Papers

Starting from the exact Projected Central Limit Theorem on hyperspheres, we rederive the Beta distribution for subsystem occupation probabilities and Lubkin's purity formula from elementary hyperspherical moments, quantifying the finite-size “platykurtic” suppression of tails relative to the Gaussian approximation used in standard eigenstate-thermalization and typicality treatments. Our main new result concerns the bipartite quantum mutual information $\langle I(A{:}B)\rangle$ for Haar-random pure states. We show that its full asymptotic expansion in $1/N$ admits a Bernoulli-factorized form in which every order $k \ge 1$ carries the symmetric factor $(d_A^{2k}-1)(d_B^{2k}-1)$ and all higher odd-order corrections vanish identically. Through an exact algebraic reorganization of Page's formula (conjectured in Ref.~\cite{Page1993} and subsequently proven~\cite{Foong1994, SanchezRuiz1995, Sen1996}), we establish that the leading finite-size correction separates into a dominant $\mathfrak{su}(d_A) \otimes \mathfrak{su}(d_B)$ bipartite quantum coherence contribution $(d_A^2 - 1)(d_B^2 - 1)/(2N)$ and a subtracted classical-probability (Cartan $\otimes$ Cartan) contribution $(d_A - 1)(d_B - 1)/(2N)$, and we trace this separation to the difference between diagonal and eigenvalue entropies via Schur's majorisation theorem, with the dimensional counts $(d-1)$ and $(d^2-1)$ acquiring meaning through the Cartan structure of the generalised Bloch decomposition. These results admit a single non-perturbative closed form: the exact typical mutual information factors as $\langle I(A{:}B)\rangle = (d_A^2-1)(d_B^2-1)\,\mathcal{G}(d_A,d_B,d_E)$, with $\mathcal{G}$ given by an explicit Bose–Einstein integral whose asymptotic expansion in $1/N$ reproduces the Bernoulli series.

The average bipartite quantum mutual information $\langle I(A{:}B)\rangle$ of Haar-random pure states can be expressed exactly through Page's formula in terms of digamma functions. We show that this quantity admits a single non-perturbative closed form: $\langle I(A{:}B)\rangle = (d_A^2-1)(d_B^2-1)\,\mathcal{G}(d_A,d_B,d_E)$, where $\mathcal{G}$ is given by an explicit convergent integral over a Bose–Einstein kernel. The overall factor $(d_A^2-1)(d_B^2-1)=\dim[\mathfrak{su}(d_A)]\cdot\dim[\mathfrak{su}(d_B)]$ is exact, not merely asymptotic. The asymptotic expansion of $\mathcal{G}$ in $1/N$ yields a Bernoulli-factorised series whose coefficients involve $\zeta(1{-}2k)$; this series diverges, and our integral is its exact Borel sum. The integral representation also makes $\langle I\rangle < (d_A^2{-}1)(d_B^2{-}1)/(2N)$ manifest via a scale-inversion symmetry of the kernel. Our derivation traces the mutual information's structure to an exact decomposition of Page's entropy into a diagonal (Dirichlet) contribution and a Schur-majorisation eigenvalue correction, whose assembly into the mutual information cleanly separates classical from quantum correlations.

We study local phase estimation for a single quantum emitter coupled to a bosonic Su-Schrieffer-Heeger (SSH) bath within a microscopic lattice model. Dimerization opens a central gap supporting an in-gap emitter-bath bound state, which suppresses complete relaxation of the emitter coherence. A Dyson-equation analysis yields the local bath Green's function, the in-gap bound-state condition, and the emitter residue controlling the retained phase information. The phase quantum Fisher information links gap formation, detuning, and emitter-bath coupling to the post-transient metrological response. At resonance, stronger coupling enhances transient hybridization but reduces the retained signal by lowering the emitter weight in the bound state. Away from resonance, late-time averages, retention times, and useful interrogation windows track how phase-information protection weakens as the emitter is tuned toward and beyond the band edge. A uniform-chain control shows that the retained signal disappears when the gap closes. In the bulk local-coupling geometry considered here, the response is insensitive to the sign of the dimerization, so the protocol probes spectral-gap physics and bound-state support rather than the SSH winding sector.

On superconducting quantum devices with sparse qubit connectivity, transpilation of long-range two-qubit interactions inserts additional SWAP gates, increasing hardware cost and execution error. Gate cutting via quasi-probability decomposition (QPD) can remove a selected two-qubit gate and thereby reduce routing overhead, but its sampling cost makes cut placement critical. We propose TW2S, a graph-only two-stage gate-cut selection method that operates on the circuit interaction graph without backend-specific transpilation at selection time. Stage 1 analyzes a min-fill elimination trace and scores edges by their contribution to a treewidth upper bound. Stage 2 ranks the resulting candidates by edge betweenness centrality with a degree penalty to identify routing bottlenecks. Across grid, Watts-Strogatz, barbell, and stochastic block model benchmarks transpiled to IBM's FakeSherbrooke backend, TW2S consistently outperforms random cut selection when the interaction graph contains identifiable sparse cuts. The advantage is governed not by absolute graph density but by moderate community structure and accessible inter-community edges. We further derive a mean-squared-error breakeven condition showing that, under a shared total shot budget, QPD is beneficial only when the ECR reduction is large enough and the signal strength is sufficient. Under an expanded per-subcircuit budget the signal-strength requirement is substantially relaxed. In noisy simulations of the J1-J2 transverse-field Ising model, TW2S achieves $\Delta$ECR = 47 for n = 8, compared with approximately 9 for random selection, and yields lower estimation error than the uncut baseline in the tested strong-signal regime, with larger gains at increased shot budgets. These results position graph-structural cut selection as a practical compiler-side tool for turning circuit cutting into a targeted routing-reduction strategy.

