Search Results (99)

It is known that the continuous-time variant of Grover’s search algorithm is characterized by quantum search frameworks that are governed by stationary Hamiltonians, which result in search trajectories confined to the two-dimensional subspace of the complete Hilbert space formed by the source and target states. Specifically, the search approach is ineffective when the source and target states are orthogonal. In this paper, we employ normalization, orthogonality, and energy limitations to demonstrate that it is unfeasible to breach time-optimality between orthogonal states with constant Hamiltonians when the evolution is limited to the two-dimensional space spanned by the initial and final states. Deviations from time-optimality for unitary evolutions between orthogonal states can only occur with time-dependent Hamiltonian evolutions or, alternatively, with constant Hamiltonian evolutions in higher-dimensional subspaces of the entire Hilbert space. Ultimately, we employ our quantitative analysis to provide meaningful insights regarding the relationship between time-optimal evolutions and analog quantum search methods. We determine that the challenge of transitioning between orthogonal states with a constant Hamiltonian in a sub-optimal time is closely linked to the shortcomings of analog quantum search when the source and target states are orthogonal and not interconnected by the search Hamiltonian. In both scenarios, the fundamental cause of the failure lies in the existence of an inherent symmetry within the system. Full article

Phase transition in quantum mechanics is interpreted as an evolution, at the end of which, typically, a parameter-dependent and Hermitizable Hamiltonian $H\left(g\right)$ loses its observability. In the language of mathematics, such a “quantum catastrophe” occurs at an exceptional point of order N (EPN). Although the Hamiltonian $H\left(g\right)$ itself becomes unphysical in the limit of $g\to g^{EPN}$, it is shown that it can play the role of an unperturbed operator in an innovative perturbation-approximation analysis of the vicinity of the EPN singularity. As long as such an analysis is elementary at $N\le 3$ and purely numerical at $N\ge 5$, we pick up $N=4$ and demonstrate that for an arbitrary quantum system, the specific (i.e., already sufficiently phenomenologically rich) EP4 degeneracy becomes accessible via a unitary evolution process. This process is shown realizable inside a parametric domain ${\mathcal{D}}_{\mathrm{physical}}$, the boundaries of which are determined, near $g^{EP4}$, non-numerically. Possible relevance of such a mathematical result in the context of non-Hermitian photonics is emphasized. Full article

In quasi-Hermitian quantum mechanics (QHQM) of unitary systems, an optimal, calculation-friendly form of Hamiltonian is generally non-Hermitian, $H\ne H^{†}$. This makes its physical interpretation ambiguous. Without altering H, this ambiguity can be resolved either via a transformation of H into its isospectral Hermitian form via a so-called Dyson map $\mathrm{\Omega }:H\to \mathfrak{h}$, or via a (formally equivalent) specification of a nontrivial physical inner-product metric $\mathrm{\Theta }$ in Hilbert space. Here, we focus on the former strategy. Our present construction of the Hermitian isospectral twins $\mathfrak{h}$ of H is exhaustive. As a byproduct, it not only restores the conventional correspondence principle between quantum and classical physics, but it also provides a framework for a systematic classification of all of the admissible probabilistic interpretations of quantum systems using a preselected H in QHQM framework. Full article

We present a general procedure to describe the dynamics of N degenerate quantized fields interacting resonantly with a two–level atom, all coupled with the same strength, within the rotating–wave approximation. Starting from the analysis of the two and three field cases, we generalize the method by identifying dynamical invariants that lead to a factorized form of the time–evolution operator. A unitary transformation reduces the problem to an effective Jaynes–Cummings Hamiltonian, where only one field interacts with the atom and the remaining modes contribute as free fields. Assuming initially coherent fields and an atomic superposition, we compute the atomic inversion and the mean photon number, revealing vacuum Rabi oscillations with a frequency determined by an effective coupling constant that exceeds the individual atom–field coupling, as well as the characteristic collapse–revival behavior. Full article

