arXiv subjects

Kazuki Ikeda

Publications and source records attributed to Kazuki Ikeda.

At least 19 recordsLinked to original sources

arXiv2026

A Zoology of Quantum Turing Patterns

We explore quantum Turing pattern zoology, where the same Lindblad equation supports a morphology atlas of stripes, spots, holes, labyrinths, and defects. The stable stripe species provides a quantitatively controlled case in which morphology and Gaussian witness loss separate parametrically. In particular, visible Turing stripes can remain after two Gaussian witness margins associated with the same $k_*$ mode cross zero in a completely positive Lindblad lattice. The witness thresholds on the exact shell fall as $\mathcal{N}^{-1}$. The stripe nematic threshold tends to a nonzero value at fixed lattice size, time window, and morphology criterion. The ratio of the morphology threshold to either witness threshold therefore grows with $\mathcal{N}$. Imaging and momentum-resolved covariance measurements probe these sectors separately.

quant-ph↗

arXiv2026

Closed Timelike Curve Decoding on Quantum Hardware

Deutsch closed timelike curves (D-CTCs) are described by a fixed-point condition for a chronology-violating register. We study a finite-dimensional circuit model that places a Hayden--Preskill/Yoshida--Kitaev recovery map inside such a consistency loop. A register-routing construction makes the Deutsch map explicit: an initial SWAP moves the incoming CTC state to an idle dump register, the scrambler and decoder act on the remaining active registers, and a final SWAP writes the recovered message back to the CTC register. When the active branch recovers the message, the induced map on the CTC register is the replacement channel $σ\mapsto ρ_M$, with the unique fixed point $ρ_M$. We implement the associated Lloyd-type post-selected decoder circuits on quantum hardware and formulate a classical-feedback iteration for the experimentally estimated map. Qiskit simulations and IBM-hardware data for single-qubit instances quantify decoder fidelity, post-selection overhead, routing-dependent noise, and quantum-geometric susceptibility.

quant-ph↗

arXiv2026

Quantum Entanglement Geometry on Severi-Brauer Schemes: Subsystem Reductions of Azumaya Algebras

Quantum entanglement is a basic resource of quantum theory, but its usual definition assumes a fixed decomposition into subsystems. We develop an algebro--geometric framework to address quantum entanglement. For the Severi--Brauer scheme $SB(\mathcal{A})\to X$ of an Azumaya algebra and a factorization type $\mathbf{d}$, we prove that a global locus of product states exists exactly when the associated torsor under $\mathrm{PGL}_n$ reduces to the stabilizer $G_{\mathbf d}$ of the Segre variety. Thus entanglement in families is measured by a geometric obstruction to global subsystem structure. Beyond this reduction criterion, we identify the cohomology that carries computable entangling obstructions. After determinant and incidence data $L\subset R\subset K$ are chosen, the relevant classes lie in the mapping cone relative cohomology $E^\bullet(BL\to BR)$. Their absolute images on $X$, modulo classes induced from $BK$, give determinant entangling obstructions beyond the Brauer class. We construct the moduli of subsystem structures as the quotient $P/G_{\mathbf d}$ and realize it as a locally closed locus in the relative Hilbert scheme, with a compactification by degenerations of product state loci. In the bipartite case, a chosen subsystem structure globalizes the Schmidt rank stratification to a flat filtration with base change compatible resolutions and fiberwise constant numerical invariants. Examples show that reducibility can depend on the underlying torsor, not only on the Brauer class, with an interpretation by entangling monodromy.

math.AG↗

arXiv2026

Quantum Turing Patterns

We construct quantum Turing patterns in Lindblad lattice dynamics and establish a rigorous theory of their nonlinear order and quantum fluctuations. For an explicit family of completely positive lattice generators with finite-range couplings, the first-moment equations undergo a supercritical instability at a nonzero wave number and admit analytic site- and bond-centered commensurate stripe branches. These branches are locally asymptotically stable in their reflection-fixed period-cell spaces, and projected coherent states exhibit extensive Bragg order on every bounded time interval in the semiclassical limit. We prove $O(N^{-1/2})$ convergence of microscopic covariances to a nonautonomous Gaussian Lyapunov flow, transferring strict partial-transpose uncertainty violations to sufficiently large $N$. In the homogeneous Gaussian sector, a single dimensionless ratio controls both the Turing stability determinant and the logarithmic negativity of opposite momenta, relating wavelength selection directly to quantum entanglement. Differential transport shifts the strongest opposite-momentum correlations from the infrared to the selected Turing scale. Numerical continuation and two-dimensional simulations display stripe, spot, and labyrinth morphologies whose Fourier modes and fluctuation spectra concentrate at the same selected wave numbers.

