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A peer-reviewed paper in PNAS predicts Shor's algorithm will fail at a few hundred error-corrected qubits — not from engineering limits, but because Hilbert space itself may be subtly wrong. Oxford's Tim Palmer argues quantum mechanics should be built on rational numbers, not the continuum.

newquantumera.comRational Quantum Mechanics and the Qubit Ceiling with Tim PalmerWhat if the mathematical foundation of quantum mechanics — the infinite continuum of Hilbert space — is subtly wrong, and quantum computers are about to prove it? Tim Palmer, Royal Society Research Professor Emeritus at Oxford and the physicist who revolutionized weather forecasting with ensemble…

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It's an interesting idea. As thermalization is fundamentally a process of spreading entanglement, I would think that this theory would imply some limit to the degree to which subsystems can thermalize and thus violations of thermodynamic laws.