Quantum Computing Labs

50 self-checking labs, from a single qubit to quantum error mitigation and hardware-style decoder costs, plus a reproducible robustness study of a variational quantum classifier.

Every lab is a standalone Python script that predicts, measures, and checks: it prints PASS/FAIL for each claim it makes (about 1,200 checks in total), so the results below are tested, not just stated.

Author: Dr. Ceasar Jackson Jr.

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Highlights

• Ran on real quantum hardware. IBM ibm_fez (156 qubits): GHZ(3) state fidelity 0.940 ± 0.011; a mirror-circuit benchmark measured 0.28% error per CNOT; a Trotterised Ising quench tracked the exact dynamics within 0.048 RMS.
• Built the simulators from scratch. A matrix-product-state simulator, DMRG (matches exact diagonalisation to 1e-8 and the Bethe-ansatz energy density to 4 decimal places), and an adjoint gradient exact to 3e-13.
• Quantum error correction. Surface-code thresholds measured at three noise levels (9.4% → 2.5% → 0.7%, matching the literature), plus a union-find decoder written from scratch and benchmarked against MWPM.
• Error mitigation, compared side by side. Zero-noise extrapolation, symmetry verification, probabilistic error cancellation and randomised compiling, including where each one fails (for example, frozen coherent errors make straight-line extrapolation worse than doing nothing).
• A reproducible ML study. A 4-qubit PennyLane classifier evaluated over a partition × initialization grid, with classical baselines, provenance hashes and stated limitations (see below).

The PennyLane study

A four-qubit variational classifier learns 4-bit parity, trained on 12 inputs and tested on the 4 held-out inputs.

Phase	Design	Result
I	5 partitions × 5 initializations, 200 steps	23/25 configurations perfect on held-out data; mean 94.0% (SD 20.8). Both failures shared one initialization seed.
II	10 new partitions × 5 new initializations, 200 steps	44/50 configurations perfect on held-out data; mean 90.0%. Every failure was a failure to train (58–67% training accuracy), never to generalize, and all six came from two initialization seeds. 20 configurations re-ran bit for bit.

What this does and does not show. There are only 16 possible inputs, so each test set has 4 examples and accuracy moves in 25-point steps. The circuit's CNOT chain is well matched to parity, so high accuracy shows a matched structure, not a quantum advantage. Full write-ups: Phase I · Phase II (PDF)

Quick start

python3 -m venv .venv && source .venv/bin/activate
pip install -r requirements.txt

python labs/lab01_single_qubit.py        # any single lab
python labs/run_all.py --skip-slow       # everything, with a summary table
python labs/pennylane_phase2_robustness.py --dry-run   # validate the study design

Tested with Python 3.13, Qiskit 2.5, PennyLane 0.45. The real-hardware labs (11, 15, 17, 44, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59) run in dry-run mode on a simulated device unless given --live; live runs read the IBM API key only from an environment variable.

GitHub Actions (.github/workflows/ci.yml) installs the pinned requirements and runs python labs/run_all.py --skip-slow on every push and pull request to main. It uses no secrets, so the hardware labs only ever run in dry-run mode there.

Repository layout

Path	Contents
labs/lab01_*.py … lab61_*.py	The labs, one topic each (full index: course-index.md)
labs/ex01_*.py … ex10_*.py	Optional exercises
labs/mpslib.py, labs/dmrgx.py, labs/pbmps.py, labs/fezdata.py, labs/noiselib.py	Shared MPS/DMRG (with symmetries and excited states), per-bond ansatz, recorded ibm_fez data, and noise/mitigation libraries
labs/PennyLane.py, labs/pennylane_*.py	The classifier and its evaluation and analysis scripts
results/pennylane/	Raw, unmodified experiment outputs (CSV/JSON)
docs/	Study write-ups

Engineering standards

Every script has a documented header, argparse CLI, exit codes (0/1/2/130), colored console plus plain-text file logging, and explanatory comments. labs/check_standards.py enforces this on every file, and all code is black-formatted. Experiment outputs are written with exclusive file creation, so a result can never be silently overwritten.