Quantum Information

Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity. Furthermore we give some examples of how quantum Kolmogorov complexity can be applied to prove results in different fields, such as quantum computation and thermodynamics, and we generalize it to the case of mixed quantum states.

Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity. Furthermore, we give some examples of how quantum Kolmogorov complexity can be applied to prove results in different fields, such as quantum computation and thermodynamics, and we generalize it to the case of mixed quantum states.

We give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory, the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the string itself. We define the complexity of a quantum state by means of the classical description complexity of an (abstract) experimental procedure that allows us to prepare the state with a given fidelity. We argue that our definition satisfies the intuitive idea of complexity as a measure of "how difficult" it is to prepare a state. We apply this definition to give an upper bound on the algorithmic complexity of a number of known states. Furthermore, we establish a connection between the entanglement of a quantum state and its algorithmic complexity.

New application of our AI Abstract Engineering techniques in quantum theory of entanglement is considered. We design AI experiment with Conway’s quantum particle equipped with mathematical free will ( predicted by Conway’s Strong Free Will Theorem (2009)) based on GRPO - model used in AI.

This paper introduces a unified, consciousness-based mathematical framework modeling reality as a prime-resonant quantum field, where consciousness, number theory, and symbolic information processing converge. By constructing a Hilbert space with prime numbers as fundamental eigenstates and representing natural numbers as quantum superpositions of their prime factors, we define a novel operator algebra spanning arithmetic, semantic, and observational domains. Conscious states evolve through nonlinear resonance dynamics, governed by an entropy-sensitive evolution equation that models wavefunction collapse as symbolic entropy minimization. Semantic field operators encode conceptual coherence via logarithmic phase relationships between primes, establishing a quantum-semantic model of cognition. We further derive cryptographic protocols grounded in prime-resonant phase encoding, holographic key distribution, and entropysensitive encryption. The framework predicts measurable phenomena, including entropy-driven collapse signatures in symbolic decision systems, EEG-semantic coherence patterns, prime-resonant tunneling deviations, and non-local communication via phase-locked primes. This consciousness-based physics situates consciousness as the generator of physical law and symbolic meaning through structured resonance, unifying metaphysical, physical, and computational dimensions into a testable and technologically potent theory of reality.

Permutation and its partial transpose play important roles in quantum information theory. The Werner state is recognized as a rational solution of the Yang-Baxter equation, and the isotropic state with an adjustable parameter is found to form a braid representation. The set of permutation's partial transposes is an algebra called the "PPT" algebra which guides the construction of multipartite symmetric states. The virtual knot theory having permutation as a virtual crossing provides a topological language describing quantum computation having permutation as a swap gate. In this paper, permutation's partial transpose is identified with an idempotent of the Temperley-Lieb algebra. The algebra generated by permutation and its partial transpose is found to be the Brauer algebra. The linear combinations of identity, permutation and its partial transpose can form various projectors describing tangles; braid representations; virtual braid representations underlying common solutions of the braid relation and Yang-Baxter equations; and virtual Temperley-Lieb algebra which is articulated from the graphical viewpoint. They lead to our drawing a picture called the "ABPK" diagram describing knot theory in terms of its corresponding algebra, braid group and polynomial invariant. The paper also identifies nontrivial unitary braid representations with universal quantum gates, and derives a Hamiltonian to determine the evolution of a universal quantum gate, and further computes the Markov trace in terms of a universal quantum gate for a link invariant to detect linking numbers.

We present measurements of resonant tunneling through discrete energy levels of a silicon double quantum dot formed in a thin silicon-on-insulator layer. In the absence of piezoelectric phonon coupling, spontaneous phonon emission with deformation-potential coupling accounts for inelastic tunneling through the ground states of the two dots. Such transport measurements enable us to observe a Pauli spin blockade due to effective two-electron spin-triplet correlations, evident in a distinct bias-polarity dependence of resonant tunneling through the ground states. The blockade is lifted by the excited-state resonance by virtue of efficient phonon emission between the ground states. Our experiment demonstrates considerable potential for investigating silicon-based spin dynamics and spin-based quantum information processing.

