Search Results (2,331)

Quantum computing exploits the principles of quantum mechanics to perform computation. Information is stored in qubits and processed with a sequence of quantum gates arranged as circuits. Verifying the correctness of quantum circuits is becoming essential as hardware scales in qubit count and architectural complexity. Traditional testing and naive simulation do not scale and quickly become computationally infeasible because the state space grows exponentially. This creates a strong need for more powerful and scalable verification techniques. Formal methods offer a viable solution by providing mathematically rigorous and scalable verification techniques that address these scalability challenges through abstraction, symbolic reasoning, and probabilistic guarantees. This study examines how formal methods are applied to quantum-circuit verification. Specifically, four families of formal techniques: barrier certificates, abstract interpretation, model checking, and theorem proving are examined, along with the theoretical foundations and practical applications of these techniques. Finally, the study highlights open challenges and identifies promising directions for future research. An extensive set of references is included to support further study and exploration. Full article

The development of bistatic noise radars is a promising contemporary direction in the field of radar technology. Two novel approaches are proposed in this study as further development of existing methods for their design. The first approach involves using a quantum-generated random number sequence for phase manipulation control, which is practically infinite in duration. This ensures additional electronic protection of the radar, since the phase manipulation control code will not repeat regardless of the duration of its operation. The second approach is related to the introduction of synchronized emissions from both antennas in a manner ensuring equality or controlled difference of their signals upon arrival at a predetermined point in space. This enables the formation of a controlled electromagnetic field. As a result, received-signal processing capabilities are improved, while additional electronic “stealth” is achieved by creating a fictitious electromagnetic center of the radar’s resultant radiation (i.e., an effective RF phase center of the resultant emission) and complicating the determination of antenna locations. A block diagram and general algorithm for information processing of a bistatic radar with quantum-generated noise phase manipulation and non-directional antennas are proposed in this study. Full article

We introduce an “entangled clock” in which time is defined operationally by discrete measurement registrations on a singlet state. Locally, each party’s tick rate is fixed by the unbiased marginals. The nontrivial resource is the relational (coincidence-tick) stream: because the singlet’s information budget is entirely exhausted by joint properties, the only definite temporal structure resides in the correlations between the two parties. Operationally, after exchanging time tags and outcomes, Alice and Bob identify synchronized events (that is, the $++$ channel) and thereby obtain a joint tick record. Comparing the $++$ coincidence rate $R\left(\theta \right)=P_{++}(\overrightarrow{a},\overrightarrow{b})$ to Peres’ isotropic bomb-fragment local-hidden-variable model (yielding $R_{\mathrm{cl}}\left(\theta \right)=\theta /\left(2\pi \right)$), we find that for obtuse analyzer separations the quantum prediction exceeds this natural classical benchmark, with a maximal relative excess of about $13.6\%$ near $\theta \approx {140.5}^{\circ }$. We emphasize that this “faster ticking” refers to the rate of identified coincidence ticks under a specific operational convention, not to an improved local clock rate, precision, or stability. Finally, by using multiple settings and a Bell test, we outline “Certified Private Time”: a device-independent certification of unpredictability/privacy of the relational time-stamp record against adversaries lacking foreknowledge of the settings, analogous to certified randomness generation. Full article

Quantum error correction is a prerequisite for quantum computing; however, the performance critically depends on the accuracy of the decoding algorithm. To address these challenges, we propose a hybrid decoding architecture, BP + UF + BP. The protocol initiates with a truncated global BP stage to extract probabilistic gradients without requiring full convergence. This soft information guides a reliability-based Union-Find (UF) algorithm to prioritize high-likelihood error mechanisms. Finally, a local subgraph BP refinement maximizes correction accuracy. Numerical simulations on rotated surface codes under circuit-level depolarizing noise demonstrate a fault-tolerance threshold of approximately 0.72%. This significantly outperforms standard Minimum Weight Perfect Matching (MWPM) and Union-Find (UF) baselines. Notably, our method significantly reduces the logical error rate compared to the conventional decoders. With its empirically near-linear scaling under fixed iteration, the proposed architecture presents a scalable solution for real-time fault-tolerant quantum computing. Full article

