Symbol S_i
is part of the quantity the equation computes from the expression on the right.
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Why this formula appears here
The technique that makes this work is the stabiliser formalism, given its general fault-tolerant treatment by Gottesman [ 4 ] . A code is defined not by listing its states but by naming a set of commuting Pauli operators — the stabiliser generators — whose joint +1 eigenspace is the code space: . An [[n, k, d]] code encodes k logical qubits into n physical qubits with distance d . The stabiliser generators are measured repeatedly. Because each commutes with every other and with the logical operators, measuring them extracts no information about which encoded state is present. What it extracts is whether an error has anticommuted with a given check — a single…
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Symbol psi_L
ps is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Symbol i
i is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Symbol n
n is one of the signed contributions combined to compute the quantity on the left.
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Published contexts (1)
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Equation 5 · Quantum Information
Error Correction Is the Whole Problem in Quantum Computing
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
The technique that makes this work is the stabiliser formalism, given its general fault-tolerant treatment by Gottesman [ 4 ] . A code is defined not by listing its states but by naming a set of commuting Pauli operators — the stabiliser generators — whose joint +1 eigenspace is the code space: . An [[n, k, d]] code encodes k logical qubits into n physical qubits with distance d . The stabiliser generators are measured repeatedly. Because each commutes with every other and with the logical operators, measuring them extracts no information about which encoded state is present. What it extracts is whether an error has anticommuted with a given check — a single…