math-ph↗

arXiv2026

Entangling Topological Invariants

An isolated occupied multiplet may admit local tensor-product descriptions without a globally consistent subsystem structure. We characterize the obstruction by comparing the transition functions of the occupied multiplet with those generated by independent basis changes in the two candidate subsystems. When a decomposition into rank-one sectors over a closed surface is specified, the resulting quotient removes row- and column-additive Chern data and yields mixed Chern classes. Momentum-dependent mixing of the sector labels adds the Gauss--Codazzi curvature of the moving lines, while in the label-conserving limit the mixed class is measured by a crossed Thouless pump. When only the factor dimensions $p$ and $q$ are specified, the comparison is made at the level of the clutching map of a rank-$pq$ bundle over $S^4$. Product frames generate winding numbers in $q\mathbb Z+p\mathbb Z$, so global factorization is possible exactly when $C_2$ is divisible by $\gcd(p,q)$; in particular, odd $C_2$ obstructs a $2\times2$ factorization. We illustrate the two settings with finite eight-level Hamiltonians and give pumping and occupied-projector tomography protocols for their readout.

quant-ph↗

arXiv2026

Quantum Information Dynamics of QED$_2$ in Expanding de Sitter Universe

We study QED$_2$ in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as $1/a(t)$ while the electric term grows as $g^2 a(t)$, sweeping the spectrum through a moving narrow-gap region in the $(τ,m)$ plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later $τ$ as the lattice spacing goes to zero, with current data favoring $τ_* \approx 3.1$, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED$_2$ as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.

hep-th↗

arXiv2026

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data

Using the spinless Haldane model, we study the witness-filtered Berry curvature, quantum geometric tensor, and quantum Fisher information on the gapped strata of the parameter space and evaluate them through the Fukui-Hatsugai-Suzuki discretization. The filtered quantities isolate the part of the geometric response carried by sublattice coherence: they suppress contributions from regions where the occupied Bloch state is locally A/B-separable and emphasize regions where curvature and coherence coexist. We derive exact lattice identities, reconstruction formulas for the curvature-weighted coherence, and bounds relating the filtered quantum geometric tensor and quantum Fisher information to single-particle mode entanglement. Across the gap-closing stratum, the quantized response changes admit a natural description in terms of Hecke modifications. We elicit a corresponding Langlands viewpoint -- not as a full correspondence, but as an organizational principle and as the mathematical shadow of these physical geometric constructions.

quant-ph↗

arXiv2026

Quantum simulation of real-time current correlators and DIS-inspired observables in the Schwinger model

Hadronic tensors encode the nonperturbative structure of hadrons probed in deep inelastic scattering (DIS), yet their direct evaluation requires real-time evolution that presents a challenge for traditional Euclidean lattice approaches. In this work, we present the first quantum simulation of real-time hadronic current-current correlators in a confining gauge theory, from which DIS-inspired structure functions are extracted as a proof-of-principle demonstration in the Schwinger model, i.e (1+1)-dimensional QED. Using two complementary quantum-simulation strategies -- quantum-circuit and tensor-network methods -- we compute the real-time current-current correlator directly on the lattice and validate our results against exact diagonalization where applicable. From this correlator, we compute the hadronic tensor and determine the longitudinal structure function, the sole nonvanishing DIS observable in two space-time dimensions. Our study demonstrates that quantum simulation offers a viable complementary pathway towards the evaluation of real-time observables relevant for hadronic structure. It also provides a foundation for extending the calculations from Schwinger model to other gauge theories.

hep-ph↗

arXiv2026

Loop-dependent entangling holonomies in localized topological quartets

A spectrally isolated quartet can admit a local two-qubit description at each point in parameter space and still acquire a loop holonomy outside the local subgroup $\mathrm{U}(2)\otimes\mathrm{U}(2)$. We study this question in three localized topological settings, a BHZ ribbon, a spinful SSH chain, and a BBH corner quartet. On a fixed quartet, changing only the loop can move the holonomy from almost local to entangling. In BHZ, co-rotating and counter-rotating edge-field loops have nearly the same eigenphase data, but only the counter-rotating loop yields an Ising-like entangler. SSH gives a controlled-rotation example in a numerically stable edge quartet. BBH shows the same issue in a higher-order corner quartet. Standard Berry data, including Berry phases, Chern numbers, determinant phases, and eigenphase spectra, do not separate these cases. The main diagnostic is the distance from the loop holonomy to the extracted local subgroup. Canonical two-qubit coordinates are used only after reduction failure has been identified. The quartet is the smallest setting in which this question can be tested explicitly. The same subgroup-reduction problem extends to any isolated multiplet with pointwise product type $D=\prod_αd_α$, where the relevant local subgroup is the embedded product group $G_{\mathbf d}=\mathrm{Im}[\prod_αU(d_α)\to U(D)]$. In the terminology of Ref.[arXiv:2601.13764], these examples realize loop-dependent entangling gluing.

