Superconducting vs All-to-All Compilation

On a superconducting chip, each qubit can only work with a few fixed neighbours. So far-apart qubits pay a "SWAP tax" of extra two-qubit gates. Trapped-ion machines let any pair work together directly, but their two-qubit gates are much slower. Neither type wins every time. The result depends on which qubits your circuit pairs up, and on which cost you care about most.

What do the two architectures look like to a compiler?

Why care? The same circuit can look cheap on one kind of machine and costly on another. Knowing why helps you pick the right machine for your job.

A superconducting processor is a chip of tiny fixed circuits, cooled to near absolute zero. Each qubit is wired to a few neighbours. So the topology, the map of which qubits are wired together, is sparse. It looks like a line, a grid, or IBM's heavy-hex pattern. This is limited connectivity. A two-qubit gate only works between wired pairs.

A trapped-ion machine holds single charged atoms, called ions, in a shared trap made of electric and magnetic fields. All the ions sit in one trap. They affect each other through the way they move together. So a two-qubit gate can link any pair. This is all-to-all connectivity.

An everyday example: an office. A chip is like desks in fixed cubicles. To talk to someone far away, you pass notes along. A trap is like one meeting room where anyone can speak to anyone. Here the example breaks. The meeting-room talks are much slower. And the example says nothing about error rates.

We will compile one logical circuit for both archetypes. An archetype is a simple model of a type of machine, not a claim about any named device. This makes the trade-offs easy to see without naming a winner.