# Demo Audit, public NETLIB benchmark

Manifest: `manifest.json` (sha256:e11a927f69827d5617ee3ce6a8f0838e057f64f7b4786f9ab8746a554129a813)
Runner: `feasibility-runner v0.2.0`
Workload: three NETLIB linear programs (afiro, adlittle, agg)
Audit tier: Standard
Publication release: named with release

## 1. Executive verdict

Across the three NETLIB instances, every route the chassis evaluated returns REDIRECT under Tier A. The hybrid quantum interior point method (QIPM), in either the modified Newton (MNES) or orthogonal subspaces (OSS) formulation, requires a logical-cycle budget of 3e10 to 5e10 to compete with classical solvers that finish the same workload in a few milliseconds. HiGHS 1.14.0 reaches optimality on the largest instance (agg) in 2.3 milliseconds; Clp 1.17.9 on the same instance is in the same order of magnitude. The dominant cost driver is not Newton-system inversion, it is full primal-dual vector output extraction via tomography. The board should fund the redirect path, not the original full-vector route.

## 2. The workload

Three benchmark linear programs from the public NETLIB suite. Dimensions before presolve:

| Instance | Rows | Columns | Nonzeros | Sparsity |
|---|---|---|---|---|
| afiro | 27 | 32 | 83 | 0.096 |
| adlittle | 56 | 97 | 383 | 0.071 |
| agg | 488 | 163 | 2410 | 0.030 |

Inputs are MPS text files decompressed from the NETLIB EMPS-compressed downloads. The three files are concatenated and hashed together; the SHA-256 of the concatenation is captured in the manifest as `workload.inputs.input_hash`. Precision target: 1e-6 relative.

## 3. The classical baseline

Two classical comparators. HiGHS 1.14.0 ran natively (Apple silicon, single core, presolve on, default dual simplex). On agg, the largest of the three, HiGHS reaches optimality in 0.0023 seconds, 102 simplex iterations. On adlittle: 0.000945 seconds, 87 iterations. On afiro: 0.0217 seconds, 6 iterations (afiro carries first-touch JIT overhead inside highspy). All three terminations: optimal. Configuration captured at `classical_baselines[0].configuration`.

The second baseline is Clp 1.17.9, a primal simplex implementation widely used as a portable open-source comparator. Runtime estimated at 0.05 seconds on agg, consistent with the COIN-OR Clp benchmark notes for NETLIB-scale instances. The second baseline is included to establish that the Tier A verdict does not hinge on a single solver. Both baselines sit in the same order of magnitude on the largest instance.

## 4. The quantum candidates

Two formulations of the same hybrid QIPM family, evaluated against both baselines under Tier A.

The MNES candidate uses the modified Newton-equation system, the standard Newton system in interior-point methods. Cost drivers: sparsity 0.030, condition-number lower bound 1e4, QLSA precision 1e-6, output extraction by tomography, state preparation by block-encoding the coefficient matrix per IPM iteration. Cycle lower bound under Tier A: 5e10 logical cycles.

The OSS candidate uses the orthogonal subspaces system, a structurally cheaper Newton variant that exploits the augmented structure of LP. Cost drivers: same sparsity, condition-number lower bound 8e3, same QLSA precision, same output mode. Cycle lower bound under Tier A: 3e10 logical cycles.

Tier A is the benevolent lower-bound regime. Noise-free, one cycle per oracle call, lower-bound condition estimates from instance structure, IPM iteration count from the source paper. No QEC overhead, no fault-tolerance overhead. The cycles reported are a floor.

## 5. The verdicts

Four routes, four REDIRECT verdicts.

`lp-qipm-mnes-vs-highs-tier-a`: 5e10 cycles to compete with 0.0023 seconds wall-clock. Break-even cycle time: 4.5e-14 seconds. The verdict flips if the output requirement collapses from a full primal-dual vector to a scalar functional. The verdict is invariant to the condition number within an order of magnitude of 1e4.

`lp-qipm-oss-vs-highs-tier-a`: 3e10 cycles. Break-even: 7.5e-14 seconds. Same dominant assumption (output extraction). Also flips if the condition number drops below 1e3 because then the dominant term shifts.

`lp-qipm-mnes-vs-clp-tier-a` and `lp-qipm-oss-vs-clp-tier-a`: same cycle counts against Clp's slower baseline, break-even at 1.0e-12 and 1.7e-12 seconds respectively. Both REDIRECT.

The most sensitive assumption across the portfolio: output extraction. The condition number is a secondary lever. None of the four routes produces a GO under Tier A on this workload.

## 6. What would change the verdicts

Three named conditions would flip the verdicts.

First, replace full primal-dual vector tomography with a single scalar amplitude estimation over a chosen linear functional of the optimum. This collapses the O(n) extraction tax into a single estimation. The chassis names this redirect path explicitly in `reformulation_log` step 0.

Second, drive logical cycle time below 1e-13 seconds at the named precision. That is roughly four orders of magnitude past current published gate-time floors at the named precision. A non-trivial threshold; the chassis does not predict when, only what would have to be true.

Third, on the OSS route specifically, find an instance class with condition number below 1e3. None of the three NETLIB instances qualify. This is a workload-selection lever, not a hardware lever.

## 7. Recommended next steps

Fund the scalar utility output redirect path. The cost of testing it is small relative to the cost of pursuing the full-vector route under Tier A. Defer the full-vector LP/QIPM until logical cycle time falls below the named threshold and the output requirement is reduced to a scalar functional. Re-audit the workload class when either condition shifts.

Two additional notes for board context. (a) The verdict is bounded by this workload (three NETLIB LPs, small to medium scale), these baselines (HiGHS, Clp), and the Tier A assumption envelope. (b) The chassis does not say quantum LP solvers will not work on any LP; it says these specific routes do not beat these specific baselines on this specific workload under benevolent assumptions. The forbidden-generalization clause is captured verbatim in the manifest's portfolio summary.

## 8. Citation and independence

Informed by published lower-bound analysis of hybrid quantum interior point methods (Binkowski, arXiv:2604.24362, 2026). DeployQuantum did not author that research. The Audit operationalizes the source paper's decision logic into a customer-facing audit workflow. Citation key, role, and licence posture are captured at `citations.primary_methodology[0]` in the manifest.