Variational Quantum Algorithms
Cerezo et al. (2020)
The definitive review of the NISQ-era workhorse: ansatz design, optimisers, barren plateaus and applications, with the open problems stated clearly.
Advanced · 9 resources
Variational algorithms (VQE & QAOA)
Hybrid loops where a shallow parameterised quantum circuit produces expectation values and a classical optimiser tunes the parameters — the dominant paradigm for near-term hardware.
Why it matters
VQE and QAOA are what most NISQ-era experiments actually run. Understanding them includes understanding their problems: barren plateaus, measurement overhead, and the absence of proven speedups.
After this you will be able to
- Implement VQE for a small molecule and QAOA for MaxCut
- Explain barren plateaus and strategies against them
- Assess whether a variational result beats classical methods
Start here
3 best places to start
Hand-picked and ordered. If you only have time for one, take the first.
A Quantum Approximate Optimization Algorithm
Farhi, Goldstone & Gutmann (2014)
The original QAOA paper, and short. It launched an enormous literature on near-term optimisation, most of which is still arguing about whether the speedup exists.
PennyLane demonstrations
Xanadu
Several hundred runnable, paper-linked notebooks on variational algorithms, quantum chemistry and QML. The closest thing the field has to a "reproduce this result" library.
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6 more resources
OpenFermion
Google Quantum AI
The library for compiling fermionic and electronic-structure problems into qubit Hamiltonians. Where quantum chemistry meets quantum circuits in practice.
PennyLane Codebook
Xanadu
Learn by writing code in the browser, exercise by exercise, from single qubits up to variational algorithms. The best option if you retain things by typing rather than reading.
Coding tutorials, seminar talks and the complete recordings of the Qiskit Global Summer Schools — which are effectively free graduate-level lecture series on algorithms and error correction.
Quantum computational chemistry
McArdle, Endo, Aspuru-Guzik, Benjamin & Yuan (2018)
A thorough review of the most commercially plausible application: mapping electronic structure onto qubits, and the algorithms that then extract energies.
Quantum Native Dojo
QunaSys
A thorough, notebook-based curriculum built on the fast Qulacs simulator, strongest on quantum chemistry and variational methods. Under-known outside Japan and better than most English equivalents.
TensorFlow Quantum
Google
Hybrid quantum-classical models built as Keras layers, for people who already know TensorFlow. The tutorials are the fastest route from ML experience into QML.
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Topics that list Variational algorithms (VQE & QAOA) as a prerequisite.