Coalescing qubits in Stairs Circuit

[rrtucci]

For the Stairs Circuit, suppose, for instance, that you have 10 qubits (0, 1, 2, ..., 9) and you want to "coalesce" qubits 5 and 6. In a fully connected quantum bayesian network, qubit 5 would have qubits (6, 7, 8, 9) as parents, and qubit 6 would have qubits (7, 8, 9) as parents. By coalescing 5 and 6, we go to a non-fully connected qb net in which 5 and 6 have the same set of parents. For instance, 5 and 6 might both have (8, 9) as parents. Thus, in this example, coalescing qubits 5 and 6 produces a node 5_6 with 4 states (qudit with d=4) and 2 parents, namely qubits (8, 9).