Benchmarking learned readout against the matched filter measures the wrong gap

We opened a direction on learned representations for classifying quantum measurement records, and closed it twice — once when the criterion turned out to be published and the core experiment already run with a contradicting result, and once when the surviving thread turned out to rest on a separation that does not exist. Two sessions, $0 each.

The useful part is a correction to how this work gets benchmarked.

The baseline is not the matched filter

The trainable temporal postprocessor of Khan et al. is a linear map over the vectorised time-resolved record, with closed-form optimal weights depending on the mean traces and the temporal correlation matrix. It is convex, costs almost nothing to train, deploys to an FPGA, and is model-free.

The load-bearing fact is what it reduces to. Under Gaussian white noise the TPP is exactly the matched filter. The matched filter is not a competing method; it is the special case that obtains when the noise has no temporal structure, and it is optimal only there.

So a neural network that beats a matched filter on finite-bandwidth, jump-prone, or high-power readout has demonstrated that the noise was correlated. It has not demonstrated that learning was necessary — a linear method with a closed-form solution captures the same thing.

The sharpest version of the point is theirs, not ours

Their Fig. 6(a) has a datapoint where the noise is exactly Gaussian and the matched filter beats the TPP, because the TPP has to learn from data what the matched filter knows analytically. When the analytic statistic is correct, learning it is strictly worse.

That is the cleanest published statement of the principle we kept rediscovering, and it is the reason the programme did not survive contact with the literature.

What this does not settle

Nonlinearity does appear to earn its keep on real multiplexed data — a properly specified linear baseline absorbs only part of the gap to the best network. We are not publishing those figures here: our record of them is second-hand from an HTML fetch rather than extracted from the PDF, and this site's rule is that a number gets quoted only when someone has checked it at the source.

There is also an unreconciled tension in the literature between a reported error reduction from nonlinear methods and a separate sweep finding that discriminator choice collapses to a few percent of logical error rate at distance 12 — different endpoints, plausibly both right. It is a real question. It is not a programme.

What would reopen it

A demonstration that some learned statistic beats a properly specified temporal postprocessor on real device data, with the interval reported — not a win against a matched-filter baseline chosen because it is easy to beat.