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Qeios

Electron Wave-Spin Qubit

Ju Gao, Fang Shen

Published Apr 29, 2025• 0 citations
Publisher

Abstract

This work proposes a wave-entity perspective of the electron spin qubit, treating the electron as a continuous physical wave rather than a point-like particle. In this theoretical framework, each spin qubit corresponds to a distinct current density configuration, offering a resolution to the paradox of a particle appearing to spin both up and down simultaneously. We further predict the existence of a persistent, azimuthally asymmetric magnetic field associated with the wave-spin qubit, an effect not anticipated by the conventional particle-spin model. Notably, the qubit’s relative phase governs the orientation of both the current and the magnetic field, suggesting a mechanism for direct, local interactions between qubits. This phase-dependent coupling could form the basis for inherently parallel quantum computing architectures, in contrast to the sequential operations of gate-based logic. While this framework is grounded in theoretical analysis, it yields testable predictions—particularly regarding the magnetic field structure—that invite experimental verification. By treating the electron wave as the fundamental physical entity, rather than a probabilistic abstraction, we explore the possibility of a quantum model that is deterministic, local, causal, and fully consistent with special relativity.

DOI
10.32388/m4x95c

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This work proposes a wave-entity perspective of the electron spin qubit, treating the electron as a continuous physical wave rather than a point-like particle. In this theoretical framework, each spin qubit corresponds to a distinct current density configuration, offering a resolution to the paradox of a particle appearing to spin both up and down simultaneously. We further predict the existence of a persistent, azimuthally asymmetric magnetic field associated with the wave-spin qubit, an effect not anticipated by the conventional particle-spin model. Notably, the qubit’s relative phase governs the orientation of both the current and the magnetic field, suggesting a mechanism for direct, local interactions between qubits. This phase-dependent coupling could form the basis for inherently parallel quantum computing architectures, in contrast to the sequential operations of gate-based logic. While this framework is grounded in theoretical analysis, it yields testable predictions—particularly regarding the magnetic field structure—that invite experimental verification. By treating the electron wave as the fundamental physical entity, rather than a probabilistic abstraction, we explore the possibility of a quantum model that is deterministic, local, causal, and fully consistent with special relativity.
Abstract As a continuation of our earlier investigations into electron wave–spin, we analyze the electron spin and its qubit in a cavity by treating the electron as a physical wave obeying the Dirac equation. In this view, a qubit is a current–density configuration whose orientation is fixed by the relative phase, rather than a particle carrying simultaneous ‘up’ and ‘down’ spin states with assigned probabilities. The resulting magnetic–moment density, derived from the current, displays a richer vector distribution and topology than the fixed axial dipole weighted by probability density in the conventional wave–particle model. Both frameworks yield the same total moment of one Bohr magneton and are indistinguishable in uniform external fields, yet their ontological differences predict distinct couplings to structured fields and spin–spin interactions. These contrasts motivate further exploration of dynamical consequences within the wave–entity framework, including Aharonov–Bohm–like responses that provide testable alternatives to conventional wave–particle duality.
As a continuation of our earlier investigations into electron wave–spin, we analyze the electron spin and its qubit in a cavity by treating the electron as a physical wave obeying the Dirac equation. In this view, a qubit is a current–density configuration whose orientation is fixed by the relative phase, rather than a particle carrying simultaneous “up” and “down” spin states with assigned probabilities. The resulting magnetic–moment density, derived from the current, displays a richer vector distribution and topology than the fixed axial dipole weighted by probability density in the conventional wave–particle model. Both frameworks yield the same total moment of one Bohr magneton and are indistinguishable in uniform external fields, yet their ontological differences predict distinct couplings to structured fields and spin–spin interactions. These contrasts motivate further exploration of dynamical consequences within the wave–entity framework, including Aharonov–Bohm–like responses that provide testable alternatives to conventional wave–particle duality.
