from qiskit.circuit import QuantumCircuit from qiskit.circuit.library import PauliEvolutionGate from qiskit.quantum_info import SparsePauliOp X = SparsePauliOp("X") Z = SparsePauliOp("Z") I = SparsePauliOp("I") # build the evolution gate operator = (Z ^ Z) - 0.1 * (X ^ I) evo = PauliEvolutionGate(operator, time=0.2) # plug it into a circuit circuit = QuantumCircuit(2) circuit.append(evo, range(2)) print(circuit.draw()) The above will print (note that the ``-0.1`` coefficient is not printed!):: ┌──────────────────────────┐ q_0: ┤0 ├ │ exp(-it (ZZ + XI))(0.2) │ q_1: ┤1 ├ └──────────────────────────┘ **References:** [1] G. Li et al. Paulihedral: A Generalized Block-Wise Compiler Optimization Framework For Quantum Simulation Kernels (2021). [`arXiv:2109.03371 `_] ?Noperator3Pauli | SparsePauliOp | list[Pauli | SparsePauliOp]timerlabel str | None synthesisEvolutionSynthesis | NonereturnNonecjt|tr d|D}nt|}|t|}t|tr |djn|j}t d||g|||_|ddlm }|}||_ dS)a: Args: operator (Pauli | SparsePauliOp | list): The operator to evolve. Can also be provided as list of non-commuting operators where the elements are sums of commuting operators. For example: ``[XY + YX, ZZ + ZI + IZ, YY]``. time: The evolution time. label: A label for the gate to display in visualizations. Per default, the label is set to ``exp(-it )`` where ```` is the sum of the Paulis. Note that the label does not include any coefficients of the Paulis. See the class docstring for an example. synthesis: A synthesis strategy. If None, the default synthesis is the Lie-Trotter product formula with a single repetition. c,g|]}t|S)_to_sparse_pauli_op.0ops \/granary/edev/quantum/lib/python3.11/site-packages/qiskit/circuit/library/pauli_evolution.py z/PauliEvolutionGate.__init__..ms!CCCB+B//CCCNrPauliEvolution)name num_qubitsparamsr) LieTrotter) isinstancelistr_get_default_labelr#super__init__rqiskit.synthesis.evolutionr%r)selfrrrrr#r% __class__s rr*zPauliEvolutionGate.__init__Ws* h % % 5CC(CCCHH*844H =&x00E/9(D/I/IbXa[++xOb  .:tf\abbb    = = = = = =" I"r c|jdS)zvReturn the evolution time as stored in the gate parameters. Returns: The evolution time. rr$r,s rrzPauliEvolutionGate.times{1~r c|g|_dS)zUSet the evolution time. Args: time: The evolution time. Nr/)r,rs rrzPauliEvolutionGate.timesf r cD|j||_dS)z4Unroll, where the default synthesis is matrix based.N)r synthesize definitionr0s r_definezPauliEvolutionGate._defines.33D99r parameterct|trt|}t|S)zz&_to_sparse_pauli_op..s- S Se:e0 1 1 S S S S S Sr z?Operator contains ParameterExpression, which are not supported.) r&rr ValueErrortypeanynp iscomplexcoeffs)r sparse_paulis rrrs(E""X$X.. Hm , ,X VT(^^VVVWWW 2< + , ,--][\\\ S S|?R S S SSS\Z[[[ r c*t|trdd|Dd}nlt|jdkr$d|jdd}n0dd|jd}|S) Nz exp(-it (cfg|].}d|j/S) + )joinpaulis to_labelsrs rrz&_get_default_label..s2RRR2UZZ (;(;(=(=>>RRRr z))zexp(-it r)rP)r&r'lenrRrSrQ)rrs rr(r(s(D!!LVRRRRRVVV x  1 $ $@x88::1=@@@EEL 8?+D+D+F+F G GKKKE Lr )r> __future__rtypingrnumpyrJqiskit.circuit.gaterqiskit.circuit.quantumcircuitr"qiskit.circuit.parameterexpressionrqiskit.quantum_inforr r+r r rr(rr rr^s76"""""" $$$$$$<<<<<<BBBBBB44444444>======~5~5~5~5~5~5~5~5B$     r