Allow partial initial_layout

[jyu00]

What should we add?

The current transpiler only allows specifying the initial layout of ALL qubits. We have users who want to fix the assignment of only some of the qubits in their circuit to physical qubits on the target QPU, and leaving the transpiler to select the layout of the remaining qubits in the circuit.

For instance, they may want to preselect the location of certain qubits in their circuit to optimize performance. In the case of the user in this story, they are attempting to create a model for combining two or more QPUs together, linking them through particular physical qubits. While the user can specify all of the qubits in the intial_layout, it will become especially cumbersome as the number of qubits in their circuits that they do not want to fix in place grows.

[jakelishman]

I've talked with a user before who wanted to do something like this, and the main blocker is that our layout-selection algorithms cannot handle having partially fixed qubits. We'd have to design and write a custom algorithm to support this use case.

It is an interesting problem and I can see how it's a useful feature. It would help if the users also have some ideas about what sort of algorithm / heuristics they had in mind to select the rest of the qubits.