---
title: QDrift (v1.0)
description: API reference for qiskit.synthesis.QDrift in qiskit v1.0
source: https://quantum.cloud.ibm.com/docs/en/api/qiskit/1.0/qiskit.synthesis.QDrift
---

# QDrift

*class* `qiskit.synthesis.QDrift(reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None, seed=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.0/qiskit/synthesis/evolution/qdrift.py#L24-L102)

Bases: [`ProductFormula`](/docs/api/qiskit/1.0/qiskit.synthesis.ProductFormula "qiskit.synthesis.evolution.product_formula.ProductFormula")

The QDrift Trotterization method, which selects each each term in the Trotterization randomly, with a probability proportional to its weight. Based on the work of Earl Campbell in Ref. \[1].

**References**

\[1]: E. Campbell, “A random compiler for fast Hamiltonian simulation” (2018). [arXiv:quant-ph/1811.08017](https://arxiv.org/abs/1811.08017)

**Parameters**

- **reps** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The number of times to repeat the Trotterization circuit.
- **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – Whether to insert barriers between the atomic evolutions.
- **cx\_structure** ([*str*](https://docs.python.org/3/library/stdtypes.html#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*](https://docs.python.org/3/library/typing.html#typing.Callable)*\[\[*[*Pauli*](/docs/api/qiskit/1.0/qiskit.quantum_info.Pauli "qiskit.quantum_info.operators.symplectic.pauli.Pauli")  *|*[*SparsePauliOp*](/docs/api/qiskit/1.0/qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.operators.symplectic.sparse_pauli_op.SparsePauliOp")*,* [*float*](https://docs.python.org/3/library/functions.html#float)*],* [*QuantumCircuit*](/docs/api/qiskit/1.0/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.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.
- **seed** ([*int*](https://docs.python.org/3/library/functions.html#int) *| None*) – An optional seed for reproducibility of the random sampling process.

## 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**](https://docs.python.org/3/library/exceptions.html#NotImplementedError) – If a custom atomic evolution is set, which cannot be serialized.

## Methods

### synthesize

`synthesize(evolution)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.0/qiskit/synthesis/evolution/qdrift.py#L60-L102)

Synthesize an `qiskit.circuit.library.PauliEvolutionGate`.

**Parameters**

**evolution** ([*PauliEvolutionGate*](/docs/api/qiskit/1.0/qiskit.circuit.library.PauliEvolutionGate "qiskit.circuit.library.PauliEvolutionGate")) – The evolution gate to synthesize.

**Returns**

A circuit implementing the evolution.

**Return type**

[QuantumCircuit](/docs/api/qiskit/1.0/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")