z inSrSSKJr SSKJr SSKJr SSKJr SSK J r SSK r SS K Jr "S S \5rg) z The Lie-Trotter product formula.) annotations)Callable)Any)QuantumCircuit) SparsePauliOpN) SuzukiTrottercz^\rSrSrSrSSS.S U4Sjjjjr\S Sj5rSrU=r $) LieTrottera+The 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 `_ F)"atomic_evolution_sparse_observablec .>[TU]SUUUUUUUS9 g)aJ 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:`~.quantum_info.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. 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. atomic_evolution_sparse_observable: If a custom ``atomic_evolution`` is passed, which does not yet support :class:`.SparseObservable`\ s as input, set this argument to ``False`` to automatically apply a conversion to :class:`.SparsePauliOp`. This argument is supported until Qiskit 2.2, at which point all atomic evolutions are required to support :class:`.SparseObservable`\ s as input. r)preserve_orderr N)super__init__) selfrepsinsert_barriers cx_structureatomic_evolutionwraprr __class__s `/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/synthesis/evolution/lie_trotter.pyrLieTrotter.__init__5s0N      )/Q  cURb [S5eURURURUR S.$)aReturn 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. zBCannot serialize a product formula with a custom atomic evolution.)rrrr)_atomic_evolutionNotImplementedErrorrr _cx_structure_wrap)rs rsettingsLieTrotter.settingsgsL  ! ! -%T  II#33 ..JJ   r)rFchainNFT)rintrboolrstrrzYCallable[[QuantumCircuit, qiskit.quantum_info.Pauli | SparsePauliOp, float], None] | Nonerr&rr&r r&returnNone)r(zdict[str, Any]) __name__ __module__ __qualname____firstlineno____doc__rpropertyr!__static_attributes__ __classcell__)rs@rr r s8 %# #0 490 0 0  0   0 0 0 -10  0 0 d  rr )r. __future__rcollections.abcrtypingrqiskit.circuit.quantumcircuitrqiskit.quantum_info.operatorsrqiskit.quantum_infoqiskitsuzuki_trotterr r r#rrr:s-'"$87)a a r