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We propose a linear-optical implementation of a hyperentanglement-assisted quantum error-correcting code. The code is hyperentanglement-assisted because the shared entanglement resource is a photonic state hyperentangled in polarization and orbital angular momentum. It is possible to encode, decode, and diagnose channel errors using linear-optical techniques. The code corrects for polarization flip errors and is thus suitable only for a proof-of-principle experiment. The encoding and decoding circuits use a Knill-Laflamme-Milburn-like scheme for transforming polarization and orbital angular momentum photonic qubits. A numerical optimization algorithm finds a unit-fidelity encoding circuit that requires only three ancilla modes and has success probability equal to 0.0097.
We report the first nonadditive quantum error-correcting code, namely, a $((9,12,3))$ code which is a 12-dimensional subspace within a 9-qubit Hilbert space, that outperforms the optimal stabilizer code of the same length by encoding more levels while correcting arbitrary single-qubit errors.
Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of pre-existing entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike stand
Kitaevs quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum error-correcting code. We offer an explicit proof that this is the case
Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal quantum er
We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes, which are pot