Table 1 Consistent assignments for a NAND gate: note that there is no restriction on the values of the inputs, their fault bits and the output (hence, we have \(2^5 = 32\) configurations).

From: Quantum annealing with special drivers for circuit fault diagnostics

(\(x_{i_1}, x_{i_2}; x_{o}\))

Consistent assignments (\(x_{i_1}, x_{i_2}, x_{o}; f_{i_1}, f_{i_2}, f_{o}\))

(0,0;0)

(0,0,0;0,0,1), (0,0,0;1,0,1), (0,0,0;0,1,1), (0,0,0;1,1,1)

(1,0;0)

(1,0,0;0,0,1), (1,0,0;1,0,1), (1,0,0;0,1,1), (1,0,0;1,1,1)

(0,1;0)

(0,1,0;0,0,1), (0,1,0;1,0,1), (0,1,0;0,1,1), (0,1,0;1,1,1)

(1,1;0)

(1,1,0;0,0,0), (1,1,0;1,0,0), (1,1,0;0,1,0), (1,1,0;1,1,0)

(0,0;1)

(0,0,1;0,0,0), (0,0,1;1,0,0), (0,0,1;0,1,0), (0,0,1;1,1,0)

(1,0;1)

(1,0,1;0,0,0), (1,0,1;1,0,0), (1,0,1;0,1,0), (1,0,1;1,1,0)

(0,1;1)

(0,1,1;0,0,0), (0,1,1;1,0,0), (0,1,1;0,1,0), (0,1,1;1,1,0)

(1,1;1)

(1,1,1;0,0,1), (1,1,1;1,0,1), (1,1,1;0,1,1), (1,1,1;1,1,1)

  1. However, the output fault bit is completely determined by the values of the inputs and the output.
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