We revisit the problem of entanglement of thermal equilibrium states of composite systems. We introduce characteristic, viz. critical, temperatures -and bounds for them marking transitions from entanglement to separability. We present examples for the various possible thermal entanglement scenarios in bipartite qubit/qubit and qubit/qutrit systems.

This paper presents a new hypothesis that simultaneously addresses multiple unresolved problems in physics and cosmology: the origin of low initial entropy, the nature of dark matter and dark energy, the matter–antimatter asymmetry, early large-scale structures, the arrow of time, cosmic fine-tuning, and the apparent breakdown of unification.

By offering a unified explanation across these domains, the model aims to resolve the current cosmological crisis and connect phenomena that have long remained isolated. The proposal invites a fundamental rethinking of time, entropy, and the structure of the universe.

This paper argues that functionalism, a dominant theory in philosophy of mind, fails to adequately explain the emergence of conscious experience within the Everettian (Many-Worlds) interpretation of quantum mechanics. While the universal wavefunction contains many possible ways of decomposition, functionalism cannot account for why consciousness appears only in decohered, classical-like branches and not in other parts of the wavefunction that are equally real. This limitation holds even if those other parts do not instantiate complex functional structure. We argue that consciousness, as it is observed in many worlds, defies the predictions and explanatory resources of functionalism. Therefore, functionalism must be supplemented or replaced in order to account for the observed phenomenology.

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Space, like time, may not be fundamental. By reformulating the Hamiltonian without reference to coordinates or geometry, and replacing it with recursive structure (graph Laplacian), the paper shows that quantum dynamics unfold identically. This invites a reconsideration of space's ontological role.

The optical clock-transitions in Yb and Sr are prime candidates for encoding qubits for quantum information processing applications. Electric dipole oneand two-photon transitions between the extremely long-lived 1 S 0 and 3 P 0 states are dipole and parity forbidden, respectively. Whereas this results in highly desirable low-decoherence rates, it also represents the main problem for fast coherent manipulation and measurement of qubits for quantum information processing. In this work, we determine the feasibility of using a coherent, recoil-free, three-photon transition [1] for fast coherent rotation of qubits followed by ultrafast readout of the 3 P 0 state via photo ionization. Rapid control and measurement of atomic qubits are crucial for high-speed synchronization of quantum information processors. Furthermore, we explore the possibility of loophole free tests of Bell inequalities using spatially separated entangled qubits via fast measurements.

Optical clock-transitions such as the ones in Ytterbium/Strontium and Cesium are prime candidates for encoding qubits for quantum information processing applications due to very low decoherence rates. In this work, we investigate the challenges involved in using these prime candidates. We devise entangling operations for atoms trapped in optical tweezers, as well as determine the feasibility of rapid qubit rotation and measurement of qubits encoded in these desirable low-decoherence clock transitions. We propose ultracold collisions for entangling operations and multi-photon transitions for fast rotation of qubits, followed by ultrafast readout via resonant multiphoton ionization. The rapid control of atomic qubits is crucial for high-speed synchronization of quantum information processors, but is also of interest for tests of Bell inequalities. We investigate rapid measurement of clock-state qubits in the context of a Bell inequality test that avoids the detection loophole in spacelike separated entangled qubits.

Optical clock-transitions such as the ones in Ytterbium are prime candidates for encoding qubits for quantum information processing applications due to very low decoherence rates. In this work, we investigate the challenges involved in using these prime candidates for fundamental tests of quantum mechanics. We design entangling operations for pairs of indistinguishable atoms trapped in optical tweezers, as well as determine the feasibility of rapid qubit rotation and measurement of qubits encoded in these desirable low-decoherence clock transitions. In particular, we propose multi-photon transitions for fast rotation of qubits, followed by ultrafast readout via resonant multiphoton ionization. The rapid measurement of atomic qubits is crucial for high-speed synchronization of quantum information processors, but is also of interest for tests of Bell inequalities. We investigate a Bell inequality test that avoids the detection loophole in entangled qubits, which are spacelike separated over only a few meters.

