Saturday, September 12, 2026 · Weekly Paper, Week 8, Part 2

A Model Cannot Know What You Missed

Part one ended on a claim: a breakdown of error sources, with a number against each one, tells you more than any headline fidelity. That claim has a catch. A breakdown is a model, and a model is only as good as the errors it knows about.

Both papers from part one put their models up against real hardware, and both found the edge. One is still chasing an error its model cannot see. The other found something that was not random noise at all. How each team handled its miss is, to me, the most useful thing in either paper.

Why anyone needs a noise model

The point of a quantum computer is to calculate what an ordinary computer cannot. The awkward problem arrives when the machine reaches a regime where the exact classical calculation is no longer available. Some answers survive that: a result that is hard to find but easy to check, a quantity physics says must stay constant, a second machine that agrees. For the many-body simulations these two papers care about, what is gone is the referee that simply tells you what the answer should have been.

That is the job of a noise model: a list of every known error source, each with its size, that can be run on an ordinary computer alongside the ideal calculation. The plan in both papers is the same. Test the model while checking is still possible, then ask whether it can be trusted once the check runs out.

So the real question is not whether a model fits. It is whether it would tell you when it was wrong.

The thermometer that disagreed

Quantinuum’s experiment measured how much entropy the machine’s errors added to a small magnet of 20 spins.¹ It did so with a mirror circuit: run the whole calculation, then run it backward. A perfect machine lands exactly back where it started. A real one misses, and the size of the miss tells you how much entropy the noise added along the way. The energy was measured separately.

That gives the paper a built-in consistency check. If noise only heats the system without distorting it, the result from part one, then a noisy run should look exactly like a clean run that simply started warmer. The authors computed that clean run. It started at an inverse temperature (one over the temperature) of 1.6, carried the same entropy as the hardware, and should have ended with an energy of $-2.22$ in the units of the model.

The hardware gave $-2.334 \pm 0.019$. The number after the $\pm$ is the measurement’s uncertainty, one standard deviation, and the gap is more than six of them. That is far too large to be bad luck.

So the authors went through the suspects one at a time.

More of the same noise. They took a depolarizing error of $1.1 \times 10^{-3}$ after every two-qubit gate, a rate that reproduces the entropy the mirror circuit measured and is consistent with the machine’s own component benchmarks, and simulated the run. It gave $-2.24$, matching the prediction and not the machine. The authors read this as a positive result too: in their argument, the agreement confirms that the protocol’s own assumptions hold approximately, namely an evolution slow enough and a system that settles locally into a thermal state. The physics passed. The noise model did not.

Coherent errors. They added the machine’s benchmarked memory error, a slow drift that rotates each qubit a little, to the simulation. No significant change.

Leakage. An ion that slips out of the two states used for 0 and 1 is read as 1 from then on, every time it is measured. That corrupts the energy, but it need not add any entropy the mirror circuit would register, so the thermometer can miss it entirely. And the data lean the right way. After the evolution, one of the measured quantities, the average spin along one axis, sits closer to the value a stuck-at-1 ion would produce than the noiseless value does, and it does so from both starting states the authors tried.

Leakage is the most likely explanation, and the authors say so. They could not confirm it. The standard test detects leaked ions partway through the circuit and throws away the affected runs, and on H1-1 that detection needs spare qubits, called ancillas. All 20 qubits were carrying the magnet. The paper leaves the question to future or bigger machines.

The hardware data were taken in August 2025. Quantinuum has since built Helios, a 98-qubit machine.² Its documentation describes a measurement that reports each qubit as 0, 1, or leaked, with no spare qubits: the two good states are parked in a separate long-lived level before the readout light arrives, so an ion that still glows must have leaked.³ That is the company’s own description, not something this paper tested. If it works as described, the test the paper could not run now exists.

Three machines, one model

Pasqal’s paper runs the same kind of test at larger scale.⁴ It built its noise model on open-source software called Pulser⁵ and calibrated it once, on a machine called FC1, accessed through the cloud in Canada. Then it compared that model with two other machines of the same generation, SA1 in Saudi Arabia and Ruby at the CEA supercomputing center in France, without refitting anything. Each ran the same two protocols on 36 atoms in a 6 by 6 grid.

A full 36-atom state already carries $2^{36}$, about 69 billion, complex amplitudes, so the classical reference used a compression method called tensor networks.

The results from all three machines fell inside the uncertainty band the single model predicted, for both the slow sweep and the sudden quench. That is a stronger statement than a model fitting one machine. It is evidence that much of the behavior is reproducible at the level of the platform rather than peculiar to one box, which is what you would want before trusting the model beyond the range you can check. The paper is careful to add that device-specific deviations remain on top of it.

The miss that was systematic

There was one place the model did not fit. In the quench where drive and interaction compete, the data at late times settled inside the model’s band, below the noiseless curve, as expected. At early times, the measured population (the fraction of atoms found in the excited state) sat above the model’s prediction, close to and sometimes above what a perfect machine would give.

The authors conclude that the random fluctuations in their model, which push one run up and the next one down and average to zero, cannot account for it. It points instead to a systematic offset: a control setting that sits slightly away from where it was programmed, the same way on every run.

