This paper presents a novel quantum state control method basedon Multi-Path Closure Time (MPCT) theory. Through purely ge-ometric dynamical processes without external Hamiltonian driving,we achieve: (1) Significant quantum state amplification with aver-age 3.29× (maximum 3.70×) local state probability enhancement viaweak marking; (2) Observation of quantized peak spacing followingn2 patterns, specifically n2 = 4 corresponding to n = 2; (3) Naturalformation of multi-peak superposition states with average 3.2 signifi-cant peaks in geometric mode. The core mechanism involves MPCTclosure phase driving for temporal emergence, geometric vibration sta-bilization for coherence maintenance, and weak dissipation balancingimplementing the Principle of Existence Cost (PEC). This work es-tablishes a new paradigm for low-energy geometric quantum control,potentially revolutionizing quantum computation approaches.
This paper presents a novel quantum state control method basedon Multi-Path Closure Time (MPCT) theory. Through purely ge-ometric dynamical processes without external Hamiltonian driving,we achieve: (1) Significant quantum state amplification with aver-age 3.29× (maximum 3.70×) local state probability enhancement viaweak marking; (2) Observation of quantized peak spacing followingn2 patterns, specifically n2 = 4 corresponding to n = 2; (3) Naturalformation of multi-peak superposition states with average 3.2 signifi-cant peaks in geometric mode. The core mechanism involves MPCTclosure phase driving for temporal emergence, geometric vibration sta-bilization for coherence maintenance, and weak dissipation balancingimplementing the Principle of Existence Cost (PEC). This work es-tablishes a new paradigm for low-energy geometric quantum control,potentially revolutionizing quantum computation approaches.
We present a novel quantum state control method based on Multi-PathClosure Time (MPCT) theory that achieves significant quantum stateamplification through purely geometric dynamics without externalHamiltonian driving. The MPCT-τ framework demonstrates: (1) Average 2.50×(maximum 3.55×) local state probability enhancement via weak periodicmarking, (2) Observation of quantized peak spacing following n² patternswith n²=4 corresponding to n=2, (3) Natural formation of multi-peaksuperposition states with average 3.4 significant peaks in geometric mode,and (4) Non-zero entanglement entropy averaging 0.44, confirming genuinequantum correlations. The core mechanism involves emergent time scalesfrom MPCT phase closures, geometric vibrations for coherence maintenance,and weak dissipation implementing the Principle of Existence Cost (PEC). Thiswork establishes a new paradigm for low-energy geometric quantum controlwith only three core parameters, potentially revolutionizing quantumcomputation approaches.Keywords: Quantum state control, Geometric quantum computation, Multipath closure, Emergent time, Quantum amplification, n² quantization
This paper introduces the MPCT-τ (Multi-Path Closure with adaptive Time-constant) protocol, a novel geometric approach for selective amplification of tar-get states in quantum networks. By leveraging geometric phase closure relationscombined with adaptive time-scale feedback and weak marking perturbations, weachieve significant amplification of specific quantum states. Numerical simulationsdemonstrate an average amplification factor of 7.44× for target states in 12-nodenetworks, substantially outperforming pure geometric evolution (0.94×). The sys-tem exhibits controllable entanglement entropy (ranging from 0.000 to 0.690) andshows promising scaling behavior with network size. The protocol operates throughthree interconnected mechanisms: (1) geometric phase closure enhancement viatriangular loops, (2) adaptive τ feedback based on closure errors, and (3) weaksymmetry-breaking marking. Our results provide a new paradigm for geomet-ric approaches to quantum state manipulation and offer potential applications inquantum-enhanced computation, state preparation, and quantum sensing.
This paper presents a novel approach to understanding quantum phenomenathrough geometric analysis of classical-like trajectories. We introduce the MultiPhase Coupling Transform (MPCT) method, which extracts quantum informationfrom complex dynamical trajectories without presupposing quantum mechanicalformalism. Through numerical simulations, we demonstrate that discrete quantumnumbers emerge naturally from topological phase conditions (2π⟨r⟩ = nλ), withexperimental accuracy better than 2%. The action variable shows clearer quantization than energy, suggesting action may be a more fundamental quantum quantity.Our results indicate that quantization may have purely geometric-topological origins, independent of specific dynamical equations. The MPCT method providesa new tool for extracting quantum information from trajectory data and offers acomplementary perspective on the emergence of quantum behavior.Keywords: Quantum emergence, geometric quantization, trajectory analysis,MPCT transform, topological quantum numbers
This paper presents a novel computational framework for electron cloud deter-mination based on the Minimal Phase Closure Triangle (MPCT) method,fundamentally distinct from traditional quantum mechanical approaches. Unlikethe Schr¨odinger equation-based methods that rely on wavefunctions and probabil-ity amplitudes, our approach derives electron distributions directly from the geo-metric properties of phase space trajectories. We introduce a two-level theoreticalfoundation: at the abstract level, a relational matrix describes quantum systemsthrough their fundamental interrelationships; at the implementation level, MPCTnetworks provide concrete geometric realizations. The method successfully com-putes hydrogen atom electron clouds with remarkable accuracy: Bohr radius de-termination within 1.9% error, n2 law verification within 0.6% error, and spectralline prediction with 0.1% accuracy. This framework offers a geometric-first alter-native to conventional quantum computation, potentially opening new avenues forquantum system analysis and material design.Keywords: Electron cloud computation; Minimal Phase Closure Triangle; Phasespace geometry; Relational quantum mechanics; Geometric quantum computation;MPCT method
This paper investigates the application of high-order geometry to quantum state control, presenting a novel approach for dynamically adjusting quantum states to enhance the performance of quantum computing. Traditional quantum state control relies on static manipulation, while this method leverages high-order geometry to achieve adaptive control. We propose a framework centered around the concept of a "geometric resonance" that allows for efficient and controlled evolution of the quantum state. The core mechanism involves the creation of a set of geometric transformations that interact with the quantum system, driving it towards a desired state. The potential benefits of this approach include increased fidelity, enhanced coherence, and the ability to tailor quantum states for specific applications. This work provides a theoretical foundation and initial experimental exploration of this promising technique.
The geometric phase stands as a foundational concept in quantum physics, revealing deep connections between geometric structures and quantum dynamical evolution. Unlike dynamical phases, geometric phases exhibit intrinsic resilience to certain types of perturbation, making them particularly valuable for quantum information processing, where maintaining coherent quantum operations is essential. This article provides a review of geometric phases in the context of universal quantum gate construction, i.e., the geometric quantum computation (GQC), with special attention to recent progress in nonadiabatic implementations that enhance gate fidelity and/or operational robustness. We first review a unified theoretical framework that can encompass all existing nonadiabatic GQC approaches, then systematically examine the design principles of nonadiabatic geometric gates with a particular focus on how optimal control techniques can be leveraged to improve the accuracy and noise resistance. In addition, we conducted detailed numerical comparisons of various nonadiabatic GQC protocols, offering a quantitative assessment of their respective performance characteristics and practical limitations. Through this focused investigation, our aim is to provide researchers with both fundamental insights and practical guidance for advancing geometric approaches in quantum computing.