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Survey of quantum error correction codes1/10/2024 ![]() Then you're just after the shortest such sequence. ![]() So long as you eliminate the possibility that it is a product of stabilizers (probably what is meant by 'non-trivial'), you've found a logical error. (Color online) (a) Schematic of various approaches for controlling a quantum system: (i) unitary control on the system alone or both the system and an ancilla (ii) quantum feedback control based on measurement of the ancilla (iii) driven-dissipative control with either engineered dissipation or Hamiltonian engineering (iv) holonomic quantum control based on only engineered dissipation. When all stabilizers commute, we've implemented a logical error or something that is a product of the stabilizers. If I apply an $X$ on that vertex, or a $Z$ on any of the neighbouring vertices, it flips whether the tensor product commutes or anti-commutes, so I simply flip the 0/1 value on the vertex. So, imagine that I store as a 0 or 1 on a give vertex whether the current tensor product of Pauli errors commutes with that stabilizer or not. Keywords: Toric Code Quantum Error Correction Machine Learning. Usually a graph state has stabilizers defined as $X$ on a vertex, and $Z$ on all the neighbouring vertices. We use supervised learning methods to study the error decoding in toric codes of. Let's see how this connects to a graph state description. A quantum code suppresses errors if the set of correctable errors contains all likely errors, with respect to a given error model. This way we achieve quasi-error-free communication and an increase of the estimated post-quantum bit-security level by 20.39 and a decrease of the communication overhead by 12.8. If I express it in terms of the stabilizers of the code, it's the smallest tensor product of single-qubit unitaries (usually Paulis) that commutes with all the generators. classical and modern codes by combining BCH and LDPC codes. The distance of an error correcting code is the smallest number of single-qubit rotations that you have to apply to map one logical codeword into an orthogonal one.
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