The paper proposes a new category of limitation on quantum computation distinct from decoherence, control error, and algorithmic complexity arising from the discreteness of an underlying periodic gauge-graph model of spacetime, and derives it explicitly as εF ≳ 2π/L from single-valuedness of the U(1) holonomy on the graph. We quantify the bound against the phase precision required by Shor's algorithm across several RSA key sizes, showing the gap is too large for any near-term cryptographic relevance, and we identify the physically meaningful, testable content as a saturation of residual phase error with hardware scale rather than the underlying cosmological number itself. What we believe is new here is the derivation: rather than asserting a fundamental limit by analogy with other Planck-scale arguments, we obtain it as a direct structural consequence of a specific lattice model and give a falsifiable laboratory protocol (Sec. V) for testing it on existing superconducting processors.
The paper proposes a new category of limitation on quantum computation distinct from decoherence, control error, and algorithmic complexity arising from the discreteness of an underlying periodic gauge-graph model of spacetime, and derives it explicitly as εF ≳ 2π/L from single-valuedness of the U(1) holonomy on the graph. We quantify the bound against the phase precision required by Shor's algorithm across several RSA key sizes, showing the gap is too large for any near-term cryptographic relevance, and we identify the physically meaningful, testable content as a saturation of residual phase error with hardware scale rather than the underlying cosmological number itself. What we believe is new here is the derivation: rather than asserting a fundamental limit by analogy with other Planck-scale arguments, we obtain it as a direct structural consequence of a specific lattice model and give a falsifiable laboratory protocol (Sec. V) for testing it on existing superconducting processors.
Since Turing, it's been generally accepted that computing systems have two types of limitations: algorithmic (some problems are fundamentally unsolvable) and engineering (the hardware is imperfect, noisy, and breaks). Quantum computing has added a third type— complexity : some problems are solvable, but require resources that grow faster than any polynomial. This supplement introduces a fourth type of restriction, previously not described in the literature: The fundamental limit of quantum computing (FQC) is a limit on the precision of any quantum computing device, which arises not from imperfections in the implementation, but from the discrete structure of spacetime at the Planck scale. This limit cannot be overcome by any technological advancement. It is not a consequence of decoherence , thermal noise, or imperfect gates. It is built into the geometry of reality—just as the speed of light is built into the structure of spacetime and cannot be overcome by any acceleration.Unlike collapse-model-based limits on quantum hardware, the Fundamental Limit of Quantum Computation is proposed as an ontological bound arising from the discrete structure of spacetime itself.
Quantum Phase Machines argues that the central obstacle to scalable quantum computing is not noise, materials, or fabrication — but the unit of information itself.After two decades of engineering progress, superconducting quantum processors still rely on fragile single-particle quantum states protected by massive error-correction overheads. This book proposes a different approach: encode information in the collective phase of macroscopic superconducting domains rather than in individual qubits. By exploiting the intrinsic rigidity of phase-locked Cooper pair ensembles, it suggests that error suppression can be achieved natively at the hardware level, without the exponential overhead of quantum error-correcting codes.The argument is developed in four parts. Part I reframes the decoherence problem in engineering terms and introduces the dynamic impedance principle underlying collective robustness. Part II proposes a physical model of structured photons and electrons that reinterprets superconductivity, entanglement, and coherence as geometric properties of extended electromagnetic systems. Part III defines the Temporal Bit (T-bit) architecture and its gate operations using existing Josephson-junction technology. Part IV presents an experimental roadmap with falsifiable predictions and concrete device proposals.Written for physicists and engineers fluent in Maxwell’s equations and solid-state physics, Quantum Phase Machines offers a radical but testable alternative to orthodox quantum computing architectures. Whether ultimately confirmed or refuted, its central claim is precise: scalable quantum computation will require exploiting collective physical structure, not merely protecting fragile quantum states.
