Ten Thousand Qubits and a Prayer
On the Fashionable Art of Mistaking Aspiration for Achievement
There is a species of scientific paper that announces what could be done in the voice of what has been done. It dresses projection in the grammar of accomplishment, drapes assumption in the robes of demonstration, and sends the result forth into the world bearing a title calculated to make headlines. One ought to recognise the genre by now. It is the native literature of the venture-funded laboratory.
The paper under examination is “Shor’s algorithm is possible with as few as 10,000 reconfigurable atomic qubits” by Cain, Xu, King, Picard, Levine, Endres, Preskill, Huang, and Bluvstein (arXiv:2603.28627, March 2026). The authors hold positions at Oratomic — a company that builds neutral-atom quantum computers — and at the California Institute of Technology. The paper claims that cryptographically relevant instances of Shor’s algorithm can be executed with as few as ten thousand physical qubits on a reconfigurable neutral-atom platform.
The claim is, to employ a technical term, bullshit.
I use the word precisely, in the sense given to it by Harry Frankfurt: a statement made with indifference to whether it is true or false, constructed to produce an impression rather than to convey a fact. The paper contains competent mathematics. It contains no outright fabrication that I can detect. What it contains — and what elevates it from mere optimism to something more corrosive — is a systematic architecture of conditional claims presented as unconditional results. Every load-bearing number in the paper depends on an assumption that has not been demonstrated, and the title reports the conclusion as though the assumptions had been discharged. That is not science. That is marketing wearing a lab coat.
Let us proceed through the structure of this edifice, brick by unsupported brick.
I. The Title Is Inconsistent With the Paper’s Own Numbers
The title says “as few as 10,000.” The paper’s smallest architecture uses 9,739 qubits. At that qubit count, the runtime for RSA-2048 — the historical benchmark — is of the order of ten thousand days. That is approximately twenty-seven years.
Twenty-seven years.
For ECC-256, the space-efficient architecture yields a runtime of roughly 2,600 days — just over seven years. No neutral-atom system has ever operated continuously for seven years. No neutral-atom system has operated continuously for seven hours at the fidelity levels required. The paper provides no analysis whatsoever of whether its hardware can sustain coherent, error-corrected operation across such durations. It does not address cumulative atom loss over years of operation. It does not address drift in laser intensity, trap frequencies, or magnetic fields over months and years. It does not address the statistical accumulation of uncorrectable errors over billions of error-correction cycles.
The “few days” figure that readers will remember — because it is designed to be remembered — requires not 10,000 qubits but 26,000, and it applies only to ECC-256, not RSA-2048. It furthermore depends on the “time-efficient architecture,” which itself depends on parallel surgery operations that have been numerically benchmarked on approximately ten simultaneous Pauli product measurements and are here assumed to scale to one hundred and thirty. For RSA-2048 at comparable speed, the paper requires 102,000 qubits — a figure that rather undermines the “as few as 10,000” in the title.
What is happening here is a conjuring trick. The qubit count is taken from the cheapest architecture. The runtime is taken from the most expensive. The title fuses the two into a single impression that corresponds to no actual configuration described in the paper. If a builder told you he could construct your house for ten thousand pounds, and upon reading the contract you discovered that at that price the house would take twenty-seven years to complete, you would not call the builder honest. You would call a solicitor.
II. The Physical Error Rate Has Not Been Achieved at the Required Scale
The entire analysis assumes a depolarising noise model with physical error rate p = 0.1%, or in some configurations even lower (0.07% and 0.093% are cited as thresholds for various circuits). The paper itself tells us that current neutral-atom systems operate at “2× below threshold” with “a path to 10× below threshold.” The threshold for these codes is roughly 0.5%–1%. Operating at 0.1% therefore requires being five to ten times below threshold.
The gap between “2× below threshold on a few hundred qubits” and “5–10× below threshold on ten thousand qubits” is not a gap that can be waved away with the word “path.” It is the gap between a laboratory demonstration and an industrial system. It is the gap between lifting a stone and building a cathedral. The paper treats it as a minor engineering detail. It is not a minor engineering detail. It is the central unsolved problem of the entire field.
