We apply Quantum State Geometry (QSG) \cite{Lau26QED}— finite Fisher wave packets, maximal energy bound, and solid worldtube corpuscles — to quantum computing materials. By identifying $L_{\min}$ as the information radius of a qubit, we derive finite exchange interaction, Podolsky-suppressed charge noise, and geometric bounds on dephasing and valley splitting. Silicon spin qubits, superconducting transmons, and topological nanowires are treated as QSG systems where the ghost pole $M_G=1/L_{\min}$ becomes a physical collective mode. *Author DisclaimerAll underlying concepts, frameworks, and core research directions are the original work of the author. Generative AI tools were used strictly for assistance in manuscript drafting, code generation, and figure preparation. All theoretical formulations and mathematical proofs included herein are unverified AI-generated drafts shared as preliminary proposals for discussion and community review.
We apply Quantum State Geometry (QSG) \cite{Lau26QED}— finite Fisher wave packets, maximal energy bound, and solid worldtube corpuscles — to quantum computing materials. By identifying Lmin as the information radius of a qubit, we derive finite exchange interaction, Podolsky-suppressed charge noise, and geometric bounds on dephasing and valley splitting. Silicon spin qubits, superconducting transmons, and topological nanowires are treated as QSG systems where the ghost pole MG=1/Lmin becomes a physical collective mode. *Author DisclaimerAll underlying concepts, frameworks, and core research directions are the original work of the author. Generative AI tools were used strictly for assistance in manuscript drafting, code generation, and figure preparation. All theoretical formulations and mathematical proofs included herein are unverified AI-generated drafts shared as preliminary proposals for discussion and community review.
We provide a philosophical analysis of Quantum State Geometry (QSG). QSG is not a new particle or a new force, but a proposal for a bounded ontology: existence is coextensive with distinguishability in a compact projective space CPn. Time is not a container but an accumulation of Fubini-Study distance, dt=ℏ/ΔEdsFS. The engine of time is not interaction but positive curvature RFS>0 driving Jacobi divergence ξ¨+RFSξ=0. We argue this constitutes a third path beyond substantival and relational time: an objective, geometric becoming that resolves the measurement problem without an external observer, and establishes a framework of Ontic Structural Realism (OSR). *Author DisclaimerAll underlying concepts, frameworks, and core research directions are the original work of the author. Generative AI tools were used strictly for assistance in manuscript drafting, code generation, and figure preparation. All theoretical formulations and mathematical proofs included herein are unverified AI-generated drafts shared as preliminary proposals for discussion and community review.
Time has long been a barrier to unifying quantum mechanics and gravity. Treated as a fundamental coordinate, it contributes directly to ultraviolet divergences and obstructs a consistent formulation of dynamics. We propose Quantum State Geometry (QSG) as a kinematic prototype in which time is emergent, defined as change of state measured by the Fubini--Study line element. This relational definition avoids treating time as an external parameter and ties evolution directly to Hilbert space geometry. Building on this foundation, we introduce three further kinematic constraints: bounded energy variance, minimal length, and commutator deformation. Together, these encode ultraviolet regularization into the algebra of observables while preserving a geometric notion of evolution. The single move reinterprets seven long-standing paradoxes -- speed of light, twin, entanglement/EPR, black hole entropy, measurement/Zeno, grandfather/CTC, and firewall -- as consequences of dsFS and Lmin. We then turn QSG on itself to expose five new paradoxes it creates -- covariance, minimal-length Lorentz contraction, clock regress, factorization, and emergence circularity -- and outline a research program via modular Hamiltonians, Bures metric, and non-commutative geometry. QSG is thus a scaffold linking relational time with UV cutoffs, bridging quantum information geometry and quantum gravity phenomenology. *Author DisclaimerAll underlying concepts, frameworks, and core research directions are the original work of the author. Generative AI tools were used strictly for assistance in manuscript drafting, code generation, and figure preparation. All theoretical formulations and mathematical proofs included herein are unverified AI-generated drafts shared as preliminary proposals for discussion and community review.
