hamiltonian_variational_ansatz

class qiskit.circuit.library.hamiltonian_variational_ansatz(hamiltonian, reps=1, insert_barriers=False, name='HVA', parameter_prefix='t')

Bases:

Construct a Hamiltonian variational ansatz.

For a Hamiltonian $H = \sum_{k=1}^K H_k$ where the terms $H_k$ consist of only commuting Paulis, but the terms do not commute among each other $[H_k, H_{k'}] \neq 0$, the Hamiltonian variational ansatz (HVA) is

where the exponentials $exp(-i\theta H_k)$ are implemented exactly [1, 2]. Note that this differs from evolved_operator_ansatz(), where no assumptions on the structure of the operators are done.

The Hamiltonian can be passed as SparsePauliOp, in which case we split the Hamiltonian into commuting terms $\{H_k\}_k$. Note, that this may not be optimal and if the minimal set of commuting terms is known it can be passed as sequence into this function.

Examples

A single operator will be split into commuting terms automatically:

from qiskit.quantum_info import SparsePauliOp
from qiskit.circuit.library import hamiltonian_variational_ansatz
 
# this Hamiltonian will be split into the two terms [ZZI, IZZ] and [IXI]
hamiltonian = SparsePauliOp(["ZZI", "IZZ", "IXI"])
ansatz = hamiltonian_variational_ansatz(hamiltonian, reps=2)
ansatz.draw("mpl")

Alternatively, we can directly provide the terms:

from qiskit.quantum_info import SparsePauliOp
from qiskit.circuit.library import hamiltonian_variational_ansatz
 
zz = SparsePauliOp(["ZZI", "IZZ"])
x = SparsePauliOp(["IXI"])
ansatz = hamiltonian_variational_ansatz([zz, x], reps=2)
ansatz.draw("mpl")

Parameters

• hamiltonian (SparsePauliOp | Sequence[SparsePauliOp]) – The Hamiltonian to evolve. If given as single operator, it will be split into commuting terms. If a sequence of SparsePauliOp, then it is assumed that each element consists of commuting terms, but the elements do not commute among each other.
• reps (int) – The number of times to repeat the evolved operators.
• insert_barriers (bool) – Whether to insert barriers in between each evolution.
• name (str) – The name of the circuit.
• parameter_prefix (str) – Set the names of the circuit parameters. If a string, the same prefix will be used for each parameters. Can also be a list to specify a prefix per operator.

Return type

QuantumCircuit

References

[1] D. Wecker et al. Progress towards practical quantum variational algorithms (2015)

Phys Rev A 92, 042303

[2] R. Wiersema et al. Exploring entanglement and optimization within the Hamiltonian

Variational Ansatz (2020) arXiv:2008.02941