Hybrid vs. fully coherent: the coherence budget
The first DOA note ended on the trade: costs coherence, buys flexibility. This note is about the trade itself - where the coherence goes, and what the two architectures in the family do differently with it.
Both architectures answer the same problem - estimating a parameter with an oracle that can learn it mid-flight. The difference is where the learning happens, and that single choice decides the cost model.
HQ-DOA: learn between runs
HQ-DOA - Hybrid Quantum DOA - is the practical entry point. The quantum circuit runs a measurement; the classical side reads the outcome, updates its model of the parameter, and steers the next run's oracle accordingly. The oracle's parameters change between runs.
- Coherence cost: near zero inside any single run. The circuit that runs is essentially a fixed-oracle circuit - a well-understood, robust object.
- Flexibility cost: the adaptation is coarse-grained. You converge run by run, not shot by shot. Rapidly drifting parameters outpace you.
- Hardware reality: runs today's NISQ devices without heroics. This is why it shipped first - and why it was the first quantum-computing publication from IIIT Nagpur.
FQ-DOA: learn inside the evolution
FQ-DOA - Fully coherent - moves the feedback inside the quantum evolution. The oracle's adaptation is unitary; the state never leaves the coherent register to consult a classical model. The parameter and the oracle co-evolve within a single run.
- Flexibility gain: continuous, shot-level adaptation. The oracle tracks the parameter as it moves, which is exactly what you want in high-rate metrology.
- Coherence cost: every adaptation step spends coherence. A coherently adaptive oracle has a finite budget of change before decoherence wins - you're buying flexibility with your most precious resource.
- Hardware reality: demanding. This is the paper now under review (IEEE Trans. Emerging Topics in Computing), and the whole point of the construction is to make the spending explicit and budgetable rather than accidental.
The budget, as a table
| HQ-DOA | FQ-DOA | |
|---|---|---|
| Where adaptation lives | classical, between runs | unitary, inside a run |
| Granularity | run-level | shot-level |
| Coherence spent per adaptation | ≈ 0 | real, finite, counted |
| Drift tolerance | slow drift | fast drift |
| Today's NISQ feasibility | now | research frontier |
| Status | published (IEEE TIM 2026) | under review (IEEE TETC) |
Why "budget" is the right word
The reason I keep calling it a budget and not a trade-off is that a budget is something you can account for. In a fixed-oracle world, coherence decay is a nuisance to be minimized away. In the FQ-DOA world, coherence is denominated - you know how much the adaptation spends, you know how much the run can afford, and you can choose the operating point: more adaptation, less run length; or longer runs, slower adaptation.
That's the shift in mindset the framework pushes for, and it's the same mindset shift I've lived through in enterprise architecture. When you treat a legacy system's downtime budget as a resource to be managed rather than a failure to be avoided, migration strategy changes entirely - you stop asking "can we afford any downtime?" and start asking "what's the cheapest state change that gets us there?"
"You can't optimize what you refuse to measure - coherence included."
- a translation of a very long footnote in the FQ-DOA draft
The morphological edge case
The third line, QDOA, is the one that escapes both columns of the table. Morphological adaptation changes the oracle's structure, not just its parameters - a different operator shape entirely. It's the least mature and the most interesting: if parameter adaptation is the budget question, morphological adaptation is the design question, and it comes with the vocabulary problem I mentioned in the welcome note. You can't grep for a thing nobody has named.
Start from the beginning if you landed here first: what an adaptive oracle actually changes. The homepage's interactive head-to-head is the fastest way to feel the difference without the math.