A conditional framework of Conditional Cosmological Recurrence (CCR) is introduced, as follows: if a causal patch admits a finite operational Hilbert space dimension D (as motivated by holographic and entropy bounds), then unitary quantum dynamics guarantee almost-periodic evolution, leading to recurrences. The central contribution is the explicit formulation of a micro-to-macro bridge, as follows: (i) finite regions discretize field modes; (ii) gravitational bounds cap entropy and energy; and (iii) the number of accessible states is finite, yielding CCR. The analysis differentiates global microstate recurrences (with double-exponential timescales in $S_{max}$) from operationally relevant coarse-grained returns (exponential in subsystem entropy), with conservative timescale estimates. For predictivity in eternally inflating settings, a causal-diamond measure with xerographic typicality and a single no-Boltzmann-brain constraint is employed, thereby avoiding volume-weighting pathologies. The scope is explicitly conditional: if future quantum gravity demonstrates $D=\infty$ for causal patches, CCR is falsified. Full article

We develop detailed quaternionic and octonionic frameworks for quantum computation grounded on normed division algebras. Our central result is to prove the polynomial computational equivalence of quaternionic and complex quantum models: Computation over $\mathbb{H}$ is polynomially equivalent to the standard complex quantum circuit model and hence captures the same complexity class BQP up to polynomial reductions. Over $\mathbb{H}$, we construct a complete model—quaternionic qubits on right $\mathbb{H}$-modules with quaternion-valued inner products, unitary dynamics, associative tensor products, and universal gate sets—and establish polynomial equivalence with the standard complex model; routes for implementation at fidelities exceeding $99\%$ via pulse-level synthesis on current hardware are discussed. Over $\mathbb{O}$, non-associativity yields path-dependent evolution, ambiguous adjoints/inner products, non-associative tensor products, and possible failure of energy conservation outside associative sectors. We formalize these obstructions and systematize four mitigation strategies: Confinement to associative subalgebras, $G_2$-invariant codes, dynamical decoupling of associator terms, and a seven-factor algebraic decomposition for gate synthesis. The results delineate the feasible quaternionic regime from the constrained octonionic landscape and point to applications in symmetry-protected architectures, algebra-aware simulation, and hypercomplex learning. Full article

As so many drugs have failed in ALS a new approach is needed. The author proposes that recent human genetic variants may play major roles in the disease, changing metabolism. Evolution of hominins was accelerated 3–2.5 Mya, by cytidine monophospho-N-acetylneuraminic acid hydroxylase (CMAH) becoming a unitary pseudogene after a pathogenic infection, changing the sialome, and hence metabolism, brain development and neuromuscular junctions (NMJs). This was when hominins evolved to run in Africa and develop bigger brains. Deletion of CMAH in mice allows them to run for longer (~50%). The enzyme CMAH is critical for the sialome, particularly the neurotrophin GM1, a critical hub for viral infection and for NMJ stability, but which is lost from NMJs at the beginning of denervation, probably due a 10-fold increase in spinal cord glucosylceramidases (non-lysosomal GBA2). A GBA2 inhibitor, ambroxol, is currently in phase II for ALS. Human-specific GM1 may be critical for human evolution, lactate metabolism and ALS. Lipid/lactate metabolism changed to support these evolutionary changes and lactate is a major body/brain fuel, but compromised in ALS patients and a marker of disease progression. Recent progress in sports science involving lactate metabolism and human performance may also be relevant to ALS therapies, and incidence. Full article

Quantum computing is an emergent field promising the improvement of processing speed in key algorithms by reducing their exponential scaling to polynomial, thus enabling solutions to problems that exceed classical computational capabilities. Gate-based quantum computing is the most common approach but still faces high levels of noise and decoherence. Gates play the role of probability mixers codifying information settled in quantum systems. However, they are deviated from their programmed behaviour due to those decoherent effects as a hidden source modifies the desired probability flux. Their quantification of such unavoidable behaviours becomes crucial for quantum error correction or mitigation. This work presents an approach to decoherence in quantum circuits using the Lindblad master equation to model the impact of noise and thermalisation underlying the ideal programmed behaviour expected for processing gates. The Lindblad approach then provides a comprehensive tool to model both probability fluxes being present in the process, thus regarding the gate and the environment. It analyses the deviation of resulting noisy states from the ideal unitary evolution of some gates considered as universal, setting some operating regimes. Thermalisation considers a radiation bath where gates are immersed as a feasible model of decoherence. Numerical simulations track the information loss as a function of the decay rate magnitude. It also exhibits the minimal impact on decoherence coming from particular quantum states being processed, but a higher impact on the number of qubits being processed by the gate. The methodology provides a unified framework to characterise the processing probability transport in quantum gates, including noise or thermalisation effects. Full article