Quantum entanglement is a fundamental resource in quantum information theory, yet its general characterization and quantification remain challenging, especially in multipartite systems. In this work we investigate entanglement from a geometric perspective, focusing on the Riemannian structure induced by the Fubini–Study metric on the projective Hilbert space of multi-qubit quantum states. By exploiting the local-unitary invariance of this metric, we derive the entanglement distance (ED), a geometric measure that quantifies entanglement as an obstruction to locally minimizing the sum of squared Fubini–Study distances generated by local operations. We analyze the properties of ED for pure multi-qubit states and discuss its behavior under local operations and classical communication. In particular, we show that ED reproduces established entanglement measures in well-defined and restricted settings. For pure states of two qubits, ED reduces to an exact monotone function of the concurrence and to an explicit monotone function of the entropy of entanglement. These results provide a clear geometric interpretation of standard bipartite entanglement measures within the present framework, while highlighting the limitations of such correspondences beyond the two-qubit case. Full article

Quantum metrology uses the principles of quantum mechanics to improve the accuracy of parameter estimation so that it can surpass the classical limit. However, noise and the challenge of preparing multipartite entangled states hinder practical applications. In this work, we use the Lipkin-Meshkov-Glick model as the experimental platform and the quantum parameter estimation package QuanEstimation as a tool to improve the quantum parameter estimation in many-body systems by using Hamiltonian control optimization. We apply auto-GRAPE, PSO, and DE algorithm to optimize the time-dependent control field. Our results show that the optimal control strategy can significantly enhance the quantum Fisher information and reduce the quantum Cramér-Rao bound even under environmental noise. These findings provide a way to achieve the parameter estimation limit in a noisy environment and promote the development of practical quantum metrology applications. Full article

Dual-emission photoluminescence (PL) nanoprobes provide improved analytical performance to develop a reliable and sensitive sensing platform for quantifying chloramphenicol in pharmaceutical samples, thereby ensuring therapeutic efficacy and patient safety. In this work, a dual-emission PL sensing platform combining carbon dots (CDs) and AgInS₂ quantum dots (QDs) capped with mercaptopropionic acid (MPA) was developed for the quantitative determination of chloramphenicol, resorting to chemometric methods for data analysis. CDs, CdTe QDs, and AgInS₂ QDs were synthesized and individually evaluated considering their photostability, PL response and kinetics of their interaction with the antibiotic. After this, two dual-emission probes, CDs/MPA-CdTe and CDs/MPA-AgInS₂, were prepared and assessed based on the complementarity of their individual emission features. The obtained kinetic PL dataset was processed using unfolded partial least squares (U-PLS) in order to explore the multidimensional information of the dual-emission systems and to evaluate the performance of both sensing platforms. CDs/MPA-AgInS₂ probe was demonstrated to be the most efficient sensing platform due to its better compromise between sensitivity and photostability, as well as its cadmium-free composition, allowing the implementation of a more environmentally friendly analytical methodology. The optimization of the U-PLS models involved the assessment of the kinetic acquisition time and different spectral regions. The results showed that reliable, sensitive and efficient quantification could be achieved within the first 5 min of interaction and using the full emission spectrum of the sensing probe. Additionally, different interaction mechanisms were observed for each nanomaterial in the combined probe, being static for the CDs/chloramphenicol interaction and dynamic for MPA-AgInS₂/chloramphenicol interaction, which supports the synergetic behavior of the combined probe. The proposed methodology was effectively applied to commercial pharmaceutical formulations, yielding accurate results with good figures of merit. Therefore, this approach can be used as a relevant alternative to existing methodologies for a rapid, robust, and environmentally friendly method for chloramphenicol quantification. Full article