Moreover, the noise model is depolarising — symmetric, memoryless, uncorrelated. Real neutral-atom systems exhibit spatially correlated errors from Rydberg crosstalk, time-varying fidelities from laser intensity fluctuations, biased noise from preferential decay channels, and atom loss events that are not depolarising at all but rather erasure errors with spatial correlations. The paper notes, in a single sentence, that heralded atom loss “could effectively lower p by a factor of two.” It does not note that this benefit requires successful erasure conversion, which has been demonstrated only in limited experimental contexts and which adds circuit complexity that is not included in the resource estimates. The asymmetry is instructive: every uncertainty that helps the numbers is mentioned; every uncertainty that hurts them is silent.
III. The 1 ms Cycle Time Is Aspirational
Every runtime in the paper is computed assuming a 1 ms stabiliser measurement cycle. The paper states, with admirable candour that is then promptly ignored in all subsequent analysis: “Although realizing this in practice may require technological development, we anticipate that it can be achieved.”
“We anticipate.” The honest man’s synonym for “we hope.”
Current demonstrated cycle times are “several ms” on systems of hundreds of qubits in experiments that “did not optimize for speed.” The paper’s 1 ms target must be achieved not on hundreds of qubits but on ten thousand or more, involving complex atom rearrangement, mid-circuit measurement, and dynamic reconfiguration of optical tweezers across a substantially larger physical area. Every runtime figure in the paper scales linearly with this assumption. If the achievable cycle time is 3 ms rather than 1 ms, every runtime triples. If it is 10 ms — which is within the range of current demonstrations — every runtime increases tenfold, and the “ten days” for ECC-256 becomes one hundred days, and the space-efficient RSA-2048 runtime becomes the better part of a century.
The paper does not present a sensitivity analysis. It does not tell you what happens to the headline numbers if this assumption fails. A man who builds his house on sand, and who neglects to mention the sand, is not presenting a resource estimate. He is presenting a fantasy with footnotes.
IV. The Code Performance Is Extrapolated From Insufficient Data
Figure 2a of the paper is the foundation upon which all resource estimates rest. It shows block error rates per cycle for several lifted-product codes and surface codes as a function of physical error rate. The critical data points — the ones at p = 0.1%, where the actual computation must occur — are not simulated. They are extrapolated.
The extrapolation procedure is as follows. For the lp₁₆ code, a power-law fit y = axb is performed using three data points at higher error rates, yielding a fitted exponent b = 7.1 ± 0.4. For the lp₂₀ and lp₂₄ codes, this same procedure yields exponents larger than d/2, which is the theoretical maximum as p → 0. The authors correctly note that these exponents are unphysical. They then adopt what they describe as a “conservative” fix: they set b = d/2 and fit the prefactor a from a single data point — the lowest simulated error rate.
Let us be precise about what this means. The theoretical maximum scaling exponent is d/2. They assume the theoretical maximum. They anchor it to one datum. They call this “conservative.”
It is not conservative. Conservative would be to use d/2 − 1 or d/2 − 2. Conservative would be to fit from the worst data point rather than the best. Conservative would be to present error bars on the extrapolated logical error rates that propagate uncertainty in the exponent through to the final resource estimates. None of this is done. The method they employ is to assume best-possible asymptotic behaviour and pin it to a single measurement. This is not conservatism. It is the opposite of conservatism wearing conservatism’s hat.
The extrapolation spans roughly an order of magnitude in physical error rate and many orders of magnitude in logical error rate. The 90% algorithmic success probability that determines whether a given architecture can complete the computation depends entirely on these extrapolated values. If the true scaling exponent is, say, 8 instead of 12 for the lp₂₄ code, the logical error rate at p = 0.1% changes by orders of magnitude, and architectures that nominally succeed at 90% probability may fail catastrophically.