The central aim of the thesis is to examine how non-classical resources in finite-dimensional quantum systems can be identified, characterized, and protected for practical use in the presence of realistic noise. Using the discrete Wigner functions (DWFs) framework, we introduce negative quantum states and examine how their Wigner negativity, mana, coherence, and teleportation fidelity evolve under unital and non-unital channels, with particular attention to non-Markovian random-telegraph and amplitude-damping dynamics. We also analyze protection strategies based on weak measurement and quantum measurement reversal, showing that these methods can enhance quantum correlations, reduce fidelity deviation, and improve teleportation performance for two-qubit negative states in memory-bearing environments. Moreover, we demonstrate that certain negative states, derived from phase-space point operators, exhibit greater resilience than Bell states in measures of entanglement under non-Markovian noise. Further, this thesis focuses on developing and implementing quantum circuits for generating these states on superconducting hardware and realizing them for the first time on IBM's ibm-Brisbane device. Their preparation is verified using quantum state tomography, demonstrating high fidelity under realistic noise conditions. We propose a teleportation scheme that leverages one of the two-qubit negative quantum states as a resource. Moreover, these two-qubit negative quantum states are also found to perform better than the Bell states for maximal CHSH violation and Fisher information in noisy conditions. We believe that these negative quantum states have the potential to be used in place of the traditional Bell states in scenarios where non-Markovian errors are prevalent. (continued in the PDF)

Quantum key distribution (QKD) via geostationary Earth orbit (GEO) satellites offers a compelling route to continuous, continental-scale secure communications. However, operation in this regime entails extreme channel loss and significant background noise, particularly if daylight operation is desired. We present a comprehensive end-to-end feasibility study of a decoy-state BB84 protocol in a GEO downlink configuration, incorporating variable-length finite-key security and tight statistical bounds to expand the achievable positive-key regime. Our analysis encompasses the principal receiver architectures relevant to downlink QKD and employs a physically realistic channel model that captures the dominant loss and noise mechanisms. We evaluate performance across rural, urban, and coastal environments at multiple wavelengths, including visible Fraunhofer absorption minima and the telecom band. Using historical cloud data across Europe, we forecast the annual secret-key yield across the continent. Through a systematic exploration of the high-dimensional parameter space, we identify key trade-offs and performance bottlenecks that determine feasibility. These results establish practical operating thresholds and provide actionable design guidelines for future GEO-QKD missions.

Efficient generation of multiquanta emission is crucial for quantum information processing but remains challenging due to its typical reliance on higher-order quantum processes. Here, we theoretically demonstrate strongly correlated photon-phonon emission enabled by direct tripartite interaction. This interaction facilitates the formation of high-order multiquanta states without more intermediate state transitions, thereby avoiding the suppressed transition rates associated with multiple sequential processes and substantially improving resonant transitions. As a result, high-efficiency strongly correlated even-quanta emission (e.g., two photons and two phonons) can be achieved in the presences of dissipation. Beyond that, we show that introducing two-photon dissipation enables strongly correlated odd-quanta emission (e.g., two photons and one phonon) in the tripartite interaction system by parity-protected suppression of single-photon loss and reconstruction of higher-order multiquanta processes. Our work extends multiquanta emission into the tripartite coupling regime and holds promising potential for applications in hybrid quantum networks.

For treating correlated electronic systems on quantum computers, we propose a quantum-classical hybrid scheme for dynamical mean-field theory (DMFT). In the quantum part of the scheme, we use modified quantum phase estimation (QPE) circuits suitable for the one-particle Green's function (GF) at a finite temperature so that we can extract spectral amplitudes and the excitation energies without knowing the excitation channel invoked at each measurement. In the classical part of the scheme, we adopt an approach that estimates reasonably the GF based on the data collected from the QPE sampling. We dub the approach the QPE averaged over variable grids (QAVG), that may help one to reconstruct the GF via optimization of trial parameters and modeling the probability distributions for various settings of the QPE circuits. We apply the QAVG-DMFT scheme to SrVO$_3$ to demonstrate its validity via numerical simulations.