cond-mat.mes-hall↗

arXiv2026

Hofstadter's Butterfly in AdS$_3$ Black Holes

We derive the reduced Dirac Hamiltonian on the non-rotating BTZ background and use its redshift structure to construct a gauge-covariant single-band lattice model on the constant-time BTZ cylinder. In equal-area coordinates the AdS radius $L$ fixes the local Gaussian curvature, while the horizon radius $r_h$ fixes the throat size and the strength of the near-horizon redshift. The lattice model therefore has a direct geometric interpretation and is not presented as an unshown reduction of the two-component Dirac lattice. Its angular Fourier transform yields an exact curved Harper equation with BTZ-dependent hopping amplitudes and a consistent dimensionless angular quasi-momentum. We then supplement global parameter scans with state-resolved diagnostics: spectra color-coded by mean radius, local density of states, direct flux-response versus radius correlations, and Aharonov--Bohm spectral flow and persistent current on the BTZ cycle. These results show that weaker curvature sharpens the butterfly-like fragmentation, whereas larger horizons suppress both magnetic and Aharonov--Bohm response by creating weakly dispersing near-horizon states.

hep-th↗

arXiv2026

Quantum Energy Teleportation Across Lattice and Continuum

Quantum energy teleportation (QET) has been studied in continuum field theory and in lattice many-body systems, but the relation between the two within a single interacting model is still not well understood. To address this question, we consider the massive Thirring model, equivalently the sine--Gordon theory. In the continuum, the trigonometric measurement is a weak binary Positive Operator-Valued Measure (POVM), and its leading signal is set by a conserved-current correlator in the bosonized theory, with both gapless behavior and gapped large-distance asymptotics. On the lattice, the conventional protocol does not access this neutral current sector. For Alice's local measurement, a lattice $U(1)$ selection rule removes the neutral current contribution from Bob's subsystem, and the separated signal lies in charged sectors. On the same lattice Hamiltonian we construct a neutral current protocol whose weak signal is exactly a coarse-grained current correlator and whose extracted energy scales quadratically with the measurement strength. This identifies the neutral sector shared by the lattice and continuum descriptions, while separating it from the charged sector that governs the conventional qubit protocol.

hep-th↗

arXiv2026

Geometry Induced Chiral Transport and Entanglement in $AdS_2$ Background

We study the real-time chiral dynamics of Dirac fermions in AdS$_2$ and AdS$_2$ black hole backgrounds. The spacetime curvature generates a spin connection term, acting as an effective magnetic field and a position-dependent chiral chemical potential. This leads to strongly asymmetric wave propagation, confined within an inhomogeneous Lieb-Robinson cone. The front velocities decrease with increasing fermion mass and horizon radius. The entanglement entropy grows inside the causal cone, and it saturates due to screening/dephasing in the finite inhomogeneous chain. In dipole-dipole collision, the central bipartite entropy rises when the inward Lieb-Robinson fronts intersect, forming a bright ridge in the local entanglement profile. Charge and current correlators peak at the front arrival, providing a real-time diagnostic of chiral transport. These results establish a causality-respecting framework, linking curvature and horizons to transport and entanglement in (1+1)-dimensional fermionic matter.

hep-th↗

arXiv2026

Quantum Simulation of Fermions in $AdS_2$ Black Hole: Chirality, Entanglement, and Spectral Crossovers

We consider free Dirac fermions on a discretized $AdS_2$ black hole background, and analyze how curved space redshift, horizons, and the spin connection induced chiral gravitational effect shape spectral, transport, and scrambling phenomena. The system is discretized via staggered fermions followed by the Jordan-Wigner transform to encode the model in qubit degrees of freedom, whose Hamiltonian carries site dependent warp factors and bond chirality terms encoding the redshift and spin connection effects. We calculate the ground state and first excited states energies, their local charge profiles, and their half-chain entanglement entropies, showing how redshift and chirality affect the transition from criticality to a gapped regime. Probing operator growth via out-of-time-order correlators, we find that horizons and the chiral coupling accelerate scrambling, yet remain within a non-chaotic regime. Finally, we map out an integrable to ergodic crossover via level-spacing statistics and Brody fits, and introduce on-site disorder to drive a many body localization transition.