As a continuation of our earlier investigations into electron wave--spin~\citep{GaoJOPCO22,EntropyEvaSpin2024}, we analyze the electron spin and its qubit in a cavity by treating the electron as a physical wave obeying the Dirac equation. In this view, a qubit is a current--density configuration whose orientation is fixed by the relative phase, rather than a particle carrying simultaneous ``up'' and ``down'' spin states with assigned probabilities. The resulting magnetic--moment density, derived from the current, displays a richer vector distribution and topology than the fixed axial dipole weighted by probability density in the conventional wave--particle model. Both frameworks yield the same total moment of one Bohr magneton and are indistinguishable in uniform external fields, yet their ontological differences predict distinct couplings to structured fields and spin--spin interactions. These contrasts motivate further exploration of dynamical consequences within the wave--entity framework, including Aharonov--Bohm--like responses that provide testable alternatives to conventional wave--particle duality.
This paper systematically reviews the theoretical progression from blackbody radiation to the foundations of quantum computing. Beginning with Planck’s energy quantization and the representation of electromagnetic wave electric field components, the wave-particle duality of photons is analogized to introduce the de Broglie relation between momentum and wave vector for matter waves, leading to the establishment of the matter wave function and the Schrödinger equation as its governing partial differential equation. The consistency between the rigorous solution for a one-dimensional infinitely deep rectangular potential well and the conclusions for a one-dimensional hydrogen atom is demonstrated. Subsequently, within the Dirac notation formalism, the wave function is expressed, and the correspondence between spatial differentiation and momentum is derived, formalizing the momentum operator (often referred to as first quantization). To lay the physical groundwork for manipulating two-qubit states in quantum computing, the potential energy function of an electron’s orbital magnetic moment in an external magnetic field is introduced, starting from the torque and work on a current-carrying rectangular coil. This is extended to the magnetic moment and potential energy of a spinning electron, where the orientation of the magnetic field determines the form of the potential and accordingly selects the three components of the Pauli operators. The properties of quantum gates corresponding to the Pauli operators are then examined for single-qubit states. A two-qubit state, constructed via the coupling of two arbitrary single-qubit states represented in a two-level system or electron spin, is shown to be uniquely expressible as a superposition of four eigen two-qubit states. The paper further investigates joint manipulations of two-qubit states, including evolution under X and Z gates conditioned on high- and low-level states, the representation of control-flow circuits (with the low-level as control), and the formulation of measurement and CNOT gates. Throughout this work, essential mathematical tools—including integration, matrix operations, complex Euler’s formula, and solutions to simple second-order ordinary differential equations—are incorporated to provide a coherent theoretical framework for state representation and gate operations in quantum computing.
Our study reveals electron spin in a cavity as a stable circulating current density, characterized by a torus topology. This current density circulates concentrically beyond the cavity boundary, illustrating the concept of evanescent wave spin. While the interaction with a uniform magnetic field aligns with established spin-field observations, our analysis of regional contributions deviates from particle-based spin predictions. The integration of charge and spin properties into a single Lorentz covariant entity suggests that the electron wave constitutes the fundamental and deterministic reality of the electron.
This work presents a structural interpretation of the electron in which its fundamental properties—charge, spin, and interaction—are derived from coherence structure rather than introduced as intrinsic postulates. The electron is described as a stable resonance configuration within a coherence-based field framework, allowing a unified physical interpretation of electromagnetic interaction, electron correlation, and atomic structure. A key aspect of the model is that the electron is not fully confined to three-dimensional space, but extends along an internal coherence dimension. Observable behavior is interpreted as a projection of this deeper structure, providing a structural basis for delocalization, tunneling, and orbital formation. Within this framework, charge arises from asymmetry in lateral coherence, while spin is understood as an internal phase-topological property. Electron–electron interaction is described in terms of coherence interference, offering a structural explanation for repulsion, pairing, and exclusion behavior. Electromagnetic phenomena are interpreted as coherence dynamics: fields correspond to continuous structure, while photons are treated as localized propagating excitations. This provides a unified but differentiated description of electromagnetic interaction. The framework is consistent with established theoretical descriptions while providing a physically interpretable basis for electron structure and its role in electromagnetism and atomic systems. It aims to clarify conceptual foundations rather than replace existing predictive models, and establishes a basis for further work in atomic structure and chemical behavior.