A error, up to the usual convention, strikes qubit of an encoded Steane codeword, in…
PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Open quantum systems, decoherence and error correction · Open quantum systems, decoherence and error correction
Quantum Information and Technology, Ch Quantum error correction
Problem
A Y4 error, Y=iXZ up to the usual convention, strikes qubit 4 of an encoded Steane codeword, in place of the single X3 or single Z6 errors worked in the text.
((a)) Give the bit-flip syndrome (from M acting on the physical qubits directly) and the phase-flip syndrome (from M acting after the Hadamard transform) that this error produces, and explain why both equal column 4 of M.
((b)) State the two single-qubit recoveries the decoder applies from these syndromes.
((c)) Show that applying both recoveries to the error Y4 restores the original state up to a global phase, and give that phase.