nLab surface code

Idea

In the area of quantum computing, surface codes are quantum error correcting codes which utilize in imaginary surface (really a discrete lattice) of physical qubits, with nearest-neighbour interactions, on which error-protected logical qubits are encoded. A key example is known as the toric code.

Surface codes are also referred to as topological quantum error correcting codes, since the effective error protection translates into topological (homotopical) properties of the approximated surface. But is important to note the difference to qubit stabilization by fundamental physical topological effects as envisioned in topological quantum computing. One may regard surface codes as implementing a quantum simulation of actual hardware-level topological protection.

Related entries

• bit flip code

• stabilizer code

• HaPPY code

• Majorana dimer code

• toric code

• Æ code

References

Original articles:

• Alexei Kitaev: Fault-tolerant quantum computation by anyons, Annals of Physics 303 1 (2003) 2–30 [doi:10.1016/S0003-4916(02)00018-000018-0), arXiv:quant-ph/9707021]

• Eric Dennis?, Alexei Kitaev, Andrew Landahl?, John Preskill: Topological quantum memory, J. Math. Phys. 43 (2002) 4452–4505 [doi:10.1063/1.1499754, arXiv:quant-ph/0110143]

Survey:

• Austin G. Fowler, Matteo Mariantoni, John M. Martinis, Andrew N. Cleland: Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86 (2012) 032324 [doi:10.1103/PhysRevA.86.032324, arXiv:1208.0928]

• errorcorrectionzoo: Kitaev surface code

• Wikipedia: Surface code