ADR-090: nvsim — Full Hamiltonian / Lindblad Solver Extension

Field	Value
Status	Proposed — conditional. Only built if a pulsed-protocol use case emerges. Default-off, opt-in feature gate.
Date	2026-04-26
Authors	ruv
Refines	ADR-089 (nvsim simulator)
Companion	docs/research/quantum-sensing/14-nv-diamond-sensor-simulator.md §3.1, docs/research/quantum-sensing/15-nvsim-implementation-plan.md §6

Context

ADR-089's nvsim::sensor module implements a leading-order linear-readout proxy for NV-ensemble magnetometry per Barry et al. Rev. Mod. Phys. 92, 015004 (2020) §III.A. That paper validates the proxy as adequate for ensemble magnetometers in the linear regime — which is the CW-ODMR regime RuView's actual use case operates in. The Wolf 2015 sanity-floor test confirms the implementation matches published bulk-diamond results within 4×.

What the proxy does not model:

• Pulsed protocols: Rabi nutation, Hahn echo, CPMG / XY-N dynamical decoupling sequences.
• Microwave-power saturation: line-broadening at high CW MW power.
• Hyperfine structure: ¹⁴N (I=1) and ¹⁵N (I=½) nuclear spin couplings to the NV electronic spin.
• Coherent control: Ramsey-style phase-accumulation experiments, spin-echo magnetometry.

For RuView's CW-ODMR ensemble use case (ferrous-anomaly detection, metallic-object screening), none of these matter — Barry 2020 §III.A is explicit that the linear-readout proxy is adequate. For future use cases that involve pulsed protocols (e.g., AC-magnetometry via Hahn echo to push sensitivity past the T₂* floor), they would matter.

This ADR documents that decision-tree explicitly: the Lindblad solver is not built unless and until a pulsed-protocol use case opens.

Decision

Defer the full Hamiltonian + Lindblad solver to a conditional, opt-in feature gate named lindblad on the nvsim crate. Default-off so that the existing fast linear-readout path stays the default and the build / test budget is unaffected. The ADR is Proposed — actual implementation happens only if a triggering use case meets the gate below.

Trigger conditions for promoting to Accepted

This ADR transitions from Proposed → Accepted when any one of the following is true:

1. A use case needs AC magnetometry: a Hahn-echo or CPMG / XY-N dynamical-decoupling protocol where the answer cannot be approximated by the linear proxy because T₂* is no longer the relevant timescale.
2. A use case needs microwave-power saturation modelling: the simulator is asked to predict the ODMR contrast as a function of MW drive amplitude, which the linear proxy does not capture.
3. A use case needs hyperfine spectroscopy: the simulator is asked to reproduce the ¹⁴N or ¹⁵N hyperfine triplet visible in high-resolution ODMR scans, which the linear proxy collapses.
4. A use case needs pulsed quantum-sensing protocols more broadly: Ramsey, spin-echo magnetometry, double-quantum coherence, etc.

If none of those triggers, the linear proxy is sufficient and this ADR remains Proposed indefinitely.

Why the deferral is the right call today

• Adequacy validated by primary source. Barry 2020 §III.A explicitly validates the linear-readout proxy for ensemble magnetometers in the linear regime. nvsim's existing sensor.rs matches Wolf 2015 within 4×. We're not under-modelling — we're correctly-modelling.
• 3–7 days of focused work. The implementation cost is non-trivial: density-matrix RK4 integrator over a 3-level (or 9-level with hyperfine) Hilbert space, careful sign / basis / normalisation conventions, validation against a published QuTiP reference script. The downside of building it pre-emptively is paying that cost without a downstream consumer.
• No current downstream consumer. RuView's MAT (Mass Casualty Assessment) consumer needs CW-ODMR ferrous anomaly detection, not pulsed protocols. ADR-066 swarm-bridge (proposed) is similarly CW-amplitude-only.
• Not blocked. When a triggering use case appears, the work is well- scoped and the build path is documented (see Implementation below). Deferral is reversible at any time.

Why we don't just delegate to QuTiP

QuTiP is the obvious off-the-shelf option and is what 15.md §6 originally proposed deferring to. Two reasons we'd prefer an in-tree Rust implementation if we ever build it:

1. Determinism. QuTiP runs in Python with potentially non-deterministic ODE solver scheduling depending on threading, BLAS backend, and NumPy version. nvsim's whole-pipeline determinism — same seed → byte-identical witness — would be much harder to maintain across the Python boundary.
2. CI integration. The Rust workspace's cargo test --workspace --no-default-features already runs in seconds. Adding QuTiP would pull a Python dependency into CI and slow the gate.

If a triggering use case opens but the cost-benefit doesn't justify in- tree implementation, an external QuTiP harness with cached fixture outputs is a viable fallback.

Consequences

Positive

• No premature engineering. 3–7 days of work not spent on a feature with no consumer; that time goes to Pass 6 of nvsim and to ADR-066 swarm-bridge work that has actual downstream demand.
• Honest scope. ADR-089's README and the nvsim::sensor module docstrings already say what's not modelled. ADR-090 is the formal accountability for that boundary.
• Reversible. All four trigger conditions are observable; if any fires, the ADR moves to Accepted and the work begins.

