Gottesman–Kitaev–Preskill code

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The Gottesman–Kitaev–Preskill (GKP) code is a quantum error correcting code that encodes logical qubits into the continuous degrees of freedom of a quantum system. It is named after Daniel Gottesman, Alexei Kitaev and John Preskill who published it together in 2001.

The code is used in continuous variable (CV) photonic quantum computing, in which logical qubits are encoded into the field quadratures of an optical mode. This modes can be thought of as the quantum harmonic oscillator with conjugate position and momentum operators. By encoding logical qubits into a single optical mode, the GKP code demonstrates greater hardware efficiency than traditional qubit codes. Instead of needing many qubits to act as redundancy for a single qubit, the GKP code instead requires a precisely constructed optical state. GKP codes are able to protect against both small shifts in the quadratures, but also loss channels such as photon loss in a photonic system.