Saturday, September 12, 2026 · Weekly Paper, Week 8, Part 1

Not How Much Noise, but Which Kind

Every quantum hardware company quotes an error rate, and the one quoted most is the two-qubit gate fidelity: how often an operation between two qubits comes out right. It is a sensible number to lead with. Two-qubit gates are the hardest operation on most machines, and a machine that gets them wrong once in a hundred tries cannot run a long calculation.

I spent the last few weeks asking whether that number tells you what you need to know. Does a machine with better gates reliably give better answers? Or does the breakdown of errors behind the headline figure carry information the figure throws away?

This part covers two papers that approach the question from opposite ends: one on trapped ions from Quantinuum, one on neutral atoms from Pasqal. Neither runs error correction. Both are trying to understand what noise does to a calculation the machine is simply absorbing. And both land in the same place. How much noise there is sets how far the machine can go. What kind of noise it is decides what it does to the answer, and the job you run decides which kind matters most.

When noise becomes heat

Start with an idea that sounds like a metaphor and is not.¹

A quantum computer that has lost information to its surroundings is no longer in a single definite state. It is in a statistical mixture of states, and a mixture has an entropy, in exactly the thermodynamic sense: a measure of how many configurations the system could be in, given what you know about it. An ideal, closed evolution does not create entropy in the full quantum state. A real machine does, because every stray interaction carries a little information away.

For a system at thermal equilibrium, energy and entropy are tied together, and the slope of one against the other is the inverse temperature:

Read it plainly: a cold system has a steep curve, gaining a great deal of entropy from a little energy. A hot one is already spread out, so its curve is flatter and extra energy barely changes it. The temperature $T$ is the inverse of that slope.

That does not mean every noisy state has a temperature. This protocol earns one. It prepares states that settle locally into equilibrium, and for those the measured energy and entropy are enough to assign a temperature.

Granet and Dreyer use this to turn noise into something you can measure. They prepare a small magnet made of interacting spins, change its controls slowly, and track the entropy the hardware adds along the way. On Quantinuum’s H1-1 trapped-ion machine they started from a state with zero entropy, ran 640 two-qubit gates on a 5 by 4 grid of 20 qubits, and measured an entropy of 0.1665 per site at the end. Combined with the measured energy, that gives a temperature of $T = 2.56 \pm 0.26$ in the units of the model.

In this run, all of that entropy came from the machine’s own errors. A perfect machine would have finished at zero temperature. The noise did not merely blur the result; it set the temperature.

Heat that does not distort

That raises the question that makes the paper worth reading. If noise heats the system, does it also corrupt the physics being measured?

They answered it in simulation, on a chain of 12 spins where the noise level could be dialed up and down. More noise raised the entropy and changed the energy, as you would expect. But when they plotted energy against the temperature each state had actually reached, the curves for every noise level fell on top of one another.

Think of that curve as the system’s thermal fingerprint: how much energy it holds at each temperature. It is the thing you set out to measure. The noise moved the system to a hotter point on the fingerprint without changing the fingerprint itself.

There is a real cost, and the paper names it. Noise puts a floor under how cold the protocol can go, and the noisier the machine, the higher the floor. Inside the reachable range, though, that energy-temperature relationship holds up remarkably well in the simulation.

That result holds for one specific kind of error: depolarizing noise, which scrambles a qubit in a random direction. The paper is explicit about the others, and the list is the most useful thing in it for anyone reading an error rate:

• Biased noise, which leans in one direction instead of scrambling evenly, can be turned into the random kind by a software technique called twirling, which averages the bias out.
• Coherent errors, small systematic drifts in the controls, add no entropy at all. Randomized compiling, again done in software, converts them into the random kind.
• Leakage, where an ion slips out of the two states being used as 0 and 1, needs a physical fix: a laser pulse that pumps the ion back where it belongs.

Four cases, and depolarizing noise is the one they simulated. Biased and coherent errors can, in principle, be randomized into something closer to it, which is not the same as making them go away. Leakage is different: it needs active physical repumping. A single fidelity figure cannot tell the cases apart.

