On 9 December 2024, Google's quantum team published a peer-reviewed result that ran through the specialist press within hours: the first logical memory to pass below the critical threshold for error correction. Their largest machine mobilises 101 of them, and that memory lives 2.4 times longer than the best qubit on the chip.

Close view of a bluish superconducting chip, etched with long folded tracks and a few cross-shaped patterns.
A four-qubit IBM chip: the long folded tracks are the resonators, the cross-shaped patterns the qubits themselves. It takes a hundred and one of these to obtain a single corrected qubit. (Photographie Jay M. Gambetta, Jerry M. Chow et Matthias Steffen, npj Quantum Information, 2017, via Wikimedia Commons, licence CC BY 4.0, source page)

A hundred and one components to obtain one.

A quantum computation, as the previous episode showed, is a piece of choreography in one continuous movement, danced without looking, whose result is read only at the end. It still has to reach that end.

How long do the dancers stay on their feet?

A qubit does not break down, it forgets

Qubits are fragile to the point where any interaction with the outside, however slight, destroys the superposition the computation rests on: physicists call that decoherence.

Engineers call lifetime the span a qubit holds before that happens. On the best superconducting chips, etched in a metal film a few hundred nanometres thick and held around ten millikelvin, it is counted in tens of microseconds, sometimes a millisecond. Past that delay the information has dissolved into the environment.

The consequence follows on its own: the computation must be finished before the forgetting, which caps the number of operations that can be chained, and specialists then speak of circuit depth. Doubling the lifetime doubles the length of the computations available.

And if a dancer stumbles along the way, no intermediate step has been kept. Everything is lost.

A logical qubit exists nowhere in particular

Physicists found a way round, and its principle throws you: it is not about protecting a fragile component by surrounding it with bodyguards, but about manufacturing a qubit that exists nowhere in particular. The procedure has a name: quantum error correction.

Take the two words materially. A physical qubit is an object you can point at: a resonator and its junction, etched on the chip. It occupies a position, it has its own frequency, it has a lifetime. A photograph is enough to capture it.

A logical qubit, no. Neither a component, nor a component escorted by others. It is what you obtain by combining several physical qubits, and its value is stored in none of them.

The physical qubit is a component you can point at. The logical qubit is contained in no component: its value is carried by the 49 data qubits together. (Schéma Shy Robotics)

Where is it, then? In the relations between them.

Those forty-nine data qubits carry the value collectively, which forces you to measure all of them and combine the results to know it. Pick one at random, isolate it, look at it: it will tell you nothing.

The forty-eight measurement qubits clear the last ambiguity: they carry no information, they check continuously whether their neighbours still agree with one another, which is called a parity, and that is enough to spot that an error has just occurred without ever learning the value. They fall into two families, one watching for value flips, the other for phase flips, and Google measures its grid separately in those two bases.

So they can be questioned continuously, while looking at the others stays forbidden. Reading a parity collapses no superposition. The whole trick lies there.

The threshold, and its two worlds

Correcting errors has a cost that must be faced squarely: the qubits added to watch the others make errors themselves, and as long as the base component stays too poor, those new errors outnumber the ones being corrected, so that adding qubits makes matters worse rather than better.

The threshold marks the tipping point between those two worlds: below it, every added layer divides the error; above it, every layer multiplies it. Google writes it in black and white, with an error rate measured at 0.143% per correction cycle on its distance-7 grid: the error decreases exponentially with the number of qubits only if the physical error rate passes below a critical threshold.

Above the threshold, adding qubits makes the error worse. Below it, every added layer divides it. Google crossed that frontier in late 2024. (Schéma Shy Robotics)

Google therefore demonstrated no useful machine, but the crossing of a frontier: for the first time, stacking qubits was good for something. For thirty years the theory had promised it without any machine showing it.

Where exactly the hundred and one come from

The size of those grids has a name: the distance. It denotes the number of surveillance layers wrapped around the information, so that more layers means more physical qubits, and a memory that holds longer.

The formula 2d² − 1 gives 97. The four missing qubits remove leakage into the transmon's parasitic states. Published total: 101. (Schéma Shy Robotics)

The formula can be checked by hand. A surface code of distance d mobilises 2d² − 1 physical qubits per logical qubit: three layers call for 17, five for 49, seven for 97.

That leaves the gap with the 101 announced, and the paper spells it out. Google's distance-7 code consists of 49 data qubits, 48 measurement qubits, and 4 further qubits for leakage removal. Forty-nine plus forty-eight plus four does indeed make a hundred and one.

