Lecture Notes on Quantum Algorithms
Andrew Childs (University of Maryland)
The algorithms course. Hidden subgroup problems, quantum walks, Hamiltonian simulation and query complexity, all treated properly. Dense, and worth every hour.
Advanced · 7 resources
Hamiltonian simulation
Simulating the time evolution of a quantum system — Feynman's original motivation — via Trotter-Suzuki product formulas, linear combination of unitaries, or qubitization.
Learn first:Quantum phase estimation
Why it matters
It is the application with the clearest theoretical case for exponential advantage, and it drives quantum chemistry and materials science, the most credible commercial targets.
After this you will be able to
- Derive and bound Trotter error
- Compare LCU and qubitization approaches
- Estimate resources for a chemistry Hamiltonian
Start here
2 best places to start
Hand-picked and ordered. If you only have time for one, take the first.
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.
Also covering this
5 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 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.
Quantum algorithm for solving linear systems of equations
Harrow, Hassidim & Lloyd (2008)
HHL, the source of most "exponential speedup for machine learning" claims. The caveats — state preparation, condition number, readout — matter more than the theorem, and are all in the paper.
Quantum Algorithm Zoo
Stephen Jordan
A comprehensive catalogue of every known quantum algorithm with its speedup and primary references. The definitive answer to "has anyone found a quantum algorithm for X?"
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.
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This unlocks
Topics that list Hamiltonian simulation as a prerequisite.