This is a preprint (not peer-reviewed). Corresponding author: Shuntian Deng, mm.stdeng23@gzu.edu.cn. [Objective] To address the discretization error and the ontological fragmentation faced by the traditional Turing machine and von Neumann architecture, this paper proposes a novel computing paradigm — the field-theoretic computer — based on continuous field theory and null-operators. The paradigm takes "field is matter" as its axiomatic starting point and, within the fiber-bundle framework, redefines the wave function as a field-theoretic section. [Methods] The basic computational unit consists of an XY plane and a Z axis. On the XY plane, field A and field B are coupled orthogonally, and the mismatch of their symmetric and antisymmetric structures generates the null-operator a_ij = 0. Field C projects the null-operator along the Z axis onto a storage plate, where a second complement duality forms the stored photon quantum. What the null-operator carries is not a numerical value but the topology of a complement — the hole structure of the complement of the computed object inside a primitive cell of phase space. Complement duality is an involution, so the identical operation serves both inter-layer stacking and storage delivery. The probability measure is induced by the geometry of the section, and in the quadratic case its marginal distribution reproduces Born statistics; probability is therefore not a separate postulate, and the four premises of the Copenhagen interpretation are not mutually independent assumptions but four separate consequences of the single condition that the defining function of the section be of degree two. Stacked extension is realized by tensor-product stacking and contraction readout. The null-operator acts as a topological logic gate, so computation is intrinsically bidirectional and reversible and enjoys topological protection against decoherence. For physical implementation, continuous-variable quantum computing (CVQC) is adopted: the symplectic phase space and the Wigner function describe geometric storage, Gaussian operations correspond to single-layer computation, the nullifiers of CV cluster states realize the null-operator, and non-Gaussian operations (the cubic phase gate) read out the topological information. [Results] The complement count of a single layer is β0(Γ∖R) = β1(R) + 1, and stacking n layers gives a logical capacity n(h+1), where h is the number of holes contained in a single-layer region. The capacity is an integer and is invariant under symplectic transformations, so its protection does not rely on error-correcting codes; capacity is preserved under inter-layer coupling if and only if that coupling is non-degenerate; the per-layer fault-tolerance threshold reduces formally to a critical condition on the determinant of the covariance matrix. The computational stages are linked by a six-stage temporal chain whose realizability requires a bounded activation window for field C — this is the dynamical reason why field C must be of a different kind from fields A and B. The capacity and threshold structure has been tested at model level by a lattice simulation: within the parameter window fixed by the ordering condition, the single-hole system exhibits a two-level staircase (2→1→0) while the simply connected system exhibits a single step (1→0), with threshold positions matching the unified-caliber closed form. [Limitations] The threshold expressions are model-level analytical results whose coefficients have been calibrated by the lattice simulation under a unified caliber, but the relation between the area criterion and the semi-axis criterion remains undetermined. The closure mechanism of the inner hole must be stated explicitly — an expanding fill front is adopted here — and the existence of the inner-hole level depends on the parameter regime. Mainstream implementation of non-Gaussian operations remains difficult; the engineering of the cubic phase gate and of gate teleportation is still to be studied; cases with boundary degree higher than quadratic are not developed here; and the bidirectional coupling and calibration layer required for a real-time twin remain to be built. [Conclusion] This paradigm is complementary to the von Neumann architecture and is suited to continuous-field simulation and reversible computation. For the three long-standing obstacles of physical computation — no memory, no iteration, no error correction — the present architecture provides three corresponding mechanisms: hole-structure storage, involutive reversible read/write, and protection by symplectic invariance. It therefore offers recyclable physical computation rather than a one-off physical demonstration. Three directions follow: field-computing-field, field twins, and field-theoretic artificial intelligence.