A single logical qubit, seen from above: 49 data qubits in a 7 by 7 grid, 48 measurement qubits between and around them, 4 leakage-removal qubits at the corners. (Schéma Shy Robotics)

Those four say something about the hardware. A superconducting qubit does not have two states but a whole ladder of energy levels, and it sometimes climbs above the one, into a parasitic state it does not come down from on its own. That leakage is drained on every cycle, through those four edge qubits.

Google's teams measured the effect, and that measurement is what makes the 2024 result valuable: every time they add two layers, the error rate falls by a factor of 2.14.

They demonstrated nothing useful, though, and that must be said at once. No algorithm ran on it. The teams obtained a memory, not a computation.

Alice & Bob's bet: remove half the problem

In Alice & Bob's laboratory the same bill reads backwards: a hundred and one components to obtain one, nobody will know how to pay that at scale. The company set out to bring it down, and its method explains the French purchase. Quantum noise has two faces: the value flip, where the qubit goes from zero to one on its own, and the phase flip, subtler, which alters the relation between the two states without changing any value.

Two ways of making a qubit. The transmon encodes in two neighbouring energy levels; the cat qubit encodes in two oscillations of opposite phase. (Schéma Shy Robotics)

An ordinary qubit encodes its zero and its one in the two lowest energy levels of a superconducting circuit. A cat qubit encloses microwave photons in the resonator, that etched and folded track, and encodes the information in two oscillations of opposite phase. Both are superconducting: this comparison plays out inside a single technological family.

The two states of a cat qubit live at opposite poles. The more photons the resonator holds, the greater the distance grows. (Schéma Shy Robotics)

The mechanism is pure geometry, and there the bet gains its subtlety: the two oscillations live very far from one another, the gap grows as photons are enclosed in the resonator, so that to flip, the system would have to cross that whole distance in one go. You might as well ask a marble to jump from one valley to the next.

The literature prices the trade without hedging: the value-flip rate falls exponentially with the number of photons enclosed, while the phase-flip rate rises linearly.

An objection arises here, and it deserves better than a pirouette. Google's grid corrects both kinds of error; Alice & Bob corrects only one. Is the protection not halved?

No, because the second error is not abandoned: it is handled elsewhere. The value flip does not disappear thanks to a code, it disappears inside the component itself. Guillaud and Mirrahimi put it this way: value flips are exponentially suppressed with the average number of photons.

Both approaches settle the same bill, then, but in two different currencies. Google pays for both errors in qubits, and the cost follows the square of the distance. Alice & Bob pays the first in photons, added to a resonator without etching anything more, and the second in qubits, on a line.

Photons cost less than qubits. The whole affair lies there.

Where the saving sits is not obvious. Google's grid occupies two dimensions because it must catch both kinds of error at once: the two families of measurement qubits interleave, and every data qubit must have neighbours in both directions.

Remove one of the two kinds and the surface loses its reason to exist. A line is then enough, where each data qubit is flanked by a measurement qubit comparing its two neighbours. Physicists call that a repetition code, and Jérémie Guillaud and Mazyar Mirrahimi published the version adapted to cat qubits in Physical Review X in 2019: a one-dimensional repetition code.

Two kinds of error demand a surface, whose cost follows the square of the distance. One kind alone is corrected on a line, whose cost follows the distance. (Schéma Shy Robotics)

The two formulas look alike, and that is what makes the gap speak. A grid of distance d costs 2d² − 1 qubits, or 97 for seven layers. A line of the same distance costs 2d − 1, or thirteen. The square has gone.

Alice & Bob's authors use an expression that sums the matter up: cat qubits reduce the hardware footprint of fault-tolerant quantum computing.

A caveat applies at once, and the paper carries it itself. That shortcut holds only if value flips are completely suppressed; if any remain, you must return to surface codes, lighter than Google's but still two-dimensional. The CEA stays cautious for the same reason: the technology natively corrects one of the two sources of noise.

One only.

Eighteen cat qubits therefore do not compare with eighteen ordinary qubits. The figure alone says nothing.

Four words to demand in front of any announced qubit count. Without them, the figure measures nothing. (Schéma Shy Robotics)

Remember the rule, it will serve to the end: a qubit count measures nothing when it arrives alone, it needs its error rate, its lifetime, and whether it is physical or logical. A bare figure belongs to a press release, not to engineering.

None of this works yet at the scale that counts. No algorithm has run on a logical memory, and the bill stays out of reach.

Why, then, does a dated deadline already exist somewhere?

The next episode answers, and the date in question comes from no laboratory.

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