LieTrotter
class LieTrotter(reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None)
Bases: qiskit.synthesis.evolution.product_formula.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:
In this implementation, the operators are provided as sum terms of a Pauli operator. For example, we approximate
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
Parameters
- 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
LieTrotter.synthesize(evolution)
Synthesize an qiskit.circuit.library.PauliEvolutionGate.
Parameters
evolution (PauliEvolutionGate) – The evolution gate to synthesize.
Returns
A circuit implementing the evolution.
Return type
Attributes
settings
Return the settings in a dictionary, which can be used to reconstruct the object.
Return type
Dict[str, Any]
Returns
A dictionary containing the settings of this product formula.
Raises
NotImplementedError – If a custom atomic evolution is set, which cannot be serialized.