Manuscript VII-J-ST@1 · VII-J-ST.tex · section · f1f1d82c

Finite evaluation table

Finite tables, resources, and checkable obligations › Finite evaluation table · lines 1738–1772

For the benchmark's two-qubit clock, the exact table is

a 00011011 e (a) 0100 (M, N, H)_{out} (0, 1, 0) (1, 0, 1) (0, 1, 0) (0, 1, 0) V_{a} SWAP SWAP (Z \otimes I) SWAP (Z \otimes I) SWAP Sig (A_{in} \to B_{out}) 1111

Each signalling entry is evaluated for that fixed programme. The full programme channel retains the record and is (eq:benchmark-channel).

The event indicator is the finite matrix

A_{event} = diag (0, 1, 0, 0) .

A nominal label, route length, duration, cycle reward, or potential value can similarly be stored as a diagonal matrix over a finite programme set. Such matrices encode declared evaluations; they are not measurements of an unknown field.

A finite time-expanded dependency graph with $N$ vertices can be represented by its Boolean adjacency matrix $A$ . Its reachability table is the Boolean matrix

I \lor A \lor \dots \lor A^{N - 1} .

Every reachable pair has a path of at most $N - 1$ edges in the DAG, which proves this finite test without numerical execution.

Displayed formulas in this passage

unlabeled · line 1741
$a 00011011 e (a) 0100 (M, N, H)_{out} (0, 1, 0) (1, 0, 1) (0, 1, 0) (0, 1, 0) V_{a} SWAP SWAP (Z \otimes I) SWAP (Z \otimes I) SWAP Sig (A_{in} \to B_{out}) 1111$
unlabeled · line 1756
$A_{event} = diag (0, 1, 0, 0) .$
unlabeled · line 1767
$I \lor A \lor \dots \lor A^{N - 1} .$