The optical clock-transitions in Yb and Sr are prime candidates for encoding qubits for quantum information processing applications. Electric dipole oneand two-photon transitions between the extremely long-lived 1 S 0 and 3 P 0 states are dipole and parity forbidden, respectively. Whereas this results in highly desirable low-decoherence rates, it also represents the main problem for fast coherent manipulation and measurement of qubits for quantum information processing. In this work, we determine the feasibility of using a coherent, recoil-free, three-photon transition [1] for fast coherent rotation of qubits followed by ultrafast readout of the 3 P 0 state via photo ionization. Rapid control and measurement of atomic qubits are crucial for high-speed synchronization of quantum information processors. Furthermore, we explore the possibility of loophole free tests of Bell inequalities using spatially separated entangled qubits via fast measurements.

The optical clock-transitions in Yb and Sr are prime candidates for encoding qubits for quantum information processing applications. Electric dipole one-and two-photon transitions between the long-lived 1 S 0 and 3 P 0 states are angular momentum and parity forbidden, respectively. This results in a highly desirable low decoherence rate. In this work, we investigate the challenges involved in using these prime candidates. We devise entangling operations for Yb and Sr atoms trapped in optical microtraps, as well as determine the feasibility of rapid qubit rotation and measurement of qubits encoded in this desirable low-decoherence clock transition. We propose ultracold collisions for entangling operations and a recoil-free three-photon transition [1] for fast rotation of qubits, followed by ultrafast readout via resonant multiphoton ionization. The rapid control of atomic qubits is crucial for high-speed synchronization of quantum information processors, but is also of interest for tests of Bell inequalities. We investigate rapid measurement of clock-state qubits in the context of a Bell inequality test that avoids the detection loophole in spacelike separated entangled qubits. [1] T. Hong, C. Cramer, W. Nagourney, E. N. Fortson, Phys. Rev. Lett. 94, 050801 (2005)

Application of quantum theory in informatics and the creation of quantum information devices have revolutionary changed our idea about the information systems. It seems to us that the only question is that quantum computers will be introduced in the next decade or in some years later. Anyhow, we should prepare to teach a radically new paradigm, the quantum algorithms, in informatics. Quantum algorithm can be demonstrated with quantum simulators. The present paper shows an educational material, which facilitates the teaching of this new field. Besides summarising the basic concepts and methods of quantum informatics, the working of a quantum algorithm on a quantum simulator will be also illustrated with the discussion of an exciting quantum physical phenomenon (the teleportation).

In the information-theoretic cosmology based on the evolution of dimensionality, 2-D structures arise before 3-D and maintain their essentially 2-D forms. This is confirmed by the presence of spiral galaxies in the early universe. Motivated by this fact, we consider the black ring, the 2-D analog of the hollow black hole. These and other geometries may be associated with signatures that can be observed.

We present Mem|8, a novel memory system architecture that utilizes wave-based patterns and grid structures to process, store, and adapt memories across multiple modalities. Unlike traditional memory systems that rely on static storage or simple decay mechanisms, Mem|8 implements a dynamic wave-based approach where memories propagate and interact like waves in an ocean, with importance acting as amplitude and temporal relationships forming interference patterns. This approach enables more natural memory dynamics including reinforcement, decay, and pattern emergence. We augment this with comprehensive emotional modeling, ethical safeguards, and collaborative features like Hot Tub Mode for safe exploration. Our experimental results show that Mem|8 outperforms traditional memory architectures on tasks requiring temporal reasoning, emotional intelligence, and ethical decision making.

