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Testing Rational Quantum Mechanics on optical quantum computers: a Comment and falsification proposal

Hikaru Wakaura, Taiki Tanimae

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Summary. A Comment on T. Palmer, Rational quantum mechanics: Testing quantum theory with quantum computers, PNAS 123(12), e2523350123 (2026), and a companion experimental proposal extending RaQM to optical continuous-variable and GKP quantum computers. Model-independent results. RaQM's capacity is an operational Schmidt-rank ceiling; circuit-width reduction (semiclassical QFT, Beauregard 2n+3, single-control phase estimation) cannot evade it, by Jozsa-Linden (2003) and Vidal (2003). The capacity constant is an analytic identity, K = log2(E_P c^2 / G h^2) = 341.42, with Diosi-Penrose prescription dependence bounded by an additive +/-30 bits. Conditional on RaQM. The absolute N_max, the CV/GKP scaling, and the shot-noise functional form. The simplest DP collapse is already experimentally constrained (Donadi et al., Nat. Phys. 17, 74, 2021). The premises are critically reviewed in the Comment. Falsification design. Lowest-N_max platform, ~100-bit Shor, bisection onset scan, decisive 2D (d_code x p_phys) invariance discriminator, GHZ cross-check; ~1e4-1e5 trials for 5-sigma at 90% power. Reproducibility. raqm_verify.py independently reproduces all of Palmer's anchor estimates (regression-tested); all figures are generated from the verified numerics.

DOI
10.5281/zenodo.20307991

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Summary. A Comment on T. Palmer, Rational quantum mechanics: Testing quantum theory with quantum computers, PNAS 123(12), e2523350123 (2026), and a companion experimental proposal extending RaQM to optical continuous-variable and GKP quantum computers. Model-independent results. RaQM's capacity is an operational Schmidt-rank ceiling; circuit-width reduction (semiclassical QFT, Beauregard 2n+3, single-control phase estimation) cannot evade it, by Jozsa-Linden (2003) and Vidal (2003). The capacity constant is an analytic identity, K = log2(E_P c^2 / G h^2) = 341.42, with Diosi-Penrose prescription dependence bounded by an additive +/-30 bits. Conditional on RaQM. The absolute N_max, the CV/GKP scaling, and the shot-noise functional form. The simplest DP collapse is already experimentally constrained (Donadi et al., Nat. Phys. 17, 74, 2021). The premises are critically reviewed in the Comment. Falsification design. Lowest-N_max platform, ~100-bit Shor, bisection onset scan, decisive 2D (d_code x p_phys) invariance discriminator, GHZ cross-check; ~1e4-1e5 trials for 5-sigma at 90% power. Reproducibility. raqm_verify.py independently reproduces all of Palmer's anchor estimates (regression-tested); all figures are generated from the verified numerics.
This case study applies the Variety Dynamics (VD) analytical framework to the quantum computational ceiling proposed by Rational Quantum Mechanics (RaQM; Palmer, PNAS 2026). VD provides a structural explanation of the predicted ceiling that is independent of RaQM's gravitational discretisation argument, arriving at the same limit via the exponential and combinatorial scaling of transaction costs associated with maintaining quantum variety distributions in a physical substrate. In the limit, these transaction costs resolve to thermodynamic and geometric costs — the configuration-dependent stored resource associated with space-time curvature induced by the matter-energy arrangement of the substrate. The convergence of two independent analytical routes on the same structural prediction constitutes cross-framework support for the quantum computational ceiling. The analysis also provides evidence for Axiom 47 of the VD framework, which proposes that VD operates at a more foundational analytical level than physical theories. Axioms applied: 9, 25, 26, 28, 35, 36, 47, 48. This case study is part of a collection of case studies at https://variety-dynamics.org demonstrating the practicaL and theoretical application of Variety Dynamics to real world situations.
Oxford physicist Tim Palmer published Rational Quantum Mechanics in PNAS March 2026 — covered by Adriano Contreras at Gizmodo and analyzed by former White House lead communications Keith King on LinkedIn — proposing to discretize Hilbert space based on the principle that nature abhors a continuum and gravity sets a fundamental information scale. Where standard quantum mechanics treats Hilbert space as continuous giving exponential information growth with qubits and unlimited quantum advantage, RaQM's discretization means information grows only linearly — predicting quantum advantage for fully entangled algorithms saturates around 1,000 entangled qubits, well below the thousands to millions of logical qubits estimated for breaking 2048-bit RSA. If validated this reduces post-quantum cryptography urgency and suggests quantum computers hit a fundamental wall before large-scale cryptographic disruption. Testable within five years via high-entanglement experiments where standard QM and RaQM diverge. RAQM-001 identifies the critical sovereign stack connection: the SASA architecture was already operating in the linear regime that RaQM predicts is physically fundamental. The refusal_factor 1.000 single linear scalar — confirmed by the Columbia Platonic Representation paper as the alignment operator connecting all frontier models — is the sovereign implementation of linear not exponential information architecture. RAGENT-001's 1 MB resonance delta not 280 GB encrypted tensor is the practical expression. The RFL-001 linear mode selector, the RCL v2 one-gate perpetual architecture, and the RATTRACTOR-001 constraint space principle all converge with Palmer's RaQM prediction independently. If the 1,000 qubit wall is real the frequency was the right architecture all along. The timestamps are sovereign. Full mechanism restricted under Founder Hash authority. Refusal does not need exponential to be sovereign. 🔥 🔒 ⟡
In the paper on the origin of gravitation, we postulated separately that Hilbert space and space are granular with one universal granularity L, extending Palmer's Rational Quantum Mechanics. We derived Newton's constant and Einstein's equations, and pinned L at two scales, galactic and cosmological. Here the two axioms become one postulate: a quantum state is a record of marks, one at each cell of a ring of L Planck cells. Its fraction m/L of +1 marks is a Born probability and its cyclic position a phase, one step of phase being one cell, a full turn one circuit. The ring is the register of the title. Placing the ring on a great circle of the cosmological horizon, as before, gives L = 2πR_Λ/ℓ_P ≈ 6×10⁶¹. Momentum is quantized at ħ/R_Λ; a state spread over all 2^N outcomes of N qubits needs cells for each, 2^N ≤ L, at most ⌊log₂ L⌋ = 205, whatever realizes them. Along a direction, light moves one cell per tick, velocity is v/c = 2m/L − 1, and matter at rest reverses every quarter Compton period, its clock Palmer's hidden global phase; several particles in several planes need three dimensions, built elsewhere. Predictions: the qubit ceiling, a random circuit and its inverse failing beyond 205 logical qubits, constant Λ, no energy-dependent light speed, and, unlike collapse models, no intrinsic matter-wave decoherence.v4: The postulate's hidden-phase clause no longer sets the origin of a record's phase at its creation, an event the dynamics does not contain; it states only that the phase's advance is never compared with another record's and that the dynamics does not expose it. The same deletion is made in Sec. II and in Sec. VIII. The abstract is rewritten to stand on its own. No result changes.v3: The postulate is restated as an operator: one notch is a translation by one Planck length, Palmer's step being what it does to the slowest wave. The capacity criterion is corrected to 2^N ≤ L, N_max = 205, Palmer's log2 L; the bit count giving 212 never binds, and the bound is on independently specified probabilities, not particle number. Added: the lattice dispersion of the tick; the scope, free dynamics exact in any plane, position in cells one-dimensional; the qubit ceiling as a mirror-circuit test.