---
title: hamiltonian_variational_ansatz (latest version)
description: API reference for qiskit.circuit.library.hamiltonian_variational_ansatz in the latest version of qiskit
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/qiskit.circuit.library.hamiltonian_variational_ansatz
---

# qiskit.circuit.library.hamiltonian\_variational\_ansatz

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

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/library/n_local/evolved_operator_ansatz.py#L192-L282)

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

$$
\prod_{r=1}^{R} \left( \prod_{k=K}^1 e^{-i\theta_{k, r} H_k} \right)
$$

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

The Hamiltonian can be passed as [`SparsePauliOp`](/docs/api/qiskit/qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.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:

```python
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")
```

![Circuit diagram output by the previous code.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/qiskit-circuit-library-hamiltonian_variational_ansatz-1.avif)

Alternatively, we can directly provide the terms:

```python
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")
```

![Circuit diagram output by the previous code.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/qiskit-circuit-library-hamiltonian_variational_ansatz-2.avif)

**Parameters**

- **hamiltonian** ([*SparsePauliOp*](/docs/api/qiskit/qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.operators.symplectic.sparse_pauli_op.SparsePauliOp")  *|*[*Sequence*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence)*\[*[*SparsePauliOp*](/docs/api/qiskit/qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.operators.symplectic.sparse_pauli_op.SparsePauliOp")*]*) – The Hamiltonian to evolve. If given as single operator, it will be split into commuting terms. If a sequence of [`SparsePauliOp`](/docs/api/qiskit/qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp"), then it is assumed that each element consists of commuting terms, but the elements do not commute among each other.
- **reps** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The number of times to repeat the evolved operators.
- **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – Whether to insert barriers in between each evolution.
- **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – The name of the circuit.
- **parameter\_prefix** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – Set the names of the circuit parameters. If a string, the same prefix will be used for each parameter. Can also be a list to specify a prefix per operator.

**Return type**

[*QuantumCircuit*](/docs/api/qiskit/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")

References:

\[1] D. Wecker et al. Progress towards practical quantum variational algorithms (2015) [Phys Rev A 92, 042303](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.042303)

\[2] R. Wiersema et al. Exploring entanglement and optimization within the Hamiltonian Variational Ansatz (2020) [arXiv:2008.02941](https://arxiv.org/abs/2008.02941)