grdZddlmZddlmZddlmZddlmZddl m Z m Z ddl m Z Gd d e Zd S) z The Lie-Trotter product formula.) annotations)Callable)Any)QuantumCircuit) SparsePauliOpPauli) SuzukiTrottercJeZdZdZ ddfd ZeddZxZS) LieTrotterakThe Lie-Trotter product formula. The Lie-Trotter formula approximates the exponential of two non-commuting operators with products of their exponentials up to a second order error: .. math:: e^{A + B} \approx e^{A}e^{B}. In this implementation, the operators are provided as sum terms of a Pauli operator. For example, we approximate .. math:: e^{-it(XI + ZZ)} = e^{-it XI}e^{-it ZZ} + \mathcal{O}(t^2). References: [1]: D. Berry, G. Ahokas, R. Cleve and B. Sanders, "Efficient quantum algorithms for simulating sparse Hamiltonians" (2006). `arXiv:quant-ph/0508139 `_ [2]: N. Hatano and M. Suzuki, "Finding Exponential Product Formulas of Higher Orders" (2005). `arXiv:math-ph/0506007 `_ r FchainNTrepsintinsert_barriersbool cx_structurestratomic_evolutionCallable[[Pauli | SparsePauliOp, float], QuantumCircuit] | Callable[[QuantumCircuit, Pauli | SparsePauliOp, float], None] | Nonewrappreserve_orderreturnNonec Xtd||||||dS)a Args: reps: The number of time steps. insert_barriers: Whether to insert barriers between the atomic evolutions. cx_structure: How to arrange the CX gates for the Pauli evolutions, can be ``"chain"``, where next neighbor connections are used, or ``"fountain"``, where all qubits are connected to one. This only takes effect when ``atomic_evolution is None``. atomic_evolution: A function to apply the evolution of a single :class:`.Pauli`, or :class:`.SparsePauliOp` of only commuting terms, to a circuit. The function takes in three arguments: the circuit to append the evolution to, the Pauli operator to evolve, and the evolution time. By default, a single Pauli evolution is decomposed into a chain of ``CX`` gates and a single ``RZ`` gate. Alternatively, the function can also take Pauli operator and evolution time as inputs and returns the circuit that will be appended to the overall circuit being built. wrap: Whether to wrap the atomic evolutions into custom gate objects. This only takes effect when ``atomic_evolution is None``. preserve_order: If ``False``, allows reordering the terms of the operator to potentially yield a shallower evolution circuit. Not relevant when synthesizing operator with a single term. r )rN)super__init__)selfrrrrrr __class__s \/granary/edev/quantum/lib/python3.11/site-packages/qiskit/synthesis/evolution/lie_trotter.pyrzLieTrotter.__init__4sFF      )      dict[str, Any]cd|jtd|j|j|j|jdS)a)Return the settings in a dictionary, which can be used to reconstruct the object. Returns: A dictionary containing the settings of this product formula. Raises: NotImplementedError: If a custom atomic evolution is set, which cannot be serialized. NzBCannot serialize a product formula with a custom atomic evolution.)rrrr)_atomic_evolutionNotImplementedErrorrr _cx_structure_wrap)rs rsettingszLieTrotter.settingsasI  ! -%T  I#3 .J    r )r Fr NFT)rrrrrrrrrrrrrr)rr!)__name__ __module__ __qualname____doc__rpropertyr' __classcell__)rs@rr r s8 %# #+ + + + + + + Z   X     r r N)r+ __future__rcollections.abcrtypingrqiskit.circuit.quantumcircuitrqiskit.quantum_info.operatorsrrsuzuki_trotterr r r rr5s'&""""""$$$$$$888888>>>>>>>>))))))\ \ \ \ \ \ \ \ \ \ r