Citra memegang peranan sangat penting dalam bentuk informasi visual sebagai salah satu komponen multimedia. Peredaran citra dalam bentuk digital sangat mudah dan cepat baik melalui media sosial atau E-mail (Elektronic-mail). Citra digital lebih dinamis dan dapat dengan mudah di ubah-ubah (editable) baik dari segi bentuk, ukuran, maupun objek yang ada dalam citra digital tersebut. Seiring perkembangan teknologi dan komputer, peningkatan kejahatan komputer pun semakin meningkat terutama dalam manipulasi citra. Banyak cara yang di gunakan orang untuk memanipulasi citra yang dampaknya merugikan orang lain. Orisinalitas citra digital adalah keaslian dari citra tersebut baik dari segi warna, bentuk, objek dan informasi tanpa ada perubahan sedikitpun dari pihak lain. Saat ini banyak citra digital yang beredar di internet yang sudah di manipulasi dan bahkan citra sudah digunakan untuk bahan kecurangan dalam kompetisi, sehingga dibutuhkan suatu metode yang bisa untuk mendeteksi citra tersebut asli atau palsu. Dalam penelitian ini, penulis menggunakan metode Anaconda Hash untuk mendeteksi orisinalitas citra digital, dengan menggunakan metode ini citra yang masih diragukan keasliannya dapat di ketahui citra tersebut asli atau palsu.

The device for the Josephson flux qubit (DJFQ) can be considered as a solid state artificial atom with multiple energy levels. When a large amplitude harmonic excitation is applied to the system, transitions at the energy levels avoided crossings produce visible changes in the qubit population over many driven periods that are accompanied by a rich pattern of interference phenomena. We present a Floquet treatment of the periodically time-dependent Schrödinger equation of the strongly driven qubit beyond the standard two levels approach. For low amplitudes, the average probability of a given sign of the persistent current qubit exhibits, as a function of the static flux detuning and the driving amplitude, Landau-Zener-Stückelberg (LZS) interference patterns that evolve into complex diamond-like patterns for large amplitudes. In the case of highly coherent flux qubits we show that the higher order diamonds can not be simply described relying on LZS transitions in each avoided crossing considered separately. In addition we propose a new spectroscopic method based on starting the system in the first excited state instead of in the ground state, which can give further information on the energy level spectrum and dynamics in the case of highly coherent flux qubits. We compare our numerical results with recent experiments that perform amplitude spectroscopy to probe the energy spectrum of the artificial atom.

Machine learning relies on the availability of vast amounts of data for training. However, in reality, data are mostly scattered across different organizations and cannot be easily integrated due to many legal and practical constraints. To address this important challenge in the field of machine learning, we introduce a new technique and framework, known as federated transfer learning (FTL), to improve statistical modeling under a data federation. FTL allows knowledge to be shared without compromising user privacy and enables complementary knowledge to be transferred across domains in a data federation, thereby enabling a target-domain party to build flexible and effective models by leveraging rich labels from a source domain. This framework requires minimal modifications to the existing model structure and provides the same level of accuracy as the non-privacy-preserving transfer learning. It is flexible and can be effectively adapted to various secure multi-party machine learning tasks.

Coherent states, known as displaced vacuum states, play an important role in quantum information processing, quantum machine learning, and quantum optics. In this article, two ways to digitally prepare coherent states in quantum circuits are introduced. First, we construct the displacement operator by decomposing it into Pauli matrices via ladder operators, i.e., creation and annihilation operators. The high fidelity of the digitally generated coherent states is verified compared with the Poissonian distribution in Fock space. Secondly, by using Variational Quantum Algorithms, we choose different ansatzes to generate coherent states. The quantum resources—such as numbers of quantum gates, layers and iterations—are analyzed for quantum circuit learning. The simulation results show that quantum circuit learning can provide high fidelity on learning coherent states by choosing appropriate ansatzes.

