Quantum Error Mitigation Tutorial Series

Error mitigation is a family of techniques for recovering accurate expectation values from a noisy quantum computer, without the qubit overhead of full quantum error correction. Rather than detecting and repairing faults as they happen, mitigation runs the noisy circuit as-is — sometimes several deliberately noisier versions of it — and removes the bias from the results in classical post-processing. The price is paid in samples, not qubits. Mitigation repairs expectation values, never states or samples, and its sampling cost grows with the noise it must undo. It is the standard way to get quantitative results from today's pre-error-corrected hardware.

This series introduces the two workhorse techniques, readout mitigation and zero-noise extrapolation (ZNE), from first principles, building each one by hand before composing them into the standard mitigation ladder and running it on real hardware via qBraid. The running experiment throughout is a four-qubit mirror circuit: a block $U$ followed by $U^\dagger$, repeated, so it always composes to the identity and its observable $\langle Z \otimes Z \otimes Z \otimes Z \rangle$ is exactly $+1$ at any depth. Every notebook measures that same observable, which makes every improvement directly comparable across the series. By the final notebook, the full ladder brings a raw hardware-model error of about $0.34$ down to about $0.02$. The four notebooks are meant to be worked through in order.

The techniques are those of Temme, Bravyi and Gambetta (arXiv:1612.02058), which introduced ZNE and probabilistic error cancellation, and Kandala et al. (arXiv:1805.04492), which first demonstrated ZNE on hardware. Familiarity with basic Qiskit concepts including circuits, transpilation, samplers, and counts is assumed; no error-correction background is needed, and Notebook 1 builds the noise vocabulary from scratch.

Launch on qBraid

Use the Launch on qBraid button on this tutorial's page in the qBraid Explore hub. It clones the repository into qBraid Lab. You will use the default environment to run this tutorial, and the notebook will ensure all required packages are installed. Run the notebooks in order, starting with 01_noise_zoo.ipynb. For selecting environments and kernels in qBraid Lab, see the environments guide.

The notebooks

The series is released one notebook per week. Notebook 1 is available now; the rest arrive on the schedule below.

#	Notebook	Status
1	The Noise Zoo — 01_noise_zoo.ipynb	Available
2	Readout Mitigation — confusion matrices, inversion vs. least squares	August 19, 2026
3	Zero-Noise Extrapolation — gate folding, linear vs. exponential fits	August 26, 2026
4	Production and Hardware — the production stack, run on a real QPU	September 02, 2026

1. The Noise Zoo 01_noise_zoo.ipynb

This notebook introduces the mirror circuit and builds the noise vocabulary from scratch: readout error, gate (depolarizing) error, and $T_1/T_2$ decay, each simulated in isolation so its fingerprint and depth signature can be seen on its own. It establishes the ground rules for the rest of the series: mitigation versus correction, bias versus variance, and why every mitigation technique pays a sampling overhead.

Requirements

The qBraid Lab default environment provides Qiskit, Qiskit Aer, qiskit-ibm-runtime, and qBraid; the install cell at the top of Notebook 1 adds the remaining packages (matplotlib and pylatexenc). For other setups, requirements.txt lists everything needed (pip install -r requirements.txt in a Python 3.10+ virtual environment).

Running the tutorials

• Run each notebook from top to bottom, in order. If the kernel state becomes inconsistent, use Kernel > Restart Kernel and Run All Cells.

Notes and troubleshooting

• Import or kernel errors immediately after launch usually mean the environment is still installing. Wait for it to finish, then select the tutorial's kernel from the kernel menu.