quant-ph↗

arXiv2026

Timelike Quantum Energy Teleportation

We establish a novel quantum protocol called Timelike Quantum Energy Teleportation (TQET) between two separated parties $A$ and $B$, designed for transporting quantum energy across spacetime. The amount of energy gained through TQET is always greater than or equal to that obtained via natural time evolution for any spin chain where $A$ and $B$ are distinguishable. This protocol uses temporal and spatial quantum correlations between agents separated by space and time. The energy supplier injects energy into the system by measuring the ground state of a many-body system that evolves over time, while the distant recipient performs a conditional operation using feedback from the supplier. When Bob acts immediately after receiving Alice's outcome, the protocol reduces to conventional QET. We present a proof-of-concept demonstration in the Ising model using quantum simulations. TQET increases energy efficiency from approximately 3\% to around 40\%, representing over a 13-fold improvement compared to QET. Furthermore, we analyzed the relationship between entanglement in time and TQET, validating the role of temporal correlations in energy activation between agents across spacetime.

quant-ph↗

arXiv2026

Introduction to Quantum Entanglement Geometry

This article is an expository account aimed at viewing entanglement in finite-dimensional quantum many-body systems as a phenomenon of global geometry. While the mathematics of general quantum states has been studied extensively, this article focuses specifically on their entanglement. When a quantum system varies over a classical parameter space, each fiber may look like the same Hilbert space, yet there may be no global identification because of twisting in the gluing data. Describing this situation by an Azumaya algebra, one always obtains the family of pure-state spaces as a Severi-Brauer scheme. The main focus is to characterize the condition under which the subsystem decomposition required to define entanglement exists globally and compatibly, by a reduction to the stabilizer subgroup of the Segre variety, and to explain that the obstruction appears in the Brauer class. As a consequence, quantum states yield a natural filtration dictated by entanglement on the Severi-Brauer scheme. Using a spin system on a torus as an example, we show concretely that the holonomy of the gluing can produce an entangling quantum gate, and can appear as an obstruction class distinct from the usual Berry numbers or Chern numbers. For instance, even for quantum systems that have traditionally been regarded as having no topological band structure, the entanglement of their eigenstates can be related to global geometric universal quantities, reflecting the background geometry.

quant-ph↗

arXiv2026

Quantum Entanglement as a Cohomological Obstruction

We recast quantum entanglement as a cohomological obstruction to reconstructing a global quantum state from locally compatible information. We address this by considering presheaf cohomologies of states and entanglement witnesses. Sheafification erases the global-from-local signature while leaving within-patch multipartite structure, captured by local entanglement groups introduced here. For smooth parameter families, the obstruction admits a differential-geometric representative obtained by pairing an appropriate witness field with the curvature of a natural unitary connection on the associated bundle of amplitudes. We also introduce a Quantum Entanglement Index (QEI) as an index-theoretic invariant of entangled states and explain its behavior. Finally, we outline a theoretical physics approach to probe these ideas in quantum many-body systems and suggest a possible entanglement-induced correction as an experimental validation. Detailed numerical implementations for concrete quantum many-body models are presented in the companion paper \cite{2026arXiv260113467I}.

math-ph↗

arXiv2026

Quantum Key Distribution by Quantum Energy Teleportation

Quantum energy teleportation (QET) is a process that leverages quantum entanglement and local operations to transfer energy between two spatially separated locations without physically transporting particles or energy carriers. We construct a QET-based quantum key distribution (QKD) protocol and analyze its security and robustness to noise in both the classical and the quantum channels. We generalize the construction to an $N$-party information sharing protocol, possessing a feature that dishonest participants can be detected.

quant-ph↗

arXiv2025

End-to-End Portfolio Optimization with Quantum Annealing

Hybrid-quantum classical optimization has emerged as a promising direction for addressing financial decision problems under current quantum hardware constraints. In this work we present a practical end-to-end portfolio optimization pipeline that combines (i) a continuous mean-variance and Sharpe-ratio formulation, (ii) a QUBO/CQM-based discrete asset selection stage solved using D-Wave's hybrid quantum annealing solver, (iii) classical convex optimization for computing optimal asset weights, and (iv) a quarterly rebalancing mechanism. Rather than claiming quantum advantage, our goal is to evaluate the feasibility and integration of these components within a deployable financial workflow. We empirically compare our hybrid pipeline against a fund manager in real time and indexes used in Indian stock market. The results indicate that the proposed framework can construct diversified portfolios and achieve competitive returns. We also report computational considerations and scalability observations drawn from the hybrid solver behaviour. While the experiments are limited to moderate sized portfolios dictated by current annealing hardware and QUBO embedding constraints, the study illustrates how quantum assisted selection and classical allocation can be combined coherently in a real-world setting. This work emphasizes methodological reproducibility and practical applicability, and aims to serve as a step toward larger-scale financial optimization workflows as quantum annealers continue to mature.

quant-ph↗