SuzukiTrotter¶
- class SuzukiTrotter(order=2, reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None)[source]¶
Bases:
qiskit.synthesis.evolution.product_formula.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 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.