Suppression of Patterning Effects in Digital Communications by an Adaptive Constrained Coding

Quantum Hamiltonian Computing protocols for molecular electronics Boolean logic gates

“…For instance, a very fast oscillation will encode for an output '1' and a very slow oscillation for a '0'. A very important advantage of this output encoding is that the tunneling current intensity passing through the measurement point of the molecule is proportional to Ω 2 ab (this was verified experimentally with the starphene molecule [16,17]).…”

“…For input (α, β) = (1, 1) the output of AND is 1, thus the kernel of H 0 (1, 1) should be one-dimensional and contain a vector of the form z = (p 1 , p 2 , p 3 , 1) so that it has a non-zero component (which we fix equal to 1) on the reading block. From (16), the condition that z belongs to the kernel of H 0 (1, 1) is equivalent to C 11 p + u = 0 and u T p + B = 0 (in this case B is just a number), with p = (p 1 , p 2 , p 3 ). The first condition gives p = −C −1 11 u.…”

“…Section II yields a solution, (12), with C αβ given by the 3 × 3 matrix (17). In order to find the most general solution, we may consider that H 0 is an N × N Hamiltonian with block structure (16), in which C αβ is now a fixed (N − 2) × (N − 2) block. Since for the three inputs (α, β) = (0, 1), (1, 0) and (1, 1) at least one of the outputs is 1, the kernel of H 0 has to be non-empty (and one-dimensional) for these three inputs.…”

“…As an illustration, we look for Hamiltonians H 0 (α, β, γ) = (h i,j ) 1≤i,j≤8 with block form (16) and…”