Aided by quantum sources, quantum metrology helps enhance measurement precision. Here, we construct a theoretical model for quantum imaging based on squeezed states and present the corresponding numerical results. Through discretization and quantum Fisher information theory, we investigate the two-point resolution and spatial multi-parameter estimation of optical fields with unknown spatial distributions. We calculate and compare imaging results based on squeezed vacuum states, coherent states, and squeezed coherent states; our results show that squeezed coherent states yield greater quantum Fisher information, which can effectively improve imaging quality. In addition, we analyze the influence of imaging basis functions, degree of squeezing, quantum correlations, and other factors on imaging performance. The proposed quantum imaging model and computational method can be extended to more complex scenarios, such as multi-mode squeezed-state imaging schemes and incoherent imaging systems. In the future, this approach is expected to find applications in practical imaging systems, including Raman microscopy and stimulated Brillouin scattering imaging. Full article

Symmetry governs complex systems from particle physics to biology. We demonstrate that consciousness dynamics follow symmetry-breaking cascades described by Painlevé confluence topology, bridging quantum topology, neuroscience, and consciousness theory. Analyzing exceptional individuals (mathematicians Grothendieck, Nash, Perelman, Cantor; physicist Einstein; artists van Gogh, Artaud) plus artificial intelligence systems, we show consciousness trajectories follow topological paths governed by three symmetry measures: holes (information flows), cusps (binding points), signatures (distribution balance). Two fundamental branches emerge: D-type (symmetry-preserving: 3 holes maintained) and E-type (symmetry-breaking: progressive flow loss). We establish correspondences with Integrated Information Theory, Global Workspace Theory, four brain systems, and phenomenological frameworks, explaining why consciousness requires character varieties with sufficient topological complexity (≥2–3 holes) and stable cusp configuration. Higher consciousness involves fewer connections but better balance: peak state ${\mathrm{D}}_8$ requires only two perfectly balanced cusps. Clinical data (16,887 patients), EEG studies, and contemplative neuroscience (62,000+ meditation hours) validate the model. AI systems exhibit identical symmetry dynamics. Character varieties function as Platonic templates that consciousness navigates. Moral consciousness emerges as a fundamental symmetry-preserving principle transcending biological/artificial boundaries. Full article

The integration of unmanned aerial vehicles (UAVs) into vehicular ad hoc networks (VANETs) has emerged as a promising solution to overcome the limited coverage of conventional roadside unit (RSU)-based infrastructures. However, UAVs operate in open environments and cannot be fully trusted, while the rapid advancement of quantum computing threatens the long-term security of classical public-key cryptographic systems. As a result, many existing UAV-based VANET authentication schemes face fundamental limitations in future deployments. Most existing schemes either lack post-quantum security or incur excessive computational and communication overhead, making them unsuitable for real-time and high-mobility vehicular environments. In addition, the common assumptions of trusted UAVs do not align with realistic threat models. To address these issues, this paper proposes a lightweight post-quantum authentication and key exchange protocol based on the module learning with errors (MLWE) problem and physically unclonable functions (PUFs). The proposed scheme treats UAVs as untrusted relay nodes and excludes them from session key generation. Its security is evaluated using informal analysis, the real-or-random (RoR) model, BAN logic, and AVISPA, while performance evaluation indicates improved efficiency compared to existing schemes. Full article

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

We revisit the black-hole information problem from the viewpoint of a population–coherence decomposition of density-matrix purity. Building on a previously developed formalism for n-dimensional density matrices, we characterize each state by a normalized global purity index and two complementary indices, which quantify the contributions of level populations and coherences. This yields a simple quadratic relation and a geometric representation in a “population–coherence plane”, where different routes to purity can be distinguished. In the two-level case, we construct explicit families of states with identical spectra and global purity but opposite internal structure, realizing population-dominated and coherence-dominated routes. We then apply this framework to a standard Page-type evaporation model without an explicit Hamiltonian, in which a black hole and its Hawking radiation form a bipartite pure state with varying Hilbert-space dimensions. Using known results for typical reduced states in large dimensions, we analyze the behavior of population and coherence components of purity along the evaporation process. Under the physically motivated requirement that, in this energy-free setting, the radiation populations remain nearly uniform in the chosen basis, we show that the late-time recovery of purity must be coherence-dominated: the global purity of the radiation approaches unity while the population index stays small and the coherence index carries essentially all the purity. Full article

