qiskit.synthesis.LieTrotter(reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None)
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
: 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) : N. Hatano and M. Suzuki, “Finding Exponential Product Formulas of Higher Orders” (2005). arXiv:math-ph/0506007 (opens in a new tab)
- reps (int (opens in a new tab)) – The number of time steps.
- insert_barriers (bool (opens in a new tab)) – Whether to insert barriers between the atomic evolutions.
- cx_structure (str (opens in a new tab)) – 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 (opens in a new tab)[[Pauli |SparsePauliOp, float (opens in a new tab)], 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.
Return the settings in a dictionary, which can be used to reconstruct the object.
A dictionary containing the settings of this product formula.
NotImplementedError (opens in a new tab) – If a custom atomic evolution is set, which cannot be serialized.
evolution (PauliEvolutionGate) – The evolution gate to synthesize.
A circuit implementing the evolution.