Quantum algorithms and benchmarks in plain language: what each family of algorithms does, which problems it addresses, how mature it is, which hardware platforms fit it and what it takes to run it, from a laptop simulation to a fault-tolerant machine.
22 algorithm families, 29 further algorithms from the Zoo index, 17 benchmarks, 11 resource estimates with 25 figures, each quoted with the assumptions and the publication it comes from.
Educational overview compiled by the portal from primary sources: papers (arXiv abstract pages and open-access articles), benchmark repositories and official pages, each read on the date shown. Resource estimates are quoted with the assumptions their authors state and change as methods improve; they are not forecasts, procurement guidance or investment advice. Summaries are in the portal’s own words. Owner-reviewed for demonstration, 28 October 2026. Compiled 2026-10-27.
3 algorithm families shown; 0 further algorithms shown.
Algorithm families
Fault-tolerant Factoring and cryptanalysis
Finds the prime factors of a large integer, or a discrete logarithm, in time that grows only polynomially with the number of digits. A large enough error-corrected quantum computer running it would break RSA and elliptic-curve public-key cryptography, which is why post-quantum cryptography is being deployed now.
Platforms: Superconducting qubits, Trapped ions, Photonic qubits
6 sourced resource estimates · 2 documented demonstrations
Details, requirements and sources Shor's algorithm: factoring and discrete logarithms
Fault-tolerant Search
Finds a marked item among N possibilities with about the square root of N checks instead of about N. Amplitude amplification generalises the idea to speed up any procedure that succeeds with some probability.
Platforms: Trapped ions, Superconducting qubits
0 sourced resource estimates · 1 documented demonstration
Details, requirements and sources Grover search and amplitude amplification
Analogue or special-purpose Simulation of physical systems
A controllable quantum system, such as atoms in optical tweezers or lattices or a chain of ions, is engineered to behave like a model of magnetism or of electrons in a solid, and is measured directly.
Platforms: Neutral atoms, Trapped ions, Analogue quantum simulators
0 sourced resource estimates · 4 documented demonstrations
Details, requirements and sources Analogue quantum simulation of spin and Hubbard models
Algorithms by hardware platform
A dash means that no source for that platform was verified for this release, not that it cannot work. Any marks families that are platform-independent.
Further algorithms (Zoo index)
Further notable quantum algorithms, found through the Quantum Algorithm Zoo and each checked against its original paper. They are mostly theoretical and need fault-tolerant machines; no resource estimate is given unless cited. Summaries and speedups are in the portal’s own words from the original papers; the Zoo category and speedup are given as the Zoo states them.
Index: the Quantum Algorithm Zoo by Stephen P. Jordan, last updated 2026-09-10, checked 2026-10-23. The portal links to it and copies no description from it. Browse the full Quantum Algorithm Zoo (external site)
These algorithms name no hardware platform, so the platform filter hides them.
Further reading
Olivier Ezratty, Understanding Quantum Technologies (CC BY-NC-ND 4.0). Links only; no text of the book is reproduced on this portal.