V. The Code Distances Are Upper Bounds Treated as Exact Values
All code parameters are reported as [[n, k, ≤d]]. The “≤” is doing rather a lot of work. The distances are upper bounds obtained from a decoder-based heuristic estimation using BP-OSD with 25,000 random trials. The true minimum distance of the code could be lower.
This matters because the entire extrapolation of logical error rates assumes the code achieves the stated distance. If the true distance of the lp₂₄ code is 20 rather than 24, the asymptotic scaling exponent drops from d/2 = 12 to 10, and the extrapolated logical error rate at p = 0.1% increases by a factor that could render the architecture insufficient.
The paper does not quantify the probability that the true distance is substantially below the reported upper bound. It does not perform a sensitivity analysis on the distance parameter. The “≤” appears in the notation and is then treated as “=” in every subsequent calculation. This is a silent substitution of a bound for a value — a move that, in any other context, we would recognise as assuming the conclusion.
VI. The Laser Rastering Claim Violates Elementary Physics
The paper observes that current laser duty cycles are approximately 0.1% — that is, gate operations of ~200 ns are separated by idle periods of ≳200 μs. It then proposes that “by rastering the beam dynamically to increase the active duty cycle, the number of atoms that can be addressed and entangled at high fidelity could thus be directly increased by three orders of magnitude.”
This is wrong. Not optimistic. Not aggressive. Wrong.
The arithmetic assumes that 0.1% can become 100%. But 100% duty cycle requires zero time for beam repositioning, zero time for settling after repositioning, zero thermal management of the optical elements under continuous high-power operation, zero timing jitter in the acousto-optic or electro-optic deflection, and zero overhead for synchronisation with the rest of the system. These are not engineering margins that can be squeezed. Zero repositioning time would require the beam to be in two places at once, which is not a matter of engineering but of the laws of optics.
A realistic estimate of the achievable improvement from beam rastering, accounting for slew time, settling time, and the irreducible overhead of beam control, is perhaps one to two orders of magnitude. Possibly less. The paper claims three. The excess order of magnitude is not a rounding error. It is a misrepresentation of what the physics permits.
VII. The Surgical Heart of the Architecture Is an “Existence Proof”
The paper’s compilation strategy depends on code surgery — the process of fault-tolerantly measuring logical Pauli operators across different code blocks. The authors admit, with a frankness that I would admire more if it were reflected in the title, that their surgery construction is “a theoretically consistent existence proof, which may not be optimal in terms of resource costs.” They further note that constructing and optimising surgery gadgets for the large memory codes is “computationally prohibitive.”
In other words: the central mechanism by which computation is actually performed in this architecture has not been constructed for the codes that the architecture uses. What has been constructed are surgery gadgets for smaller processor codes, which introduce time overhead multipliers of 10× to 72× per Toffoli gate. The surgery error rates are stated to be “within an order of magnitude” of the processor code rates based on numerical simulation.
“Within an order of magnitude” is a phrase that, in ordinary life, would cause alarm. If your builder told you the cost would be “within an order of magnitude” of the estimate, you would understand that the house might cost ten times what you were quoted. An order-of-magnitude uncertainty in surgery error rates propagates directly into the total algorithmic failure probability, especially when the base rates are themselves extrapolated.
VIII. The Time-Efficient Architecture Depends on Unpublished Work
The headline “10 days for ECC-256” comes from the time-efficient architecture. This architecture uses codes from Reference [125]: “Caltech & Oratomic. Atlas of atomic fault-tolerant quantum memory (2026). In preparation.” It also relies on Reference [113]: “Zheng, Zheng, Jiang & Xu. In preparation (2026).”
Let me state this plainly. The most striking claims in the paper depend on results that have not been published, have not been peer-reviewed, and cannot be independently verified. The codes used in the time-efficient architecture do not exist in the public literature. The low-weight logical operators that enable the architecture’s ancilla efficiency are justified by a citation to a paper that does not yet exist.
Building resource estimates on the foundation of unpublished results is not unusual in preprints. What is unusual — and what crosses the line from aggressive to dishonest — is putting the results of those unpublished-work-dependent calculations into headline claims and press-friendly titles. The title does not say “10,000 qubits, contingent on results to be published later.” It says “10,000 qubits.” Period. The qualification is buried in the appendix. The impression is broadcast in the title.