One machine, ranked two ways

The Pasqal paper does something a single-number benchmark cannot do at all. It separates the noise in a neutral-atom machine into its sources and measures what each one costs.²

In these machines, atoms are held in place by tightly focused laser beams and arranged into a pattern. How far apart they sit sets how strongly neighbors interact. A separate laser then drives the whole array at once. The paper models five families of imperfection: atoms warm enough to sit slightly off their programmed positions; drive lasers that wobble in strength and frequency; atoms that decay and lose phase; detectors that misread; and calibration sitting slightly off its setpoint. Each gets a number. The detuning calibration is good to about 100 kilohertz, thermal motion produces Doppler shifts of around 50 kilohertz, laser fluctuations sit near 8 kilohertz, and the atoms are held at roughly 20 millionths of a degree above absolute zero.

They ran two different experiments and, in simulation, switched each noise source on by itself to see what it did.

The first was a slow sweep that coaxes the atoms into a checkerboard pattern. There, temperature and decoherence were the expensive errors. Readout mistakes shifted the answer but could mostly be subtracted afterwards in software. Laser wobble barely registered, because a slow sweep forgives small errors in the controls.

The second was a sudden quench, in which the controls jump to new values and the system is left to evolve. They ran it twice. With the drive about 14.5 times stronger than the interaction between neighbors, laser noise was what washed out the signal, and temperature was almost negligible. With drive and interaction comparable, the ranking reversed. Thermal disorder became the dominant limitation, and laser noise barely showed.

Same processor, same protocol, same calibrated noise model. What changed was the program: how hard the laser drives the atoms and how far apart they sit.

Why being in the wrong place only matters sometimes

The reversal has a clean explanation, and it is the best single idea in either paper.

In a neutral-atom machine, the interaction energy between two atoms falls very steeply with their separation $r$:

where $C_6$ is a constant fixed by the type of atom. A steep power law amplifies small errors. If a warm atom sits a small fraction $\delta r / r$ away from its programmed position, the interaction changes by

An atom one percent out of place changes its interaction by six percent. Every run of the experiment sees a slightly different set of interactions, and averaging over runs blurs the result.

But that only matters if the interaction matters. When the drive dominates, each atom effectively ignores its neighbors and simply oscillates under the laser. Its exact position is irrelevant, so thermal jitter does almost nothing. What hurts is the drive being slightly different from one run to the next, so that the atoms drift out of step. When the interaction competes with the drive, position becomes everything, and thermal jitter takes over.

The hardware supplies the imperfections. The calculation decides which ones get amplified.

My takeaway. Two papers, two architectures, one lesson. How much noise there is sets how far the machine can go. What kind it is decides what it does to the answer, and the workload decides which kind dominates. A single error figure averages over failures that behave very differently.

The investor’s read

The point is not that gate fidelity is useless. It is incomplete in a specific and predictable way.

A headline two-qubit fidelity tells you roughly how often the machine errs. It does not tell you whether those errors mainly move the system along the same thermal curve, distort it coherently in a way software can randomize, or leak out of the computation entirely. Nor does it tell you which of them will dominate the calculation a customer actually wants to run, because on the same hardware that answer changes with the workload.

That makes the more informative disclosures the ones that break the budget down: which error sources a company has measured, how large each one is, and whether the ranking has been checked on the kinds of problem the machine is being sold for. A budget with a number against each source is worth more than a better headline figure without one.

What would raise my confidence further is a budget used to predict a workload it was not built from.

Where I land

As a physicist, I find the temperature idea genuinely lovely. Noise stops being an abstract rate and becomes heat, with a thermometer built out of the machine itself.

As an investor, I come away more wary of single numbers than I started. Taken together, the two papers show that the same hardware can be limited by different things depending on the task, and that some of the errors that matter most are exactly the ones a fidelity figure cannot distinguish from harmless ones.

Which leaves a harder question. If what counts is a model of every error source, how good are those models? That is where both papers become more uncomfortable, and it is the subject of part two.

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.
2. 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).