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LieTrotter
class qiskit.synthesis.LieTrotter(reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None, wrap=False)
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:
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
Deprecated since version 1.2_pending
The ‘Callable[[Pauli | SparsePauliOp, float], QuantumCircuit]’ signature of the ‘atomic_evolution’ argument is pending deprecation as of qiskit 1.2. It will be marked deprecated in a future release, and then removed no earlier than 3 months after the release date. Instead you should update your ‘atomic_evolution’ function to be of the following type: ‘Callable[[QuantumCircuit, Pauli | SparsePauliOp, float], None]’.
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. This only takes effect whenatomic_evolution is None
. - atomic_evolution (Callable[[Pauli |SparsePauliOp, float], QuantumCircuit] | Callable[[QuantumCircuit, Pauli |SparsePauliOp, float], None] | None) – A function to apply the evolution of a single
Pauli
, orSparsePauliOp
of only commuting terms, to a circuit. The function takes in three arguments: the circuit to append the evolution to, the Pauli operator to evolve, and the evolution time. By default, a single Pauli evolution is decomposed into a chain ofCX
gates and a singleRZ
gate. Alternatively, the function can also take Pauli operator and evolution time as inputs and returns the circuit that will be appended to the overall circuit being built. - wrap (bool) – Whether to wrap the atomic evolutions into custom gate objects. This only takes effect when
atomic_evolution is None
.
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
synthesize(evolution)
Synthesize an qiskit.circuit.library.PauliEvolutionGate
.
Parameters
evolution (PauliEvolutionGate) – The evolution gate to synthesize.
Returns
A circuit implementing the evolution.
Return type
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