Follow up on this post: #1457723

Seems like the paper finally got published in a peer reviewed journal (actually, that's a bit of a stretch, as contributed articles in PNAS, at least until the end of this year, let the authors decide who will referee their paper... so it is quite standard for the authors to ask some of their friends where they make sure to get the promise for a positive review ahead of time).

Of course, LARPers like Fred Krueger (https://x.com/dotkrueger/status/2093960825962930561) and Elon Musk (https://x.com/elonmusk/status/2093626798575624520) have already commented on it.

Significance

Is there a fundamental reason why quantum computers cannot factor large integers used for encryption today? We introduce a theory of quantum physics based on the notion that the continuum nature of quantum mechanics’ state space approximates something inherently discrete, and argue that the reason for such discreteness is gravity. From this we predict that quantum computers will never break realistic RSA-encrypted messages, for fundamental rather than practical reasons. This predicted breakdown of quantum theory may be falsifiable in a few years. If verified, quantum computers’ biggest impact may be in the development of new finite theories which synthesize quantum and gravitational physics, potentially with commercial benefits (albeit for future generations) eclipsing those derived from quantum mechanics alone.

Abstract

Motivated in part by John Wheeler’s assertion that the continuum nature of Hilbert Space conceals the “it-from-bit” information-theoretic character of the quantum wavefunction, a theory of quantum physics (Rational Quantum Mechanics–RaQM) is proposed based on a specific discretization of complex Hilbert Space. The Schrödinger equation is not modified in RaQM, even during measurement. However, the bases in which the quantum state is defined must satisfy certain rational-number constraints. These constraints lead to the notion of finite qubit information capacity : For any  qubit state, there is insufficient information in the  qubits (linearly growing in ) to allocate even one bit to each of all  continuum degrees of freedom (exponentially growing in ) associated with quantum mechanics/theory (QM, where ). It is proposed that the discretization of Hilbert Space in RaQM is due to gravity, hence QM is the (singular) continuum limit of RaQM at . On this basis, it is estimated that  lies between about 200 and 400 for current qubit technologies, and will never exceed 1,000. While QM and RaQM are experimentally indistinguishable for small numbers of qubits, RaQM predicts that the exponential advantage of quantum algorithms which, like Shor’s, require bases with maximal -qubit superposition/entanglement, will have saturated at 1,000 perfect qubits. Hence, insofar as a classical computer will never factor a 2,048-bit RSA integer, RaQM predicts that a quantum computer will not either. This predicted breakdown of QM could be testable in less than 5 y.

In case @ScottAaronson still lurks around after his AMA (#1477467), I'd wonder what he has to say. He's mentioned Tim Palmer (the author of the PNAS article) before in his blog: https://scottaaronson.blog/?p=9138#comment-2016194.

flergalwit #139: Imagine that someone completely rejected Darwinian natural selection. So then, every time you asked them how complex adaptations arose in life on earth, they gave a whole incomprehensible patter about p-adic numbers, the upshot of which seemed to be that life just kind of arose because of a tendency built into the universe from the beginning.

“So then, we’re basically back to creationism?” you ask. “Intelligent design?”

“NO!” they bellow. “I said nothing about any Creator! Stop putting words into my mouth!”

This is how I feel about Sabine and Tim Palmer’s stance on superdeterminism. It’s insanity without even the saving grace of clarity.

(emphasis mine)