Tutorials
qcr:2606.26556.1

Noisy Circuits in PennyLane

This PennyLane tutorial introduces how to model and simulate noisy quantum circuits, an essential skill for understanding how algorithms behave on imperfect near-term hardware and for developing error-mitigation strategies. It explains the language of open quantum systems used to describe noise: quantum channels that act on density matrices, including familiar examples such as bit-flip, phase-flip, depolarizing, and amplitude-damping channels. Using PennyLane's mixed-state (density-matrix) simulator, the tutorial shows how to insert these noise channels into a circuit, simulate the resulting non-unitary dynamics, and observe how the measurement statistics degrade compared to the ideal noiseless case. Crucially, because PennyLane is differentiable, it then demonstrates a distinctive capability: differentiating through the noisy simulation to optimize circuit parameters in the presence of noise, or even to fit the parameters of a noise model to match observed data. By treating noise as a first-class, differentiable part of the computation, the tutorial gives a hands-on introduction to realistic device modeling and noise-aware optimization in PennyLane.
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Overview

PennyLaneAI/demos
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README.md

Noisy Circuits in PennyLane

This PennyLane tutorial introduces how to model and simulate noisy quantum circuits, an essential skill for understanding how algorithms behave on imperfect near-term hardware and for developing error-mitigation strategies. It explains the language of open quantum systems used to describe noise: quantum channels that act on density matrices, including familiar examples such as bit-flip, phase-flip, depolarizing, and amplitude-damping channels. Using PennyLane's mixed-state (density-matrix) simulator, the tutorial shows how to insert these noise channels into a circuit, simulate the resulting non-unitary dynamics, and observe how the measurement statistics degrade compared to the ideal noiseless case. Crucially, because PennyLane is differentiable, it then demonstrates a distinctive capability: differentiating through the noisy simulation to optimize circuit parameters in the presence of noise, or even to fit the parameters of a noise model to match observed data. By treating noise as a first-class, differentiable part of the computation, the tutorial gives a hands-on introduction to realistic device modeling and noise-aware optimization in PennyLane.

Run it

pip install -r requirements.txt
python demo.py

Source and license

Imported from demonstrations_v2/tutorial_noisy_circuits/demo.py in PennyLaneAI/demos at c52c0abeb5122218aa96b38eea848864cce7323f, under the Apache License 2.0. Original authors: Xanadu and the PennyLane community. The upstream LICENSE is included alongside this example.

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Versions

v1 Latest
Jun 17, 2026
qcr:2606.26556.1

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Tools used

PennyLane

Keywords

noise
density-matrix
pennylane
open-quantum-systems
channels

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