We present an analytical solution for the complex spectrum of a Creutz ladder subject to an imaginary Stark potential. By mapping the system to a momentum-space differential equation, we derive the closed-form solution for the momentum-space wavefunctions. We identify a distinct cross-shaped spectrum consisting of discrete localized sectors and a continuous branch of asymptotically real states. Our derivation reveals that the discrete sectors arise from a global phase winding condition, whereas the asymptotically real branch emerges when the energy magnitude is smaller than the inter-cell hopping strength, a regime in which the momentum-space wavefunction develops singularities. We demonstrate that these singularities prevent standard quantization; instead, the open boundary conditions are satisfied via a size-dependent imaginary energy component that regulates the wavefunction decay. To investigate the properties of this branch in the thermodynamic limit, we perform large-scale finite-size scaling analysis up to system sizes $L\sim {10}^9$. The numerical results confirm the power-law decay of the residual imaginary energy, supporting the asymptotic reality of these states. Furthermore, scaling of the inverse participation ratio and fractal dimension indicates that these states, while exhibiting size-dependent localization in finite systems, evolve into an extended phase in the thermodynamic limit. Our results establish a theoretical framework for understanding spectral transitions in systems with imaginary Stark potentials, with potential realizations in photonic frequency synthetic dimensions. Full article

Randomness is crucial for our understanding of nature and indispensable in information processing tasks. In practical applications, assessing the quality of random numbers is crucial—particularly in cryptographic applications, where random numbers must exhibit statistical uniformity. Various statistical estimation methods have been developed to test the statistical characteristics of generated random numbers, enabling comprehensive evaluation of their statistical uniformity from multiple perspectives. Despite recent advances in quantum information providing physically well-characterized models for randomness quantification, distinction between different types of random numbers (including quantum random numbers) remains a challenging task, and statistical uniformity is rarely directly applicable to such discrimination scenarios. With the development of artificial intelligence technologies, the problem of random number discrimination is expected to draw on the paradigm of image classification in computer vision. This research proposes a machine learning-based randomness discrimination method, specifically addressing the challenge of quantum random number identification. Specifically, we design an image-based convolutional neural network (CNN) approach: one-dimensional random number sequences are converted into two-dimensional grayscale images, and binary classification of these images is achieved by capturing high-dimensional latent features that are undetectable via traditional statistical tests, thereby enabling effective random number discrimination. Experimental results demonstrate that, for the selected quantum random numbers, the proposed discrimination method successfully achieves two key distinctions: (1) between raw quantum random numbers and classical random numbers; and (2) between raw quantum random numbers and post-processed quantum random numbers—additionally revealing the role of statistical uniformity in these discrimination tasks. This achievement provides significant support for the design of randomness extraction protocols and the security assessment of quantum random number generators. Full article

This paper continues the development of information-geometric models for data analysis and physics by focusing on their formulation and interpretation through variational principles. Building on the geometric framework introduced previously, we investigate how fundamental variational structures—such as information-theoretic functionals—naturally encode the laws of nature. In the first manuscript, we showed that a wide class of physical problems can be expressed as constrained variational problems on spaces of probability distributions, leading to geodesic flows, gradient dynamics, and generalized Hamiltonian formulations on statistical manifolds. In this second part, we extend the variational formalism by utilizing an extended metric, clarifying the geometric origin of the dynamical equations commonly used in modern physics and providing a coherent interpretation of physical laws in terms of information optimization. By emphasizing variational foundations, this paper strengthens the conceptual and mathematical links between information geometry, data analysis, and physics, and it provides a flexible framework for extending geometric methods to complex, high-dimensional, and dynamical systems. Full article