Rural tourism is a key engine for sustainable development, elevated to a strategic level under China’s “Rural Revitalization Strategy”, creating a complex multi-level governance (MLG) policy system whose internal mechanisms are not fully understood. This study aims to analyze the thematic structure, spatio-temporal evolution, and transmission mechanisms of China’s rural tourism policy across central, provincial, and city/county levels. We applied BERTopic topic modeling and spatio-temporal analysis to a corpus of 1174 policy documents from 2005 to 2024. The results reveal a “centrally guided Type I governance” model with a clear functional division: the central level acts as a “top-level strategic designer”, the provincial level as a “key regional hub” for adaptation, and the city/county level as the “frontline of policy implementation”. We identified a vertical transmission chain characterized by a 1–2-year lag, alongside spatial differentiation driven by regional resource endowments at the provincial level and functional needs at the city/county level. This study concludes that China’s rural tourism governance framework is an efficient synergistic system that combines strong central guidance with dynamic local adaptation, providing empirical support for MLG theory in a unitary state and offering insights for optimizing policy coordination. Full article

We extend the Quantum Memory Matrix (QMM) framework—previously shown to unify gauge interactions and reproduce cold dark matter phenomenology—to account for the observed late-time cosmic acceleration. In QMM, each Planck-scale cell carries a finite-dimensional Hilbert space of quantum imprints. We show that (1) once local unitary evolution saturates the available micro-states, a uniform residual “vacuum-imprint energy” remains; its stress–energy tensor is of pure cosmological-constant form, with magnitude suppressed by the cell capacity, naturally yielding ${\rho }_{\mathrm{\Lambda }}\simeq {(2\times {10}^{-3}\mathrm{eV})}^4$; and (2) if imprint writes continue but are overdamped by cosmic expansion, the coarse-grained entropy field $S\left(t\right)$ undergoes slow-roll evolution, generating an effective equation of state $w\left(z\right)\approx -1+\mathcal{O}\left({10}^{-2}\right)$ that is testable by DESI, Euclid, and Roman. We derive the modified Friedmann equations, linear perturbations, and joint constraints from Planck 2018, BAO, and Pantheon +, finding that the QMM imprint model reproduces the observed TT, TE, and EE spectra without introducing additional free parameters and alleviates the $H_0$ tension while remaining consistent with the large-scale structure. In this picture, dark matter and dark energy arise as gradient-dominated and potential-dominated limits of the same underlying information field, completing the QMM cosmological sector with predictive power and internal consistency. Full article

In this work, we investigate the quantum coherence and purity in hydrogen atoms under dissipative dynamics, with a focus on the hyperfine structure states arising from the electron–proton spin interaction. Using the Lindblad master equation, we model the time evolution of the density matrix of the system, incorporating both the unitary dynamics driven by the hyperfine Hamiltonian and the dissipative effects due to environmental interactions. Quantum coherence is quantified using the $L_1$ norm and relative entropy measures, while purity is assessed via von Neumann entropy, for initial states, including a maximally entangled Bell state and a separable state. Our results reveal distinct dynamics: for the Bell states, both coherence and purity decay exponentially with a rate proportional to the dissipation parameter, whereas for a kind of separable state, coherence exhibits oscillatory behavior modulated via the hyperfine coupling constant, superimposed on an exponential decay, and accompanied by a steady increase in entropy. Higher dissipation rates accelerate the loss of coherence and the growth of von Neumann entropy, underscoring the environment’s role in suppressing quantum superposition and driving the system towards mixed states. These findings enhance our understanding of coherence and purity preservation in atomic systems and offer insights for quantum information applications where robustness against dissipation is critical. Full article

