Coupling maps in quantum computation

Question

Perhaps a bit naive question from my side, but I could not find any satisfactory answer elsewhere:

What exactly are the coupling maps in quantum computation and, more particularly, how do those maps translate to CouplingMap objects in qiskit?

Intuitively, I do get that it is a way to express a connections between the qubits, but are then those physical connections between the physical qubits or something else? Any explanation here would be welcome. If it helps in any way, for instance, the figure below is often used to illustrate coupling map for a particular qiskit hardware setup, which I unfortunately cannot read at this point:

Answer 1

You can think of the qubits as nodes on a graph, and their connections as edges. Then the coupling map is just the adjacency matrix, specifying how the nodes (qubits) are connected.

For example, if you have the following device of 5 qubits with the following qubit layout:

Then its coupling map is: $$[[0, 1], [1, 0], [1, 2], [2, 1], [2, 3], [3, 2], [3, 4], [4, 3]]$$

• $[0, 1], [1, 0]$ indicate that $0$ and $1$ are connected.
• $[1, 2], [2, 1]$ indicate $1$ and $2$ are connected.

and so on. Note that you don't see $[0,2],[2,0]$ since $0$ and $2$ are not connected in the graph above.