Quantum computers could have a fundamental limit after all - Phys.org

The interesting thing about Tim Palmer’s new argument on quantum computing is not the headline-friendly claim that the field may run into a hard limit. It is that the limit does not come from a lab finding, a fabrication bottleneck, or 1,001 qubits refusing to cooperate on schedule. It comes from a new paper by Tim Palmer, a physicist at the University of Oxford, in the Proceedings of the National Academy of Sciences proposing a replacement framework for quantum theory itself.

The accessible version of that argument is Palmer’s arXiv preprint, “Rational Quantum Mechanics: Testing Quantum Theory with Quantum Computers”. There, Palmer argues that the standard Hilbert-space description of quantum mechanics is too mathematically generous for large entangled systems. In his framework, which he calls Rational Quantum Mechanics, the information capacity of qubits is finite, the continuum underlying standard quantum theory is effectively discarded, and the exponential advantage promised by algorithms such as Shor’s should saturate at around 1,000 perfect qubits. That is a provocative claim. It is also very much not the same thing as discovering that real hardware has already hit a fundamental wall.

That distinction matters because the story reached the wire as if physics had quietly served the quantum industry a legal notice. The actual paper is a foundations proposal. Palmer writes that for sufficiently large numbers of qubits there is “insufficient information” in the system to support the full continuum of degrees of freedom assumed in standard quantum mechanics, and from that derives an upper bound Nmax of roughly 200 to 400 for current technologies and, eventually, no more than about 1,000 even for ideal devices, according to the arXiv preprint. In practical terms, he argues that Shor-style factoring would stop scaling exponentially before it could threaten 2048-bit RSA.

The University of Oxford’s Department of Physics, in its release on the work, makes the experimental pitch more explicit. The university says Palmer’s theory predicts that Shor-like algorithms should begin to fail once a few hundred error-corrected qubits are entangled, and frames the work as part of a broader attempt to connect quantum theory to gravity by removing the continuum from complex Hilbert space. That is the real novelty here. Palmer is not just offering another skeptical take on aggressive hardware roadmaps. He is trying to turn future quantum computers into tests of quantum theory itself.

For builders and investors, that puts this paper in an unusual category. Most debate over quantum advantage lives in familiar territory: error rates, fault tolerance overhead, decoder performance, cryogenics, control electronics, and whether useful applications arrive before the money gets bored. Palmer’s paper relocates the fight to the foundations of physics. The claim is not that engineers are behind schedule. The claim is that the theory telling them what should be possible may be too permissive.

That is why the strongest caveat belongs near the top, not hidden in paragraph nine like an apology. Standard quantum mechanics is one of the most empirically tested frameworks in science. Replacing part of its mathematical structure is an ambitious move, to put it gently. Gizmodo’s coverage correctly treated the paper as a large speculative swing rather than a consensus update from the quantum-computing field. Publication in PNAS means the argument got a serious hearing. It does not mean the field has signed a confession.

Palmer’s new paper also is not an isolated one-off. A companion arXiv preprint from February, “Solving the Mysteries of Quantum Mechanics: Why Nature Abhors a Continuum”, places the 1,000-qubit ceiling inside a much broader program touching Bell’s theorem, uncertainty, holism, and gravity. That context is useful because it shows where the claim comes from: not from a surprise hardware anomaly, but from a long-running attempt to rebuild quantum mechanics on continuum-free foundations. Readers deciding how seriously to take the ceiling should know they are being asked to buy into the larger package.

The crypto angle is part of why this argument is getting attention. If Palmer is right, the widely discussed long-term threat that fault-tolerant quantum machines pose to RSA would be sharply constrained. The Quantum Insider, a trade publication covering the quantum industry, leaned into that implication. But “RSA may be safe after all” is still a conditional statement resting on a minority theoretical framework, not a newly observed failure mode in quantum processors.

What to watch next is straightforward enough. If larger, cleaner, more deeply error-corrected quantum systems arrive over the next several years, they will not just test company roadmaps; under Palmer’s framing, they could test whether standard quantum mechanics remains the right description at scale. That is a far more interesting story than “quantum computers have a fundamental limit,” and also a less lazy one. For now, Palmer has offered the field a wager. Nature has not yet cashed it.