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LieTrotter

qiskit.synthesis.LieTrotter(reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None)GitHub(opens in a new tab)

Bases: 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:

eA+BeAeB.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

eit(XX+ZZ)=eitXXeitZZ+O(t2).e^{-it(XX + ZZ)} = e^{-it XX}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(opens in a new tab) [2]: N. Hatano and M. Suzuki, “Finding Exponential Product Formulas of Higher Orders” (2005). arXiv:math-ph/0506007(opens in a new tab)

Parameters


Attributes

settings

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(opens in a new tab) – If a custom atomic evolution is set, which cannot be serialized.


Methods

synthesize

synthesize(evolution)

Synthesize an qiskit.circuit.library.PauliEvolutionGate.

Parameters

evolution (PauliEvolutionGate) – The evolution gate to synthesize.

Returns

A circuit implementing the evolution.

Return type

QuantumCircuit

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