A detuning offset of $-0.2$ MHz accounts for it. The detuning is how far the laser’s frequency sits from the atom’s natural resonance, one of the two knobs, along with the drive strength, that a program sets. The stated calibration precision is about 0.1 MHz, so the offset is about twice that.

Here the skeptic objects, and rightly. The $-0.2$ was inferred from the very comparison it explains, and any fitted number will explain the data it was fitted to.

So they tested it. They deliberately programmed an offset of $+0.67$ MHz, far larger than either the calibration precision or the inferred bias, and ran the experiment again. The model, evaluated at the programmed offset, quantitatively predicted the strong drop in population that followed. And the measured population again sat slightly above the prediction, just as the same hidden $-0.2$ MHz bias would make it. One residual offset explained both datasets.

That is how a fit becomes a prediction: change the machine on purpose and check that the model follows.

The authors do not oversell it. An offset like this, they write, “is, by definition, not known a priori,” meaning it cannot be known in advance, and they cannot rule out similar offsets in the drive strength or the atom spacing playing a comparable role. The test shows a detuning offset is consistent with both datasets. It does not show that detuning is the only thing off.

What the two misses have in common

Put the two papers side by side and the misses share a shape. Each model was built from what the team had measured, and each ran into something its calibration could not see: for Quantinuum a leading suspect it could not confirm, for Pasqal an offset the model did not contain. Leakage need not add entropy, so an entropy thermometer can be blind to it. A static offset is the same on every run, so it never shows up as scatter, and a model built from fluctuations is blind to it too.

A model cannot know what you missed. It can only contain the errors someone thought to measure, at the size they were measured.

What made both papers useful is that they went looking for the miss rather than tuning it away. Quantinuum’s model made a firm prediction and failed it by six standard deviations, and the failure is what pointed at leakage. Pasqal’s model left a gap at early times, and the team did not stop at the fit that explained it: they mistuned their own machine to see whether the explanation held.

My takeaway. A breakdown of errors beats a headline number only if the breakdown is complete. Both papers found a residual their model did not explain, and both found it because the model made a prediction firm enough to fail.

The investor’s read

For Pasqal, the claim worth weighing is transfer. One model, calibrated on one machine, described three machines in three countries without refitting. For a company offering several machines of one generation, that is evidence the units behave alike, which is what a customer needs before moving a job from one to another. The emulator is built on open-source software, so outsiders can inspect the model and run it, though repeating the three-machine test needs access to the three machines. The paper also argues that the breakdown shows which hardware improvements would pay off most for a given application. The caveat is in the paper itself: systematic offsets beyond calibration precision remain, and the model has so far been validated only where a classical reference exists, not yet where it is meant to earn its keep.

For Quantinuum, the result is an open question with a date on it. The data come from H1-1 in August 2025, and the one test that would settle it needed hardware that machine did not have. Its newer machine is described as having it, on the company’s own account. The thing to look for is a rerun, or any published leakage rate measured during a real workload.

For both, and for anyone else, one habit carries over. A noise model that predicted a result before the run is evidence. A number inferred afterward is a hypothesis until someone changes the machine and checks.

Where I land

As a physicist, the $+0.67$ MHz run is my favorite moment of the week: a team deliberately mistuning its own machine to test an explanation it could easily have left alone.

As an investor, I end part two more careful than I ended part one. A detailed error budget is better than a headline number, but it has blind spots too, and the blind spots are where the surprises live. The companies I would trust most are the ones that publish their misses along with their fits, and say plainly what they could not test.

Neither paper turned error correction on. IonQ did, and that is a different story.

Sources & notes

1. E. Granet and H. Dreyer, “Adiabatic preparation of thermal states and entropy-noise relation on noisy quantum computers,” npj Quantum Information 12, 105 (2026). doi:10.1038/s41534-026-01320-0. Hardware data from Quantinuum’s H1-1 system, taken in August 2025. The paper prints the warm-start comparison as an energy of $-2.22$ and a final temperature of 1.93 in its text, and as $-2.21$ and 1.91 in its Table 1. Neither difference changes the conclusion: the energy gap is more than six standard deviations either way.
2. A. Ransford et al., “A 98-qubit trapped-ion quantum computer with all-to-all connectivity,” Nature 655, 81-86 (2026). doi:10.1038/s41586-026-10676-4.
3. Quantinuum, Helios user documentation, leakage measurement guide, https://docs.quantinuum.com/systems/trainings/helios/getting_started/leakage_measurement.html (accessed 2026). Company documentation describing the company’s own system; not independently verified.
4. C. Dalyac, S. Julià-Farré, L. Leclerc, V. Vitale et al. (Pasqal), “Noise-aware emulation and cross-device validation of neutral atom analog quantum processing units,” arXiv:2607.28364 (2026).
5. H. Silvério, S. Grijalva, C. Dalyac, L. Leclerc, P. J. Karalekas, N. Shammah, M. Beji, L.-P. Henry, and L. Henriet, “Pulser: An open-source package for the design of pulse sequences in programmable neutral-atom arrays,” Quantum 6, 629 (2022).