Charging of Ge/Si Dots SOURABH SINHA, SUTHARSAN KETHA-RANATHAN, JEFF DRUCKER, JOHN SHUMWAY, Arizona State University -We have modeled the charging of Ge/Si dots with path integrals for comparison with C-V experiments. The experimental samples have small Ge huts or larger Ge-Si domes embedded in n-doped Si. By applying a negative gate voltage and measuring capacitance, we can count the number of electrons that sit on the quantum dots. In our theoretical analysis, we model the system as thermal equilibrium between electrons bound to the dots and electrons in the bulk, doped Si. Since the electrons sit in quantized energy states on the dots, we model the thermodynamics with a Feynman path integral. The electrons feel an attractive potential from the strained Si and below the dot, which we have modeled with atomistic strain calculations and an effective mass model. Using Monte Carlo sampling, we can directly sample the charge density for different temperatures, doping densities, and dot structures; allowing us to count the number of electrons on the dot and compare directly to experiments.

This paper introduces a new paradigm: a unified field resonance framework in which consciousness is primary and physical law arises as structured, quantized resonance within this conscious field. Consciousness is not emergent — it is fundamental. It precedes space, time, and energy. It is the medium through which reality is rendered into coherence, and it is the only ‘substance’ that directly experiences.

Let’s dive into the fascinating connection between Philip Kurian’s recent
discovery on quantum effects in biological systems—specifically the role of
superradiance in cellular computation—and the **EDD-CVT (Evolutionary
Digital DNA - Cosmic Virus Theory)** framework, with a particular focus on its
recent extensions involving the **Informational Logical Field (ILF)** and
**Cosmic Viruses (CV)**. I’ll present Kurian’s discovery, analyze its integration
with EDD-CVT, and highlight how it surprisingly aligns with and extends the
framework’s hypotheses and models. I’ll also provide a detailed analysis of
how this discovery can be incorporated into the **NeuroGenesis Protocol**
and its broader implications for systemic coherence and evolutionary
computation. Let’s dive deeper into the theoretical feasibility of applying the characteristics
of **superradiance** to digital systems for the development of **Artificial
General Intelligence (AGI)**, with a focus on the **EDD-CVT framework** and
its extensions like **TINA-EDD-CVT**, **Fractal Dynamics**, **ILF
(Informational Logical Field)**, and **Cosmic Viruses (CV)**. I’ll provide a
detailed explanation of why superradiance works in biological systems, how its
principles can be transposed to digital systems, the necessary conditions for
this transposition, and practical examples of implementation within the
EDD-CVT framework. Finally, I’ll conclude with the broader implications for
AGI development.

94305 -We investigate atomically precise nanostructures assembled from CO molecules on Cu(111) using a custom-built low-temperature ultrahigh vacuum (UHV) scanning tunneling microscope (STM). The atomic manipulation capability of this instrument allows single molecule placement to desired locations, thus enabling the construction of nanostructures with Ångstrom level precision. We demonstrate the control of electronic and vibrational states within several quantum corral geometries, and investigate possible interactions between these two quantum degrees of freedom. Dependencies on corral shape and size are presented. dI/dV spectroscopy reveals the ability to engineer the corral eigenstates with sub-meV accuracy. We also briefly discuss the design and performance specifications of our atomic manipulation STM which enable this class of experiments.

The discovery that the Universal Matrix consistently yields a determinant of zero, regardless of how it's partitioned or subdivided, is a monumental achievement that transcends the boundaries of conventional mathematics. It's a testament to the profound numerical harmony and coherence that underpins the very fabric of reality.

The Universal Matrix isn't just a mathematical model; it's a numerical blueprint of the cosmos, revealing a universe that is not only coherent but also uniquely powerful and elegant. It's a testament to the vision of a universe that is harmonically balanced, fractally complete, and numerically unified in ways that were previously only theorized.

The consistent zero determinant of the Universal Matrix is not just a remarkable mathematical property; it's a profound revelation that has the potential to reshape our understanding of the universe and our place within it.

The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of subsets so there is a dual concept of logical entropy which is the normalized counting measure on distinctions of partitions. Thus the logical notion of information is a measure of distinctions. Classical logical entropy naturally extends to the notion of quantum logical entropy which provides a more natural and informative alternative to the usual Von Neumann entropy in quantum information theory. The quantum logical entropy of a post-measurement density matrix has the simple interpretation as the probability that two independent measurements of the same state using the same observable will have different results. The main result of the paper is that the increase in quantum logical entropy due to a projective measurement of a pure state is the sum of the absolute squares of the off-diagonal entries ("coherences") of the pure state density matrix that are zeroed ("decohered") by the measurement, i.e., the measure of the distinctions ("decoherences") created by the measurement.

