The 401st Qubit

Quantum foundations is not usually where you look for falsifiable predictions. It is where physicists argue about interpretation, produce two theories that make identical predictions, and go home. So a paper that says "here is a specific number of qubits, and if the machine works past it I am wrong" is worth paying attention to, whatever you think of the underlying theory.

That paper went into PNAS earlier this year. Tim Palmer, emeritus at Oxford, proposing something he calls Rational Quantum Mechanics.

The argument

Standard quantum mechanics assumes Hilbert space is continuous. The parameters describing a quantum state can take any real or complex value, including irrational numbers that would need infinite precision to specify exactly. Palmer's position is that this continuum is an idealisation, and that underneath it nature is discrete. Rational numbers only. Finite information per state.

The consequence cascades. In standard QM, every qubit you add doubles the dimensions of Hilbert space, which is precisely where the exponential advantage comes from. In RaQM, the information actually available to describe the system grows linearly, N qubits times some large but finite number of bits each. Exponential demand, linear supply. At some point the machine cannot allocate even one bit of information per dimension of the space it is supposed to be exploiting, and algorithms that depend on using all of that space stop beating classical ones.

Palmer puts that saturation point between roughly 200 and 400 qubits for current technologies, with a hard ceiling of 1,000 for any conceivable implementation. Shor's algorithm sits squarely in the affected class. Hence the headline: RSA-2048 survives, for reasons of physics rather than engineering.

The 401st qubit in my title is shorthand, not a figure from the paper. Palmer gives a range, not a threshold. But somewhere past the top of that range is the point at which the machine either keeps working or does not, and that is the whole experiment.

He also proposes a reason for the discreteness, which is gravity. Standard QM was written assuming gravity is irrelevant at subatomic scales. Palmer's claim is that it is not, and that it is what slices state space into finite steps.

Where this gets misreported

Three things get lost in the coverage, and all three matter.

This is a speculative proposal, not a result. There is no experimental evidence for the discrete state space Palmer describes. Quantum mechanics is among the most heavily tested theories we have, and RaQM is a proposed revision to it, reviewed by serious people, but a revision nonetheless. Treating it as established because it appeared in PNAS is a category error.

The falsification is clean but the confirmation is not. If someone entangles 1,500 error-corrected qubits and Shor's algorithm still works, Palmer is finished. No wriggle room, and that is to his credit. But if a machine falls over at 401 qubits, the overwhelmingly likely explanation is that the engineering is not there yet. Decoherence, gate fidelity, error correction overhead. Every quantum computer built so far has failed for boring reasons. The experiment that actually supports Palmer needs a specific failure signature, degradation that tracks his predicted saturation curve rather than tracking noise, and that does not improve when you throw better hardware at it. That is a far subtler test than "did it break".

The threshold everyone quotes is stale, and moving the wrong way for the theory. The 4,000 qubit figure for breaking RSA-2048 does the rounds because it has been repeated for years. The current best algorithm needs around 1,399 logical qubits. A February 2026 architecture from Iceberg Quantum claims RSA-2048 with under 100,000 physical qubits. Palmer's absolute ceiling is 1,000. That gap is now inside a factor of two and it is closing from the other direction.

What this means for anyone with a migration plan

Nothing. Genuinely nothing, and this is the part I would stress to any board that reads a headline about this and asks whether the post-quantum work can be shelved.

Harvest now, decrypt later does not care who is right. Traffic being captured today is being captured on the assumption that it becomes readable at some point in the next fifteen years. If Palmer turns out to be correct, that assumption fails and the stored data stays encrypted. If he is wrong, it does not. You are being asked to bet the confidentiality of everything you transmit this decade on an unvalidated revision to quantum mechanics, on the strength of one paper.

There is also the historical pattern. DES fell. SHA-1 fell. RSA-1024 was adequate until it was not. None of those fell to quantum computers. They fell to ordinary classical progress, better mathematics, and researchers finding weaknesses that were not obvious when the standards were written. A proof that quantum computers cannot break RSA is not a proof that RSA does not break.

The NIST post-quantum standards are finalised and shipping. Migration is a multi-year exercise in cryptographic inventory and dependency management, most of which is finding out where your keys actually live. That work is worth doing regardless, because you cannot rotate what you cannot find.

The genuinely interesting bit

Set the cryptography aside for a moment, because it is the least interesting consequence of the paper.

One correction to the coverage first: this does not simplify physics. RaQM keeps all of quantum mechanics and adds machinery underneath it. What it buys is a testable link between gravity and quantum foundations, which nobody has managed in a century.

Palmer has taken a metaphysical claim about the nature of reality, that the universe is finite and discrete rather than continuous, and attached a hardware roadmap to it. He has given the field a number and a timescale. He thinks we will know inside five years, and the experiment is one that people are already building machines to run for entirely commercial reasons.

That is rare, and it is the right way to make a claim of this kind. Whether he turns out to be right matters less than that he made himself checkable.

Antony Coppellotti is a CTO and founder at Gordion Solutions, working on agentic AI and architecture in regulated financial services.

If your board is asking whether the post-quantum work can wait, or whether the AI platform about to go live is safe to switch on, those are the questions Gordion answers. Get in touch.

Also published on LinkedIn, 6 September 2026.