# LieTrotter¶

class LieTrotter(reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None)[소스]

기반 클래스: ProductFormula

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:

$e^{A + B} \approx e^{A}e^{B}.$

In this implementation, the operators are provided as sum terms of a Pauli operator. For example, we approximate

$e^{-it(XX + ZZ)} = e^{-it XX}e^{-it ZZ} + \mathcal{O}(t^2).$

참조

[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

매개변수
• reps (int) – The number of time steps.

• insert_barriers (bool) – Whether to insert barriers between the atomic evolutions.

• cx_structure (str) – 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.

• atomic_evolution (Optional[Callable[[Union[Pauli, SparsePauliOp], float], QuantumCircuit]]) – A function to construct the circuit for the evolution of single Pauli string. Per default, a single Pauli evolution is decomopsed in a CX chain and a single qubit Z rotation.

Methods

 synthesize Synthesize an qiskit.circuit.library.PauliEvolutionGate.

Attributes

settings

Return the settings in a dictionary, which can be used to reconstruct the object.

반환 형식

Dict[str, Any]

반환

A dictionary containing the settings of this product formula.

예외 발생

NotImplementedError – If a custom atomic evolution is set, which cannot be serialized.