Syndrome Table Capacity Boundary Scan - Quantum Mechanics V: Error Correction and Stabilizer Checks Step by Step

Two syndrome bits make four table rows, so double-error aliases cannot be new rows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Two syndrome bits give four table rows

The table capacity is fixed by the two checked parity bits.

N_{\text{rows}}=4

Demand rows bracket the syndrome table capacity

Adding the zero-syndrome row fills the table. Treating a double error as new demand overfills it.

\begin{array}{c|c|c|c}N_{\text{demand}}&N_{\text{rows}}&m&\text{gate}\\3&4&1&\text{pass}\\4&4&0&\text{pass}\\5&4&-1&\text{fail}\\\end{array}

A double-error class aliases an existing row

The lookup helper shows the double-error syndrome is not a new independent table row.

m=-1\quad \text{fail}