IX. Decoding Latency Is Ignored
For a system running at 1 ms cycle times, the classical decoder must return syndrome-processing results within 1 ms. The paper uses a belief-propagation decoder with localised statistics. For codes with thousands of physical qubits and complex Tanner graph structures, the latency of this decoder at the required scale has not been demonstrated. The paper does not analyse whether real-time decoding is achievable.
This is not a theoretical nicety. If the decoder cannot keep up with the syndrome extraction rate, there are exactly two options: slow down the cycle time (which linearly increases all runtimes) or allow a decoding backlog to accumulate (which degrades error correction performance in ways that are not captured by the paper’s error model). Either way, the resource estimates change. The paper does not mention this.
X. The Conflict of Interest
The first affiliation is Oratomic. Oratomic is a company whose commercial value depends on the perception that neutral-atom quantum computers are close to practical utility. The paper’s headline claim — that neutral-atom systems can break widely deployed cryptography with a surprisingly small number of qubits — is the single most commercially valuable claim that could be made on Oratomic’s behalf.
This does not make the results false. But it creates a systematic incentive toward optimism that a reader must weigh when evaluating the hedging language. When the paper says “we anticipate,” the reader must understand that the authors have a financial interest in your sharing their anticipation. When the paper says “under plausible assumptions,” the reader must understand that the plausibility of those assumptions is not disinterested.
Science is not corrupted by the existence of commercial interest. It is corrupted when commercial interest is permitted to determine the framing of results, and when that framing is constructed to produce an impression that the technical content does not support. That is what has happened here.
The Sum of the Parts
Let us count the assumptions that must hold simultaneously for the title to be true:-
Physical error rates of 0.07%–0.1% must be achieved across ten thousand or more qubits. (Not demonstrated.)
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A 1 ms stabiliser measurement cycle must be achieved at this scale. (Not demonstrated.)
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The extrapolated logical error rates must hold across orders of magnitude of extrapolation. (Not verified.)
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The code distances must equal their upper bounds. (Not established.)
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Surgery gadgets must perform within an order of magnitude of the processor codes. (Loosely bounded.)
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Parallel surgery must scale from 10 benchmarked PPMs to 130. (Not demonstrated.)
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Codes from unpublished work must perform as projected. (Not available for review.)
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Real-time decoding must keep pace with the cycle time. (Not analysed.)
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Continuous operation must be sustained for days to years. (Not analysed.)
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The depolarising noise model must adequately capture real device physics. (Not established.)
Each of these is independently capable of invalidating the headline numbers. Several of them — the error rate, the cycle time, the continuous operation, the parallel surgery scaling — are individually sufficient to change the results by orders of magnitude if they fail. The probability that all ten hold simultaneously is the product of their individual probabilities. Even if each is independently “plausible” at, say, 70%, the joint probability is 0.710 ≈ 3%.
Three per cent is not “possible.” It is a prayer.
The paper should have been titled: “Theoretical resource estimates for Shor’s algorithm using high-rate qLDPC codes on reconfigurable neutral-atom arrays.” That title is accurate. It describes what the paper actually contains: a theoretical analysis of what would be required if a substantial number of undemonstrated conditions were met. There is genuine value in such analysis. It narrows the field. It identifies which engineering targets matter most. It moves the conversation forward.
But that is not what the title says. The title says the thing “is possible.” And the thing is not possible. Not yet. Not with ten thousand qubits. Not with any number of qubits that currently exist. What is possible is the theory that it might one day be possible. The distance between those two claims is the distance between science and salesmanship.
One must have a heart of stone to read this paper’s title without laughing. And one must have a mind of rather softer material to read its assumptions without objecting.
The truth is not determined by what is convenient, what is fundable, or what makes an attractive headline. It is determined by what can be demonstrated. Everything else — however beautifully constructed, however ingeniously argued, however prestigiously authored — is commentary.