This is a preprint (not peer-reviewed). Corresponding author: Shuntian Deng, mm.stdeng23@gzu.edu.cn. [Objective] To address the discretization error and the ontological fragmentation faced by the traditional Turing machine and von Neumann architecture, this paper proposes a novel computing paradigm — the field-theoretic computer — based on continuous field theory and null-operators. The paradigm takes "field is matter" as its axiomatic starting point and, within the fiber-bundle framework, redefines the wave function as a field-theoretic section. [Methods] The basic computational unit consists of an XY plane and a Z axis. On the XY plane, field A and field B are coupled orthogonally, and the mismatch of their symmetric and antisymmetric structures generates the null-operator a_ij = 0. Field C projects the null-operator along the Z axis onto a storage plate, where a second complement duality forms the stored photon quantum. What the null-operator carries is not a numerical value but the topology of a complement — the hole structure of the complement of the computed object inside a primitive cell of phase space. Complement duality is an involution, so the identical operation serves both inter-layer stacking and storage delivery. The probability measure is induced by the geometry of the section, and in the quadratic case its marginal distribution reproduces Born statistics; probability is therefore not a separate postulate, and the four premises of the Copenhagen interpretation are not mutually independent assumptions but four separate consequences of the single condition that the defining function of the section be of degree two. Stacked extension is realized by tensor-product stacking and contraction readout. The null-operator acts as a topological logic gate, so computation is intrinsically bidirectional and reversible and enjoys topological protection against decoherence. For physical implementation, continuous-variable quantum computing (CVQC) is adopted: the symplectic phase space and the Wigner function describe geometric storage, Gaussian operations correspond to single-layer computation, the nullifiers of CV cluster states realize the null-operator, and non-Gaussian operations (the cubic phase gate) read out the topological information. [Results] The complement count of a single layer is β0(Γ∖R) = β1(R) + 1, and stacking n layers gives a logical capacity n(h+1), where h is the number of holes contained in a single-layer region. The capacity is an integer and is invariant under symplectic transformations, so its protection does not rely on error-correcting codes; capacity is preserved under inter-layer coupling if and only if that coupling is non-degenerate; the per-layer fault-tolerance threshold reduces formally to a critical condition on the determinant of the covariance matrix. The computational stages are linked by a six-stage temporal chain whose realizability requires a bounded activation window for field C — this is the dynamical reason why field C must be of a different kind from fields A and B. The capacity and threshold structure has been tested at model level by a lattice simulation: within the parameter window fixed by the ordering condition, the single-hole system exhibits a two-level staircase (2→1→0) while the simply connected system exhibits a single step (1→0), with threshold positions matching the unified-caliber closed form. [Limitations] The threshold expressions are model-level analytical results whose coefficients have been calibrated by the lattice simulation under a unified caliber, but the relation between the area criterion and the semi-axis criterion remains undetermined. The closure mechanism of the inner hole must be stated explicitly — an expanding fill front is adopted here — and the existence of the inner-hole level depends on the parameter regime. Mainstream implementation of non-Gaussian operations remains difficult; the engineering of the cubic phase gate and of gate teleportation is still to be studied; cases with boundary degree higher than quadratic are not developed here; and the bidirectional coupling and calibration layer required for a real-time twin remain to be built. [Conclusion] This paradigm is complementary to the von Neumann architecture and is suited to continuous-field simulation and reversible computation. For the three long-standing obstacles of physical computation — no memory, no iteration, no error correction — the present architecture provides three corresponding mechanisms: hole-structure storage, involutive reversible read/write, and protection by symplectic invariance. It therefore offers recyclable physical computation rather than a one-off physical demonstration. Three directions follow: field-computing-field, field twins, and field-theoretic artificial intelligence.
