This task is possible for a set of operators E if inner products of the form (*) "bra-psi E-sub-i-dagger E-sub-j ket psi" are elements of an Hermitian matrix, by the Knill-Laflamme conditions. A class of methods for this task are named for abelian subgroups of the Pauli group P-sub-n whose elements share an invariant subspace, exemplified by the CSS method. The star and planchette operators are the stabilizers in a square lattice model that performs this task by annihilating anyonic (“any-onic”) excitations. Schemes for this task with distance 3, 5, and 7 were implemented on Google’s Willow chip in the first demonstration of the threshold theorem. Logical qubits require multiple physical qubits because the auxiliary qubits perform this task. For 10 points, Shor’s code is a method for what task that involves fixing phase flips and bit flips? ■END■
ANSWER: quantum error correction [accept answers describing correcting qubit errors or correcting errors in quantum computers or circuits; accept quantum error-correcting codes; prompt on encoding or decoding quantum information; prompt on quantum computing or achieving fault-tolerance or robustness in quantum computing] (The second clue refers to stabilizer codes. The third clue refers to the toric code.)
<VD, Other Science>
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