Quantum geometry - including both the quantum metric and Berry curvature - arises from the non-zero overlap of well-defined eigenstates and their adiabatic evolution across the Brillouin zone. It has revolutionized condensed matter physics and material science by explaining quantum Hall effects, establishing the modern theory of polarization, and enabling a systematic search for topological materials on a large scale. Yet, despite these advances, we lack a framework for leveraging quantum geometry in the strongly interacting regime. Bridging this gap is critical: if we can harness geometric responses in correlated metals, we stand to engineer desirable transport and optical properties using existing material platforms, thus bypassing the complex task of designing materials with tailored quantum geometry from scratch. In this thesis, we take steps toward such a framework. First, we analyze the resilience of topological boundary modes in the presence of electronic correlations, identifying when interactions preserve, diminish, or destroy boundary modes. Second, we reveal geometric fingerprints of fluctuations in magnetically ordered systems, tying the electric quantum metric to the formation of instabilities and chiral quasi-particle excitations. Third, we generalize quantum geometry to describe families of many-body wave functions, providing a new algorithm to compute state-manifold curvatures suited to interacting phases. Our approach combines analytical theory with numerical methods, including density functional theory and tensor-network simulations, and is supported by open-source software developed during the PhD. Together, these results advance the topological classification of interacting phases and extend quantum geometry from single-particle bands to correlation functions, providing tools to design materials and devices with targeted geometric responses.
Quantum geometry - including both the quantum metric and Berry curvature - arises from the non-zero overlap of well-defined eigenstates and their adiabatic evolution across the Brillouin zone. It has revolutionized condensed matter physics and material science by explaining quantum Hall effects, establishing the modern theory of polarization, and enabling a systematic search for topological materials on a large scale. Yet, despite these advances, we lack a framework for leveraging quantum geometry in the strongly interacting regime. Bridging this gap is critical: if we can harness geometric responses in correlated metals, we stand to engineer desirable transport and optical properties using existing material platforms, thus bypassing the complex task of designing materials with tailored quantum geometry from scratch. In this thesis, we take steps toward such a framework. First, we analyze the resilience of topological boundary modes in the presence of electronic correlations, identifying when interactions preserve, diminish, or destroy boundary modes. Second, we reveal geometric fingerprints of fluctuations in magnetically ordered systems, tying the electric quantum metric to the formation of instabilities and chiral quasi-particle excitations. Third, we generalize quantum geometry to describe families of many-body wave functions, providing a new algorithm to compute state-manifold curvatures suited to interacting phases. Our approach combines analytical theory with numerical methods, including density functional theory and tensor-network simulations, and is supported by open-source software developed during the PhD. Together, these results advance the topological classification of interacting phases and extend quantum geometry from single-particle bands to correlation functions, providing tools to design materials and devices with targeted geometric responses.
This work investigates whether macroscopic quantum teleportation — the idea of “teleporting ourselves” — is possible under the laws of physics. While quantum teleportation is exact for single qubits, extending the protocol to biological organisms faces insurmountable barriers. We demonstrate that exponential Hilbert‑space growth, rapid decoherence at biological temperatures, chaotic error amplification, and hard thermodynamic limits (energy‑time uncertainty and the Bekenstein bound) render human‑scale teleportation fundamentally impossible. Corrected quantitative estimates show decoherence times as short as 10−19 seconds and power requirements exceeding 1014 watts, grounding the argument in concrete physics. The paper distinguishes between what quantum mechanics permits in principle and what thermodynamics forbids in practice, offering a rigorous synthesis of quantum information theory and physical law. *Author DisclaimerAll underlying concepts, frameworks, and core research directions are the original work of the author. Generative AI tools were used strictly for assistance in manuscript drafting, code generation, and figure preparation. All theoretical formulations and mathematical proofs included herein are unverified AI-generated drafts shared as preliminary proposals for discussion and community review.
Quantum geometry – including both the quantum metric and Berry curvature – arises from the non-zero overlap of well-defined eigenstates and their adiabatic evolution across the Brillouin zone. It has revolutionized condensed matter physics and material science by explaining quantum Hall effects, establishing the modern theory of polarization, and enabling a systematic search for topological materials on a large scale. Yet, despite these advances, we lack a framework for leveraging quantum geometry in the strongly interacting regime. Bridging this gap is critical: if we can harness geometric responses in correlated metals, we stand to engineer desirable transport and optical properties using existing material platforms, thus bypassing the complex task of designing materials with tailored quantum geometry from scratch. In this thesis, we take steps toward such a framework. First, we analyze the resilience of topological boundary modes in the presence of electronic correlations, identifying when interactions preserve, diminish, or destroy boundary modes. Second, we reveal geometric fingerprints of fluctuations in magnetically ordered systems, tying the electric quantum metric to the formation of instabilities and chiral quasi-particle excitations. Third, we generalize quantum geometry to describe families of many-body wave functions, providing a new algorithm to compute state-manifold curvatures suited to interacting phases. Our approach combines analytical theory with numerical methods, including density functional theory and tensor-network simulations, and is supported by open-source software developed during the PhD. Together, these results advance the topological classification of interacting phases and extend quantum geometry from single-particle bands to correlation functions, providing tools to design materials and devices with targeted geometric responses.