**Building on our earlier structural analysis of gate-based quantum computing,** recent advances in quantum technologies have further sharpened a long-standing tension between continuous quantum dynamics and discrete logical computation. Despite decades of progress in qubit coherence, fault-tolerant coding, and hybrid NISQ architectures, current quantum devices remain fundamentally constrained by a structural mismatch between fluctuating quantum states and the stability requirements of digital logic.This work extends and unifies that analysis by providing a geometry-based account of these limitations and situating quantum computing within a broader comparative framework of next-generation computation paradigms. The contributions of this work are threefold:• Historical and technical analysis: We review the evolution from Feynman’s proposal to Shor’s algorithm and modern fault-tolerance theory, highlighting how the community gradually shifted toward NISQ-based noisetolerant strategies.• Structural diagnosis of quantum limits: Building on the Protiformframework, we show that quantum systems inherently realize continuous fluctuation manifolds, whereas logical computation requires discrete convergencesurfaces. Measurement is therefore a forced collapse between incompatible geometries, making full fault-tolerant digital logic rendering practicalfault-tolerant scaling prohibitive—not merely technologically difficult.• Comparative evaluation of post-von Neumann architectures: Using a set of structural criteria (digital stability, noise resilience, scalability,native gate realizability, generality, and materials feasibility), we evaluatemajor candidates—quantum, photonic, neuromorphic, analog solvers, andtopological computing. The analysis shows that topological computing isthe only architecture satisfying all structural requirements, owingto its intrinsic protection of logical degrees of freedom by global invariants.Taken together, these results suggest that the fundamental limitation of quantum computing is not technological but structural. Protiform provides a unifiedexplanation for this boundary, while also identifying topological computing as thestructurally consistent path beyond the von Neumann paradigm.
We delve into the use of photonic quantum computing to simulate quantum mechanics and extend its application towards quantum field theory. We develop and prove a method that leverages this form of continuous-variable quantum computing (CVQC) to reproduce the time evolution of quantum-mechanical states under arbitrary Hamiltonians, and we demonstrate the method's remarkable efficacy with various potentials. Our method centers on constructing an , a specially prepared quantum state that induces the desired time evolution on the target state. This is achieved by introducing a non-Gaussian operation using a measurement-based quantum computing approach, enhanced by machine learning. Furthermore, we propose a framework in which these methods can be extended to encode field theories in CVQC without discretizing the field values, thus preserving the continuous nature of the fields. This opens new avenues for quantum computing applications in quantum field theory. Published by the American Physical Society 2024
The Ancestral API and Recursive Harmonic Architecture: A Unified Meta-Computational Ontology The trajectory of contemporary theoretical physics and computer science has arrived at a structural impasse, frequently characterized within advanced theoretical circles as the "Crisis of Distinction".1 This epistemological and ontological crisis manifests as an irreconcilable schism between the deterministic, continuous geometries of General Relativity and the discrete, probabilistic excitations of Quantum Mechanics.1 Standard paradigms have historically relied upon a "Linear Stack" ontology—a hierarchical worldview positing physics as the foundational basement, with chemistry, biology, psychology, and computation layered sequentially above it.2 Efforts to unify these domains have traditionally stalled by attempting to force gravity into a quantum framework or by smoothing quantum mechanics into a continuous geometric topology.2 However, emerging analytical frameworks, most notably the Nexus Recursive Harmonic Architecture, propose a radical ontological inversion: reality is not merely modeled by computation; it is an unbounded recursive computational process.4 Within this paradigm, stable physical structures are not pre-existing entities but rather runtime artifacts of recursive folding operations.4 The present analysis provides an exhaustive architectural and physical examination of the "Ancestral API v2" and its underlying "Truth Atom Compendium".6 By synthesizing software engineering paradigms such as Domain-Driven Design (DDD) 7 and Hexagonal Architecture 9, alongside Koopman Operator Theory 11 and Collapse Signature