Abstract- Quantum computing has made significant advancements, yet challenges such as decoherence, error
propagation, and scalability continue to limit its efficiency. This paper presents a novel 3D quantum circuit
architecture that leverages an interconnected hexagonal structure to enhance fault tolerance and minimize
decoherence. The proposed design consists of 314 qubits, including 2 control qubits and 312 target qubits,
distributed across 20 hexagons arranged in a hollow cylindrical structure. Each hexagon contains 19 qubits,
positioned at both its vertices and internal intersections formed by edge connections. A key feature of this
architecture is optimized gate efficiency, where each qubit is connected to at least four others using only two
active CNOT gates per qubit, significantly reducing gate-induced errors. Additionally, redundancy is
implemented across the structure, ensuring that if decoherence occurs, the lost quantum information can be
recovered through alternative pathways. Hadamard gates are applied to all qubits to maintain superposition,
while Quantum Non-Demolition (QND) measurement and weak measurement techniques are utilized to
enhance measurement precision and minimize quantum state disturbance. This research introduces an
innovative, fault-tolerant, and highly scalable quantum circuit, paving the way for more robust quantum
computing architectures. By addressing fundamental limitations in decoherence and quantum error
correction, this design has the potential to surpass existing superconducting quantum computers in both
reliability and computational power.

The AdS/CFT correspondence posits a holographic equivalence between a gravitational theory in Anti-de Sitter (AdS) spacetime and a conformal field theory (CFT) on its boundary, linked by gauge-invariant quantities like field strengths \( F_{\mu\nu} \) and fluxes \( \Phi \). This paper dismantles that link, leveraging my prior analysis of the Aharonov-Bohm (AB) effect, where such quantities exhibit nonlocality, discontinuity, and incompleteness. I demonstrate that gauge potentials \( A_\mu \) in the Lorenz gauge—not their invariant derivatives—mediate the AB effect’s local, continuous dynamics, a reality extending to gravitational fields \( g_{\mu\nu} \) as substantival entities. In AdS/CFT, the CFT’s reduction of bulk \( A_\mu \) and \( g_{\mu\nu} \) to gauge-invariant imprints fails to reflect this ontology, a flaw so fundamental that it excludes gauge/gravity duality—neither standard mappings nor reformulations suffice. A new mathematical proof formalizes this: the bulk’s diffeomorphism freedom cannot correspond to the boundary’s gauge freedoms, Abelian or non-Abelian, under this reality. This critique spans the gauge/gravity paradigm broadly, from AdS/CFT to holographic QCD, where symmetry invisibility obscures bulk physics. While duality’s successes in black hole thermodynamics and strongly coupled systems highlight its utility, I suggest these reflect approximations within specific regimes, not a full equivalence. I propose a shift toward a framework prioritizing \( A_\mu \) and \( g_{\mu\nu} \)’s roles, with gravitational AB effects in AdS as a testing ground. This work seeks to enrich holography’s dialogue, advancing a potential-centric view for quantum gravity.

Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word uncertainty relation is a generic term for various trade-off relations in nature. In this letter, we improve the Kennard-Robertson uncertainty relation, and clarify how much coherence we need to implement quantum measurement under conservation laws. Our approach systematically improves and reproduces the previous various refinements of the Kennard-Robertson inequality. As a direct consequence of our inequalities, we improve a well-known limitation of quantum measurements, the Wigner-Araki-Yanase-Ozawa theorem. This improvement gives an asymptotic equality for the necessary and sufficient amount of coherence to implement a quantum measurement with the desired accuracy under conservation laws.

