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# SuzukiTrotter¶

class SuzukiTrotter(order=2, reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None)[source]

Bases: ProductFormula

The (higher order) Suzuki-Trotter product formula.

The Suzuki-Trotter formulas improve the error of the Lie-Trotter approximation. For example, the second order decomposition is

$e^{A + B} \approx e^{B/2} e^{A} e^{B/2}.$

Higher order decompositions are based on recursions, see Ref. [1] for more details.

In this implementation, the operators are provided as sum terms of a Pauli operator. For example, in the second order Suzuki-Trotter decomposition we approximate

$e^{-it(XX + ZZ)} = e^{-it/2 ZZ}e^{-it XX}e^{-it/2 ZZ} + \mathcal{O}(t^3).$

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
• order (int) -- The order of the product formula.

• 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.

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.