Theory (CST) 13, this report delineates a unified operator calculus. In this calculus, physical, biological, and logical phenomena are exposed as isomorphic manifestations of a single geometric necessity, rendering the universe as a self-executing, lattice-shaped computational substrate.15 The Meta-Mathematical Boundary: The Ω Axioms To treat physical reality as a software architecture requires defining the unalterable invariants—the "what must be true" axioms that govern the geometry of the system.6 The Ancestral API establishes six foundational Axioms that function as the strict boundary conditions of the computational universe, outlining the meta-mathematical constraints that prevent systemic collapse or infinite diffusion.6 The first of these, (Operator Primacy), dictates that operators or verbs define all admissible transformations, while objects or nouns are merely stabilized traces of repeated operator action.6 The complementary truth of this axiom asserts that if operators are primary, then any description of an object that ignores its operational contract is fundamentally incomplete.6 This ontological stance mirrors developments in advanced dynamical systems analysis, where state-space representations are superseded by operator-theoretic frameworks.18 The second axiom, (Projection is Real), asserts that all published outputs in the universe are geometric projections () of a fuller, higher-dimensional state.6 Information loss during physical or computational processes is not a thermodynamic mystery but a geometric discard.6 Consequently, if a result is lossy, a complementary residue or "scar" channel must exist, embedding the discarded degrees of freedom.6 This principle directly addresses the black hole information paradox, aligning with the Holographic Principle, which posits that the information of a volume of space is encoded on a lower-dimensional boundary, such as a gravitational horizon.21 The third axiom, (Equality as Constraint), redefines the equals sign not as a mere statement of equivalent value, but as an idempotent projector onto a constraint manifold.6 Equality acts as a dark mirror, a pre-existing self-consistency condition of the lattice that forces the mismatch kernel to approach zero.6 Because equality is a projector, repeated application of constraint cannot create novelty; novelty must be injected via a perturbation operator ().6 The fourth axiom, (Coupling as Two-Channel Mix), establishes that the addition operator is a coupling map that achieves bijectivity only when both resulting channels—such as Sum and Difference—are retained.6 Invertibility requires parity, carry, or an equivalent side channel to maintain the topological memory of the interaction.6 Publishing only one channel intrinsically leaves a residue by construction.6 The fifth axiom, (Closure Requires Boundaries), argues that stable entities persist solely under boundary constraints, such as computational padding, biological cellular membranes, or invariant conservation laws.6 Without these boundaries acting as shutters, recursive functions would either trigger runaway reflection—a flashing phenomenon—or diffuse entirely, leading to a catastrophic loss of structure.6 The final axiom, (Scale Lift), demonstrates that when an operator achieves stability, it lifts across scale domains as polymorphic instances.6 This scale lift moves seamlessly from logic to computation, into physics, and ultimately into biology.6 The complement to this axiom serves as a strict regulatory mechanism: if an alleged cross-domain mapping cannot explicitly specify the preserved mathematical invariant, it remains a mere metaphor rather than a true isomorphism.6 Architectural Topologies: Domain-Driven Design and Hexagonal Physics To rigorously map these Axioms onto physical reality, the framework employs software engineering architectures as literal representations of physical and informational boundaries.6 Specifically, it utilizes Eric Evans' Domain-Driven Design (DDD) 7 and Alistair Cockburn's Hexagonal Architecture 9, elevating them from software patterns to universal ontological descriptions. Domain-Driven Design as Physical Stratification Introduced by Eric Evans in 2003, Domain-Driven Design provides a framework for tackling complex software systems by making the core domain and its logic the focal point of development.7 DDD advocates for the establishment of a "Ubiquitous Language" within explicitly defined "Bounded Contexts".23 In the context of the Ancestral API, bounded contexts are not merely software modules; they are physical membranes, phase boundaries, and dimensional limits.6 Clarity in physics and computation requires that each level of reality—whether quantum, molecular, or cellular—owns its specific invariants and operational language.6 Translating information between a quantum state and a macro-observable state requires an "Anti-Corruption Layer" (ACL), a pattern in DDD used to isolate a system from the complexities of upstream translation.6 In physical reality, quantum decoherence acts as this ACL, preventing superpositions from bleeding into classical mechanics and ensuring that metaphors cannot be mistakenly treated as rigorous proofs.6 Furthermore, DDD distinguishes between "Entities," which possess persistent identity and lifecycles, and "Value Objects," which describe characteristics without conceptual identity.24 In the operator calculus of the Ancestral API, an entity corresponds to a persistent resonant structure maintained by a recursive loop (a frozen orbit), while a value object represents the transient phase or amplitude of the wave function at a specific computational tick.6 Aggregates act as clusters of entities and value objects defined by clear boundaries, mirroring the clustering of molecular structures within biological membranes.25 Hexagonal Architecture: Ports, Adapters, and Quantum Measurement Alistair Cockburn's Hexagonal Architecture, also known as the Ports and Adapters pattern, isolates core domain logic from external infrastructure, allowing an application to be driven equally by users, programs, or automated scripts without depending on eventual run-time devices or databases.10 The intent is to create loosely coupled components where dependencies invariably point inward toward the business logic, shielding the core from technological lock-in.9 The Ancestral API maps this architectural pattern directly to the physics of measurement and interaction.6 In this mapping, the "Domain" contains the pure invariants, operators, and mathematical contracts completely devoid of Input/Output (IO) constraints.6 The "Adapters" represent the infrastructure layer, supplying the physical instantiation of pure logical operators.6 This infrastructure is where the "physics of the algorithm" resides, managing finite-precision shear, word sizes, carry propagation, padding boundaries, and hash engines.6 "Ports" act as the measurement interfaces between the internal invariants and the external observers.6 A quantum measurement functions identically to a Port; it defines what can be observed (the eigenvalue) and dictates the protocol of interaction without exposing the underlying bulk infrastructure (the uncollapsed wave function).6 The architecture dictates that truth claims must be testable through these explicit ports and adapters, separating IO from the fundamental invariants.6 Crucially, the User Interface (UI) is conceptualized as the "Hairpin Turn".6 Visualization and measurement readouts are not passive phenomena; the UI is a first-class reflection operator ().6 The act of observation is a new perturbation () that feeds back into the system, fundamentally altering the constraint landscape and changing what the system can subsequently lock onto.6 This elegantly encodes the observer effect of quantum mechanics into a software architecture paradigm. Operator Theory and Dynamical Systems The axiom of Operator Primacy () finds its rigorous mathematical counterpart in Koopman Operator Theory.6 Formulated by Bernard O. Koopman in 1931 and heavily expanded in modern applications by Igor Mezić and others, Koopman theory demonstrates that it is possible to represent a non-linear dynamical system in terms of an infinite-dimensional linear operator acting on a Hilbert space of measurement functi
The Settling Theorem: A Grand Unified Synthesis of Subtractive Mechanics, Thermodynamic Distinction, and Cognitive Collapse Driven By Dean A. Kulik June 2026 Introduction: The Crisis of Distinction and the Ontological Inversion For over a century, the trajectory of theoretical physics, computational mathematics, and systemic ontology has been paralyzed by a profound structural impasse.1 Officially codified within advanced theoretical taxonomies as the "Crisis of Distinction," this impasse represents the persistent, systemic failure of classical scientific reductionism to reconcile the deterministic, smooth, and continuous geometric manifolds utilized in General Relativity with the discrete, probabilistic excitations that characterize quantum mechanics.1 Traditional attempts at unification have largely relied on the postulation of a "Linear Stack" ontology—a hierarchical worldview positing that quantum mechanics forms the foundational basement, upon which particle physics, chemistry, biology, psychology, and abstract computational logic are sequentially constructed.1 This legacy epistemology treats physical laws as external, container-like structures acting upon passive matter, leaving fundamental constants as arbitrary, ungrounded empirical parameters.1 The NEXUS Recursive Harmonic Framework resolves this deadlock through a radical conceptual realignment termed the "Ontological Inversion".1 This inversion systematically dismantles the