LieTrotter

class qiskit.synthesis.LieTrotter(reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None)

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:

\[e^{A + B} \approx e^{A}e^{B}.\]

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

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

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 (Callable[[Pauli | SparsePauliOp, float], QuantumCircuit] | None) -- A function to construct the circuit for the evolution of single Pauli string. Per default, a single Pauli evolution is decomposed in a CX chain and a single qubit Z rotation.

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

Methods

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