Semiclassical (SC) approximations for various representations of a quantum state are constructed on a single (Lagrangian) surface in the phase space but such surface is not available for chaotic systems. An analogous evolution surface underlies SC representations of the evolution operator, albeit in a doubled phase space. Here, it is shown that corresponding to the Fourier transform on a unitary operator, represented as a Green function or spectral Wigner function, a Legendre transform generates a resolvent surface as the classical basis for SC representations of the resolvent operator in the double-phase space, independently of the integrable or chaotic nature of the system. This surface coincides with derivatives of action functions (or generating functions) depending on the choice of appropriate coordinates, and its growth departs from the energy shell following trajectories in the double-phase space. In an initial study of the resolvent surface based on its caustics, its complex nature is revealed to be analogous to a multidimensional sponge. Resummation of the trace of the resolvent in terms of linear combinations of periodic orbits, known as pseudo orbits or composite orbits, provides a cutoff to the SC sum at the Heisenberg time. Here, it is shown that the corresponding actions for higher times can be approximately included within true secondary periodic orbits, in which heteroclinic orbits join multiple windings of relatively short periodic orbits into larger circuits. Full article

One of the fundamental problems of quantum statistical physics is how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here, we study, via explicit time evolution for the generic model system of an interacting, trapped Bose gas with discrete single-particle levels, how the measurement of one or more observables subdivides the system into observed and non-observed Hilbert subspaces and the tracing over the non-measured quantum numbers defines an effective, thermodynamic bath, induces the entanglement of the observed Hilbert subspace with the bath, and leads to a bi-exponential approach of the entanglement entropy and of the measured observables to thermal equilibrium behavior as a function of time. We find this to be more generally fulfilled than in the scenario of the eigenstate thermalization hypothesis (ETH), namely for both local particle occupation numbers and non-local density correlation functions, and independent of the specific initial quantum state of the time evolution. Full article

We pose and address the radical question of whether quantum mechanics, known for its firm internal structure and enormous empirical success, carries in itself the genomes of larger quantum theories that have higher internal intricacy and phenomenological versatility. In other words, we consider, at the basic level of closed quantum systems and regardless of interpretational aspects, whether standard quantum theory (SQT) harbors quantum theories with context-based deformed principles or structures, having definite predictive power within much broader scopes. We answer this question in the affirmative following complementary evidence and reasoning arising from quantum-computation-based quantum simulation and fundamental, general, and abstract rationales within the frameworks of information theory, fundamental or functional emergence, and participatory agency. In this light, as we show, one is led to the recently proposed experience-centric quantum theory (ECQT), which is a larger and richer theory of quantum behaviors with drastically generalized quantum dynamics. ECQT allows the quantum information of the closed quantum system’s developed state history to continually contribute to defining and updating the many-body interactions, the Hamiltonians, and even the internal elements and “particles” of the total system. Hence, the unitary evolutions are continually impacted and become guidable by the agent system’s experience. The intrinsic interplay of unitarity and non-Markovianity in ECQT brings about a host of diverse behavioral phases, which concurrently infuse closed and open quantum system characteristics, and it even surpasses the theory of open systems in SQT. From a broader perspective, a focus of our investigation is the existence of the quantum interactome—the interactive landscape of all coexisting, independent, context-based quantum theories that emerge from inferential participatory agencies—and its predictive phenomenological utility. Full article

We determine the evolving probability representation of entangled cat states in the potential of either the harmonic oscillator or the inverted oscillator, assuming that the states are initially prepared in the potential of the harmonic oscillator. Such states have several applications in quantum information processing. The inverted quantum harmonic oscillator, where the potential energy corresponds to imaginary frequencies of the oscillator, can be applied in relation to cosmological problems. We also determine the evolving probability representation of cat states of an oscillating spin-1/2 particle of the inverted oscillator, in which the time evolution of the spin state is described by an arbitrary unitary operator. The properties of the determined entangled probability distributions are discussed. Full article