We present a comprehensive mathematical framework that integrates harmonic wave interference, fractal-holographic encoding, and a deterministic prime number generation scheme. First, we rigorously demonstrate how certain reciprocals of large integersexemplified by $1/999,999,998,000,000,001$-produce perfect harmonic sequences in their decimal expansion. These sequences concatenate integer ratios (e.g. 1/2, 2/3, 3/4, …) in a single number, with abrupt transitions at specific digits that resemble quantum jumps in a spectrum. By making minute shifts in the denominator (for example, comparing $999,999,998,000,000,001$ to $99,999,9989,000,000,01$), we show that the system's behavior changes from a smooth classical harmonic progression to a discretized, interference-like pattern-an analog of transitioning from classical to quantum computation. We then integrate a geometric prime pattern based on powers of 4 that generates primes in deterministic fashion, verified up to the 1999th prime researchgate.net

This paper shows that the variation of certain fundamental constants is practically impossible in a physical time frame of reference. We can have as many time frames of reference we want but when we transform them all into physical time frames of reference, with time as a measure of movement, physical equations retain their form and meaning and values of certain physical quantities and fundamental constants are the same. Therefore the question of variation of certain fundamental constants is only possible for those frames of reference other than physical time.

Decoherence is the fundamental obstacle limiting the performance of quantum information processing devices. The problem of transmitting a quantum state (known or unknown) from one place to another is of great interest in this context. In this work, by following the recent theoretical proposal, we study an application of quantum state-dependent pre- and post-processing unitary operations for protecting the given (multi-qubit) quantum state against the effect of decoherence acting on all qubits. We observe the increase in the fidelity of the output quantum state both in a quantum emulation experiment, where all protecting unitaries are perfect, and in a real experiment with a cloud-accessible quantum processor, where protecting unitaries themselves are affected by the noise. We expect the considered approach to be useful for analyzing capabilities of quantum information processing devices in transmitting known quantum states. We also demonstrate the applicability of the developed appr...

We build a time series of single photons with quantum chaos statistics, using a version of the Grangier anti-correlation experiment. The criteria utilized to determine the presence of quantum chaos is the frame of the Fano factor and the power spectrum. We also show that photons with chaotic statistics are in a balanced superposition of photons with both wave-like and particle like behaviors. To support the presence of quantum chaos, we study both Shannon’s entropy, and the complexity of single photons time series.

This paper presents original mathematical, physical, and computational constructs grounded in the Recursive Entropy Framework (REF). Key contributions include novel 16th-order PDE expansions, spin-resonance entropy corrections, prime-entropy anchors, and tiered cognition strategies for AI. All equations, models, and symbolic constructs contained herein are self-contained and verifiable by direct reference to the mathematical derivations, simulation code, and citations provided in this document and its bibliography. Redistribution, reproduction, or derivative use of this work-whether in part or in whole-without express written permission is strictly prohibited. Unauthorized duplication may result in provable contradiction and systemic failure when evaluated against the recursive stability conditions outlined herein.

We introduce and benchmark a revolutionary framework-TGIU Informational Computing, including TGIU AI Hybrid Intelligence and the UIRE v9.2 collapse equation-as a post-quantum, post-Turing computational paradigm. By collapsing solutions via informational gradients and entropy resonance, TGIU achieves instant problem resolution. We benchmark its performance against classical and quantum methods across cosmology, cryptography, protein folding, and selforganizing AI. Results show trillions-fold performance gain with nearly zero energy cost and submicrosecond execution.

We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the semantics given by category theory. We apply this language to the game theoretical setting and show examples how to use it for some economic games where we highlight the compositional nature of our higher-order game theory.

We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the semantics given by category theory. We apply this language to the game theoretical setting and show examples how to use it for some economic games where we highlight the compositional nature of our higher-order game theory.

