SuzukiTrotter

class qiskit.synthesis.SuzukiTrotter(order=2, reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None)[source]

Bases: 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 (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.

Raises:

ValueError – If order is not even

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)[source]

Synthesize an qiskit.circuit.library.PauliEvolutionGate.

Parameters:

evolution (PauliEvolutionGate) – The evolution gate to synthesize.

Returns:

A circuit implementing the evolution.

Return type:

QuantumCircuit