We derive a fundamental lower bound on the gate error rate of any quantum computing platform from the K-functional framework. Two irreducible error sources compete: K_rec record back-action (the environment acquires information about which gate was applied, corrupting the qubit) and K_ent thermal decoherence (the qubit thermalizes during the gate operation). The K_rec error decreases with weaker qubit-control coupling while the K_ent error increases, producing a U-shaped curve with a minimum at the optimal coupling g/w = (8pi/Q)^(1/3), where Q is the qubit quality factor. The minimum error rate is e_floor = 0.512 Q^(-2/3). At this minimum, K_rec contributes exactly one-third of the total error and K_ent contributes two-thirds, a ratio fixed by the cubic optimization and not adjustable by engineering. The floor scales as Q^(-2/3), not Q^(-1) as standard decoherence theory would suggest. This sub-linear scaling is a testable prediction: on a log-log plot of error rate versus quality factor across platforms, the K-functional predicts slope -2/3 rather than -1. The same one-loop factor 1/(16pi^2) that governs the chiral anomaly (Paper 12) and the cosmological constant (Paper 13) sets the K_rec back-action rate, connecting quantum computing errors to fundamental physics. The Bekenstein bound limits the maximum quality factor to Q_max = S_Bek = 2piER/(hbar c), giving an absolute error floor of 0.512 S_Bek^(-2/3). At the Planck scale (the monopole of Paper 3), S_Bek = 2pi, giving a 15% per-operation error rate, above the fault-tolerance threshold. The gauge algebra SU(3) x SU(2) x U(1) survives the cosmological bounce because 2pi bits is just sufficient to encode the algebra, and the bounce attractor (Paper 11, gain 0.23) provides cross-cycle error correction. The algebra is selected in a single bounce: it is the only key that fits a 2pi-bit lock.
Quantum computers pose a fundamental threat to widely deployed public-key cryptosystems, such as RSA and ECC, by enabling efficient integer factorization using Shor's algorithm. Theoretical resource estimates suggest that 2048-bit RSA keys could be broken using Shor's algorithm with fewer than a million noisy qubits. Although such machines do not yet exist, the availability of smaller, cloud-accessible quantum processors and open-source implementations of Shor's algorithm raises the question of what key sizes can realistically be factored with today's platforms. In this work, we experimentally investigate Shor's algorithm on several cloud-based quantum computers using publicly available implementations. Our results reveal a substantial gap between the capabilities of current quantum hardware and the requirements for factoring cryptographically relevant integers. In particular, we observe that circuit constructions still need to be highly specific for each modulus, and that machine fidelities are unstable, with high and fluctuating error rates.
This revision withdraws the claim, present in earlier circulated versions of this preprint, that FLQC renders Shor's algorithm physically unrealisable for RSA-2048 and sets an obstruction threshold at n* ≈ 100 bits (formerly §3.1). That argument rested on an invalid premise: that a single physical rotation gate must directly realise an exponentially small ideal phase angle. This is contradicted by established results in quantum-circuit compilation (Solovay–Kitaev/Ross–Selinger synthesis into a fixed discrete gate set; Coppersmith's approximate quantum Fourier transform) and by an explicit, quantitative treatment of exactly this question already in the peer-reviewed literature (Fowler & Hollenberg, Phys. Rev. A 70, 032329, 2004), which shows that factoring integers of thousands of bits requires no controlled rotation finer than - roughly 28 orders of magnitude coarser than the Δθmin estimate used throughout this work. The corrected argument is given in §3.1 and Part V.. Numerical simulation phase-resolution test protocol with qiskit: https://github.com/SergejMaterov/FLQC-Protocol
Standard quantum decoherence theory explains the loss of quantum coherence as arising entirely from the coupling between a system and its external environment. In that framework, the decoherence rate decreases as temperature drops and environmental coupling weakens, vanishing in the ideal limit of absolute zero. This prediction relies on the assumption that time is continuous at the most fundamental scale. We explore the consequences of relaxing that assumption. If physical time possesses a smallest unit τ, then each discrete update of a quantum state necessarily involves at least one irreducible phase refresh. From this we derive a lower bound on the decoherence rate that is independent of any environment: Γ_disc = 1/(2πτ). The bound is intrinsic to the discrete structure of time and cannot be eliminated by cooling or isolating the system. The value of τ is fixed by matching the kinetic term of a discrete U(1) gauge field to the standard continuum theory, yielding τ ≈ 29.7 Planck times. This gives Γ_disc ≈ 3.45 × 10^41 s^{-1}, on the order of the Planck frequency. A crucial difference from standard decoherence theory emerges: while the standard framework permits the decoherence rate to approach zero at absolute zero, the discrete-time framework forbids this convergence absolutely. The two theories thus make mutually exclusive predictions, offering a clear conceptual criterion for experimental distinction. We discuss experimental prospects with full transparency. Current environmental decoherence rates (kHz to GHz) lie many orders of magnitude above Γ_disc, so a direct measurement of the predicted plateau is not feasible with present technology. The falsifiability of the prediction rests on the qualitative, principle-level claim that a strictly zero decoherence rate can never be observed, no matter how perfectly isolated a system becomes. As ultralow-temperature techniques advance, a persistent non-zero decoherence floor would support the discrete-time picture. The paper is part of the Generative Discrete Action Principle series. All derivations leading to Γ_disc > 0 are self-contained and rely only on the three explicitly stated premises of a minimum time step, positive-definite state-update records, and S¹ periodicity of phase. Results borrowed from the broader framework, such as the numerical prefactor that fixes τ, are clearly labeled as citations.