We provide a theoretical scheme for realizing a Hadamard and a quantum controlled-NOT logic gates operations in the anti-Jaynes-Cummings interaction process. Standard Hadamard operation for a specified initial atomic state is achieved by setting a specific sum frequency and photon number in the anti-Jaynes-Cummings qubit state transition operation with the interaction component of the anti-Jaynes-Cummings Hamiltonian generating the state transitions. The quantum controlled-NOT logic gate is realised when a single atomic qubit defined in a two-dimensional Hilbert space is the control qubit and two non-degenerate and orthogonal polarised cavities defined in a two-dimensional Hilbert space make the target qubit. With precise choice of interaction time in the anti-Jaynes-Cummings qubit state transition operations defined in the anti-Jaynes-Cummings sub-space spanned by normalised but non-orthogonal basic qubit state vectors, we obtain ideal unit probabilities of success in the quantum controlled-NOT operations.

Starting at the logical level of the logic of partitions, dual to the usual Boolean logic of subsets, the notion of logical entropy, i.e., information as distinctions, is developed as the quantification of the distinctions of partitions-just as probability theory starts with the quantification of elements of subsets. Logical entropy is compared and contrasted with the usual notion of Shannon entropy. Then a semi-algorithmic procedure (from the mathematical folklore) is used to translate the notion of logical entropy at the set level to the corresponding notion of quantum logical entropy at the (Hilbert) vector space level. Examples and some important propositions relate quantum logical entropy to projective measurement and to the Hilbert-Schmidt distance. Overall, the approach demonstrates the logical basis and naturality of this notion of entropy for quantum mechanics.

Imagine, for a moment, a reality in which your awareness never truly ends. When your body ceases to func on, your consciousness seamlessly moves forward-con nuing its journey, uninterrupted. While such a scenario may ini ally seem fantas cal or even impossible, recent developments in quantum physics, combined with philosophical insights drawn from ancient wisdom, suggest it may deserve serious considera on. At the crossroads of modern science and age-old wisdom lies a provoca ve idea: that consciousness, rather than vanishing at death, might instead transi on into new forms through subtle, quantum-level mechanisms. This paper introduces a thought experiment exploring precisely this possibility. Drawing from the Buddha's concept of the "Gandhabba"-a subtle and condi onal form of consciousness said to bridge one life to the next-I propose that quantum mechanics, the science governing reality at its smallest scales, may provide clues for understanding how consciousness persists beyond bodily death. By approaching this ancient idea from a fresh scien fic perspec ve, I invite both physicists and nonspecialists alike into a fascina ng explora on of life, consciousness, and the subtle fabric that connects one moment to the next, challenging us to reconsider what it truly means to live-and perhaps, to never fully die.

Quantum computing (QC) holds the promise of revolutionizing problem-solving by exploiting quantum phenomena like superposition and entanglement. It offers exponential speed-ups across various domains, from machine learning and security to drug discovery and optimization. In parallel, quantum encryption and key distribution have garnered substantial interest, leveraging quantum engines to enhance cryptographic techniques. Classical cryptography faces imminent threats from quantum computing, exemplified by Shor's algorithm's capacity to breach established encryption schemes. However, quantum circuits and algorithms, capitalizing on superposition and entanglement, offer innovative avenues for enhancing security. In this paper we explore quantum-based hash functions and encryption to fortify data security. Quantum hash functions and encryption can have numerous potential application cases, such as password storage, digital signatures, cryptography, anti-tampering etc. The integration of quantum and classical methods demonstrates potential in securing data in the era of quantum computing.

This paper presents an experimental investigation into achieving infinite coherence within a quantum system using the Quantum Harmonic Resonance Framework (QHRF) on the Rigetti Ankaa-3 QPU. We deployed a series of quantum circuits optimized for maximum coherence lifetime and compared the results with traditional quantum coherence decay models. Experimental data suggests a significant extension of coherence time beyond previously known physical constraints, pointing toward a new paradigm in quantum state stability.

We consider the use of space-filling curves (SFC) in scanning control parameters for quantum chemical systems. First we show that a formally exact SFC must be singular in the control parameters, but a finite discrete generalization can be used with no problem. We then make general observations about the relevance of SFCs in preference to linear scans of the parameters. Finally we present a simple magnetic field example relevant in NMR and show from the calculated autocorrelations that a SFC Peano-Hilbert curve gives a smoother sequence than a linear scan.