Stabilizer code

rdf:langString Stabilizer code

rdf:langString The theory of quantum error correction plays a prominent role in the practical realization and engineering ofquantum computing and quantum communication devices. The first quantumerror-correcting codes are strikingly similar to classical block codes in theiroperation and performance. Quantum error-correcting codes restore a noisy,decohered quantum state to a pure quantum state. Astabilizer quantum error-correcting code appends ancilla qubitsto qubits that we want to protect. A unitary encoding circuit rotates theglobal state into a subspace of a larger Hilbert space. This highly entangled,encoded state corrects for local noisy errors. A quantum error-correcting code makes quantum computationand quantum communication practical by providing a way for a sender andreceiver to simulate a noiseless qubit channel given a noisy qubit channelwhose noise conforms to a particular error model. The stabilizer theory of quantum error correction allows one to import someclassical binary or quaternary codes for use as a quantum code. However, when importing theclassical code, it must satisfy the dual-containing (or self-orthogonality)constraint. Researchers have found many examples of classical codes satisfyingthis constraint, but most classical codes do not. Nevertheless, it is still useful to import classical codes in this way (though, see how the entanglement-assisted stabilizer formalism overcomes this difficulty).