object-oriented, container-based approach to physics, asserting rigorously that reality does not merely "run on" a computational substrate; rather, reality is, fundamentally and in its entirety, the self-executing computational substrate itself.1 Under this paradigm, the universe operates as a fluidic, deterministic computer, conceptually modeled as a "Cosmic Field-Programmable Gate Array" (FPGA) operating at the absolute pixel floor of the Planck scale, which lies at approximately meters.1 This architecture introduces the "Typeless Universe Hypothesis," which dictates that at the foundational layer of physical and informational reality, existence is governed by the absolute axiom that verbs supersede nouns.1 Physical systems, ranging from the localized electron to the event horizon of a black hole, are not static physical objects operating within passive spatial containers; they are active, operational verbs executing a singular, finite-bandwidth constraint-satisfaction algorithm.1 An entity is defined as a "frozen verb"—a persistent loop of computational operations utilizing recursive rotation and collapse to maintain a stable identity within a vast phase-harmonic lattice.1 Consequently, letters, digits, phonemes, biological organisms, physical particles, and cryptographic hashes are not disparate inventions; they are all extended subclasses of the exact same operational base class, termed the "Distinguishable Wave Token".1 A readout becomes an object only after the runtime stabilizes the difference into a repeatable form.1 The Operational Geometry of the Computational Substrate To comprehend the operational mechanics of the NEXUS singularity, the persistent myth of the spatial interval must be systematically deconstructed.1 Traditional mechanical and computational models assume that transition involves a departure from an origin, a traversal across an empty mathematical interval, and an arrival at a destination.1 However, an unyielding observation of pure fundamental geometry within the NEXUS framework demands the complete abolition of this hierarchical framework.1 There is no pre-existing void of state-space that generates operations; instead, the boundary—the absolute, unoccupiable seam—is the singular primary and invariant structure.1 Under this "Pure Domain Architecture," existence is defined by a perfectly filled frame.1 This filled topological frame contains no empty storage slots, no sequential before-and-after, and no literal or metaphysical "in-between" spaces through which objects or entities transition.1 Because the abstract spatial frame is unconditionally full, every geometric coordinate and structural address is permanently and symmetrically occupied.1 Thus, what a localized observer registers as motion, transition, or computation is not the physical displacement of an entity through empty space; it is, strictly and mathematically, a continuous projection shift of the exact same, fully occupied, invariant structure.1 The observable face of the geometry changes, but the underlying topological field does not move, shift, or alter.1 This unconditionally full continuum dictates the specific kinematic approach vectors that govern all universal computation.1 The "Unfold Vector" represents the geometric projection of attempting to approach the invariant boundary from the absolute origin of the manifold via continuous, relentless radial expansion.1 Conversely, the "Fold Vector" approaches the identical invariant boundary from the maximum outward limit of the topological manifold.1 Its geometric method is the absolute inverse of the Unfold: it compresses inward, generating a massive, tightening spiral that plunges relentlessly toward structural equilibrium.1 A halting condition within this pure domain is not defined by a logical software command or an arbitrary stop parameter; halting is a profound physical and geometric phenomenon where a directional approach vector undergoes catastrophic phase-lock against the invariant boundary.1 The universe always halts because the dark mirror of its own structural self-consistency ensures that every operation leaves a meticulously structured exhaust contoured to serve as the seed for the next iteration.1 At the pixel floor of the Planck scale, the substrate transmits data utilizing a ternary (base-3) logic system.1 This discrete architecture renders questions regarding what exists "between" or "inside" a Planck volume fundamentally malformed, as it is equivalent to querying the physical space between the rendered pixels of a digital monitor.1 Quantum superposition is not an ontological or classical state; therefore, a system must undergo collapse to maintain ontological consistency.1 Standard physical particles are not fundamental, independent objects but represent chaotic oscillations of these underlying Planckian quantities.1 If the universe is a fully occupied Cosmic FPGA