Quantum Domain

Many of us are hopeful that quantum computers will become practical and useful computing devices some time during the 21st century. It is probably fair to say, though, that none of us can now envision exactly what the hardware of that machine of the future will be like; surely, it will be much different than the sort of hardware that experimental physicists are investigating these days. But of one thing we can be quite confident—that a practical quantum computer will incorporate some type of error correction into its operation. Quantum computers are far more susceptible to making errors than conventional digital computers, and some method of controlling and correcting those errors will be needed to prevent a quantum computer from crashing.
John Preskill, 1997

Welcome to the Quantum Domain

Codes for quantum communication over quantum channels

Kingdoms:

  • Qubit Kingdom (298 codes)
  • Modular-qudit Kingdom (41 codes)
  • Galois-qudit Kingdom (47 codes)
  • Bosonic Kingdom (68 codes)
  • Spin Kingdom (14 codes)
  • Group quantum Kingdom (43 codes)
  • Homogeneous-space quantum Kingdom (4 codes)
  • Category Kingdom (12 codes)
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Classical Domain

  • Binary Kingdom
  • Galois-field Kingdom
  • Matrix Kingdom
  • Analog Kingdom
  • Spherical Kingdom
  • Ring Kingdom
  • Group Kingdom
  • Homogeneous-space Kingdom

Quantum Domain

  • Qubit Kingdom
  • Modular-qudit Kingdom
  • Galois-qudit Kingdom
  • Bosonic Kingdom
  • Spin Kingdom
  • Group quantum Kingdom
  • Homogeneous-space quantum Kingdom
  • Category Kingdom

Classical-quantum Domain

  • Binary c-q Kingdom
  • Analog c-q Kingdom

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Error correction zoo by Victor V. Albert, Philippe Faist, and many contributors. This work is licensed under a CC-BY-SA License. See how to contribute.