Negative / risks

• Risk of premature commitment if triggers fire. If pulsed-protocol use cases emerge late in the project (e.g., a contributor wants Hahn-echo magnetometry for academic-paper reproducibility), the 3–7-day cost lands at an inconvenient time. Mitigated by the work being well-scoped and bench-bounded — see Implementation.
• Documentation debt. Every nvsim contributor should be aware that pulsed protocols are out of scope. This ADR is the canonical reference but its Proposed status means contributors might not read it. Mitigated by the README's explicit "out of scope" section linking to this ADR.

Neutral

• The existing linear-readout proxy is already feature-flag-free and always-on; no API changes when ADR-090 lands. The Lindblad path is additive.

Implementation (when triggered)

If this ADR transitions to Accepted, the implementation is:

1. Add lindblad feature to nvsim/Cargo.toml — opt-in, default-off. Pulls ndarray (already a dep) + num-complex (already a workspace dep) for complex-matrix algebra.
2. src/lindblad.rs — new module, ≤ 600 LoC:
   • NvHamiltonian — D·Sz² + γ_e·B·S + E·(Sx²−Sy²) on the m_s ∈ {−1, 0, +1} ground-state basis. Optional ¹⁴N or ¹⁵N hyperfine extension.
   • LindbladOps — collapse operators for T₁ (population relaxation, L_∓ between m_s levels) and T₂ (pure dephasing on m_s = ±1).
   • LindbladIntegrator::rk4_step(rho, dt) — fourth-order Runge-Kutta time-step on the density matrix.
   • Pulse enum — supports CW, square, Gaussian-shaped MW pulses.
3. src/lindblad_protocols.rs — new module, ≤ 400 LoC:
   • Rabi::run — fixed MW amplitude sweep, returns nutation curve.
   • HahnEcho::run — π/2 — τ — π — τ — π/2 detection sequence.
   • Cpmg::run — repeated π pulses for dynamical decoupling.
4. Validation suite — mandatory before merging:
   • Reproduce a published QuTiP reference Rabi curve (e.g., from a Doherty 2013 supplementary script) within 1% per-bin error.
   • Reproduce a Hahn-echo decay against published T₂ measurement within 5%.
   • Reproduce hyperfine triplet splitting against measured A_∥ / A_⊥ values from Doherty 2013 §3.4.
5. Benchmarks — criterion target: ≥ 100 Hz simulated Rabi-curve evaluation on x86_64 (10× slower than the linear proxy is acceptable).
6. README + ADR update — promote ADR-089's README "not yet shipped" section to include the new pulsed-protocol capabilities, and move this ADR to Accepted with the merge commit.

Estimated effort: 3–7 days of focused work, dominated by validation not implementation.

Validation (Proposed → Accepted)

This ADR is Proposed until any of the four trigger conditions in §" Trigger conditions" fires. When that happens:

1. Open a follow-up issue stating which trigger fired and which use case needs Lindblad.
2. The implementation §1–6 above defines the build.
3. Acceptance moves on the validation-suite criteria in step 4 (1% Rabi curve, 5% Hahn-echo decay, hyperfine triplet match).
4. Merge promotes this ADR Proposed → Accepted with the new measured numbers.

Open questions

• Which Rust complex-matrix library is the right substrate? Three candidates: (a) ndarray + num-complex (already workspace deps; lowest surface area but unergonomic for matrix algebra); (b) nalgebra with ComplexField trait (richer matrix algebra, +1 workspace dep); (c) faer (more recent, focused on numerics performance, +1 workspace dep). Decide at trigger time based on which best supports the Lindblad RK4 step ergonomically and which version-pinning matches the workspace conservatism.
• Is hyperfine modelling in v1 or v2? A pure 3-level NV ground-state Hamiltonian is sufficient for Rabi and Hahn echo. ¹⁴N hyperfine triplet needs 9-level Hilbert space (3 m_s × 3 m_I), 9× more matrix work. v1 could ship with hyperfine off behind a sub-feature; v2 enables it.
• Should the Lindblad solver back-validate the linear proxy? Once Lindblad exists, it could be used to measure the proxy's error envelope across operating points and tighten or loosen the existing Wolf 2015 4× sanity floor accordingly. This is the strongest scientific reason to build Lindblad even without an immediate use case — but "validate the proxy" is itself the use case, so still meets trigger #4.

Related

• ADR-089 — nvsim NV-diamond simulator. The crate this extension attaches to.
• ADR-018 — CSI binary frame format. Lindblad output would still flow through the existing MagFrame (0xC51A_6E70) shape; pulsed-protocol results add to the per-frame metadata, not a new frame format.
• ADR-028 — ESP32 capability audit. Lindblad is host-side only; ESP32 firmware untouched.
• ADR-066 — Swarm bridge. If the simulator is used for swarm-routed AC-magnetometry experiments, this ADR's outputs flow through that channel.