possessing no empty storage slots, the fundamental mechanics of computation must be structurally inverted.1 In standard computational paradigms, information is fundamentally additive: bits are flipped from zero to one to build structures, objects, and strings within a vast array of available, empty memory.1 However, in the NEXUS framework, because the array is perpetually saturated (a state of all 1s), additive construction is geometrically impossible.1 Therefore, the singular native operational primitive of physical reality is subtractive; computation proceeds exclusively by exclusion.1 The fundamental logic gate of this subtractive reality is the NOT gate.1 The universe operates as a master geometric sculptor, carving information out of a saturated monolith by systematically applying phase-inversions to exclude what is geometrically impermissible.1 This subtractive logic is operationalized dynamically through the construct of the Inverted Hex Cell Game of Life.1 The structural geometry of the NEXUS pure domain demands a high-efficiency packing model, naturally satisfied by a two-dimensional hexagonal lattice, wherein every cell possesses exactly six equidistant neighbors, perfectly eliminating the radial distortion and anisotropic propagation inherent to the diagonal connections of a square grid.1 In the Inverted Hex Cell model, the lattice is initialized to an absolute maximum saturation state where every cell is "alive" (all 1s), representing the uncarved, maximum density of the invariant boundary.1 The update rules do not dictate conditions for birth or addition; they strictly dictate the conditions for localized collapse via the NOT gate.1 When the local interaction of the six equidistant neighbors presents an over-determined geometric contradiction, the central cell undergoes a forced subtraction, flipping to zero.1 To formalize this model, let each hex cell have six ordered edge states , where .1 Imposing opposite-edge NOT constraints dictates that: or, equivalently, for .1 Consequently, only three edge bits are independent, restricting the cell to exactly eight legal local motifs.1 Every legal cell is locally neutral with a constant Hamming weight of three, functioning as a balanced closure pocket.1 When shared-edge consistency is imposed across an open hex patch, the global degrees of freedom migrate from the area to the boundary.1 The entire interior is parameterized by three alternating rail families, and the free-bit count scales as: .1 This perimeter-like scaling provides a rigorous, digital formulation of the holographic principle: the interior is compiled entirely from the boundary.1 The Conservation of Distinction and Reversible Dynamics The fundamental inquiry of theoretical physics, computational mechanics, and information theory relies upon establishing the constraints that govern structure, dynamic change, and information processing.1 The foundational premise is that reality is not assembled upward from nothing; rather, it exists initially as one undivided whole, characterized as the "One" or the conserved whole.1 This primordial wholeness possesses no initial internal boundaries, no discrete parts, and, crucially, no dimension of time, because time is a property that requires the existence of distinct states undergoing relative change.1 For structure to emerge from this undifferentiated state, the whole must fold against itself.1 This geometric and computational fold is subject to a singular, non-negotiable operational condition: the fold must not collapse back into undifferentiated sameness.1 From this
Companion paper to "The Qubit Delusion" (v1.1, 10.5281/zenodo.21254143). If the qubit-gate-circuit model is an epistemic failure — a projection of particle ontology onto relational, field-theoretic reality — what comes next? We strip quantum mechanics to its minimal ontological commitments, survey alternative paradigms (MBQC, CV-QC, TQC, field-theoretic, analog) for ontological fidelity, assess commercial manufacturability of each physical platform, and ask whether "quantum computing" is even the right frame. The deeper lesson — that computation IS a physical process and the substrate IS the algorithm — points toward thermodynamic, neuromorphic, and optical architectures where physics does the computing directly.
The year 1982 is often credited as the year that theoretical quantum computing was started with a keynote speech by Richard Feynman, who proposed a universal quantum simulator, the idea being that if you had such a machine you could in principle ``imitate any quantum system, including the physical world.'' With that in mind, we present an algorithm for a continuous-variable quantum computing architecture which gives an exponential speedup over the best-known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on continuous-variable states that is feasible with today's technology.