rewrite from qubit dialect to wire dialect

[Roger-luo]

implement a rewrite rule that uses analysis to track the dependencies of qubits and rewrite that into wires. This is similar to CUDA Q's quake pass. How this can be implemented is by maintaining a virtual table inside the rewrite rule and update the table with new allocated wire and replace the previous wire, e.g

# SSA corresponding to the QReg => SSA corresponding to the current Wire
qreg2wire: dict[ir.SSAValue, ir.SSAValue]

┆Issue is synchronized with this Jira Task by Unito

[weinbe58]

we might need an array of wires to rewrite functions where a qubit reigster is an argument or we need to have an unwrap statement like in quake.

def subroutine(q: QReg):
    apply(h(), q[0])

[weinbe58]

@Roger-luo actually this simple example is why we need wrap and unwrap.

def subroutine(q: Qubit):
    apply(h(), q)
# rewrites to:
def subroutine(w: Wire):
    unwrap(apply(h(), w))

we need some way of marking this program non-pure without measurements. Similarly other functions won't accept qubit/wire types so we probably need some way of converting back to qubit in case we have functions that are being invoked that can't be rewritten.

[Roger-luo]

Ah yeah I see why this makes sense. I think this another reason that quake is a great layer of IR to interop with directly. Without wrap/unwrap this won't be exactly equivalent.

[weinbe58]

@Roger-luo I'm thinking that maybe this rewrite could be implemented using a code-gen pass instead? that way the current implementation of the rewrites would not need to have an entire frame infrastructure we can just use the interpreter's frame. I think this is probably a more general issue of when to do a rewrite vs when to do a code generation of Kirin IR between dialects.

We could also cross reference this issue in Kirin as well since it seems like more of a convention question than specific to bloqade.

cc: @kaihsin

[kaihsin]

port some of the discussion here: I think in this scenario (where we convert one dialect group to another) we actually want codegen, but we are abusing similar() + rewrite just because it's very obnoxious to create/codegen another ir.Method