Quantum phase estimation (QPE) is an underlying technology for extracting the excitation spectra of many-electron systems, yet its practical use on current hardware is hindered by low grid resolution and environmental noises. Here we propose QPE averaged over variable grids (QAVG), a vernier-type approach that combines low-resolution QPE with multiple origin shifts and physically motivated continuous parametrization to reconstruct the spectra accurately. We introduce this approach into an end-to-end workflow for the ab initio-based model system for a CO molecule adsorbed onto the $\chi$-Fe$_5$C$_2$ surface. We perform experiments on Quantinuum H2-2 using both physical QPE circuits and logical QPE circuits encoded in the Steane code with offline bit-flip correction. We demonstrate that QAVG accurately reconstructs the spectra with deviations much smaller than the nominal QPE resolution, even when the noisy histograms are used. The cost landscapes averaged over the shifted grids substantially suppress the local minima arising from the spectral leakage, thereby stabilizing the optimization of trial parameters. These results indicate that QAVG provides a robust route to quantum simulations of correlated spectra toward the era of early-fault-tolerant quantum computers.

Recoil heating from photon scattering is a fundamental source of decoherence in optical trapping, severely limiting the preparation of nonclassical motional states. In cavity setups in the coherent scattering configuration, a predictive theory of recoil heating rate is missing, as usual perturbative approaches fail in the presence of sharp optical resonances. Hence, current works assume that the recoil heating rate is approximately equal to its free-space value. Here we show that this is not the case, as the electromagnetic environment can strongly modify recoil heating rate by the Purcell effect. Specifically, we predict that this rate can be significantly suppressed in state-of-the-art microcavities, for both center-of-mass and librational motion. To establish these results, we develop a general theoretical framework based on macroscopic quantum electrodynamics and on the few-mode quantization approach developed in nanophotonics. Our method applies to particles trapped in the presence of arbitrary electromagnetic structures, thus providing a route to engineering motional decoherence in levitated optomechanics by photonic structure design.

Photon superbunching, which occurs when the second-order correlation satisfies $g^{(2)}> 2$, is typically associated with strong optical nonlinearities or collective multi-photon emission processes. We predict that extreme superbunching can also arise in systems of weakly-nonlinear photonic cavities, via the creation of a squeezed vacuum through interference engineering by fine-tuning inter-cavity couplings and drive parameters. We present numerical calculations indicating that a system of four photonic resonators containing representative Kerr media can achieve $g^{(2)}(0) = 135$ with a $80\,\text{kHz}$ emission rate. Unlike earlier superbunching schemes, this mechanism is highly compatible with integrated photonic platforms constructed using conventional optical media.

The empirical proof of Bell inequality violations was a landmark moment for research into quantum foundations. It commits us to a universe without strict relativistic locality or requires that we escape through a potential loophole like many-worlds or superdeterminism. In this work, we consider a sequential, single-spin experiment whose auto-correlations match the two-spin entangled correlations of a Bell scenario. We use a counterfactual equivalence between the two to argue that Bell-type correlations are actually just a different implementation of the sequential experiment. This comports well with the counterfactual basis of the original EPR argument, and explains any apparent non-locality as a consequence of indirectly measuring quantities that do not have predefined values, due to the state-altering nature of sequential spin measurements.

Machine learning models can inherit hidden behavioral traits through innocuous public interfaces, a phenomenon known as subliminal learning. Here we extend this framework to quantum models and study two distillation pathways: an auxiliary channel on random inputs and a restricted task channel in which the student matches a public supervised output while the hidden behavior resides on a disjoint task. Both classical and quantum neural networks (QNNs) exhibit efficient auxiliary-channel subliminal learning, but the task channel shows strong architecture dependence. Classical neural networks transmit little hidden-task information through the public-task interface, whereas QNNs retain most of the hidden-task signal. We show that a unified geometric picture explains both regimes: transmission is controlled by the teacher drift magnitude together with the fraction of hidden-task-relevant drift that remains visible through the public interface. These results identify a concrete security concern for quantum model supply chains and suggest a controlled route for hidden-information transfer in quantum information processing.

In this study, we analyze the Rademacher complexity $ \mathcal{R}_{M} $ of a parameterized unitary whose generators are chosen from $ n $-qubit Pauli strings. Although generalization bounds for quantum machine learning models have been studied in several settings, explicit Rademacher-complexity bounds for parameterized unitaries generated by Pauli strings remain less transparent. We derive simple scaling bounds in terms of the number of parameters $ L $ and the number of training samples $ M $: $ \mathcal{O}(\frac{L^{\frac{3}{2}}}{\sqrt{M}}) $ for the full parameter domain and $ \mathcal{O}(\frac{L}{\sqrt{M}}) $ for a restricted parameter domain. Furthermore, we compare the obtained results with those for a classical linear model class and suggest a potential statistical-complexity advantage when the norms of both the input and the parameter in the classical model scale with the number of parameters. Numerical experiments provide qualitative evidence consistent with the predicted scaling.

We study single-photon scattering by atoms in arrays of one-way waveguides. We investigate both chiral and antichiral arrays, where the one-way waveguides are aligned in the same and opposite directions, respectively. In the chiral array, reciprocity is broken: one of the (spatial) dimensions is time-like, resulting in a light-cone feature of the scattered fields. In contrast, the antichiral array preserves reciprocity and exhibit scattering behavior typical of wave systems. In analogy with classical physical optics, we exmaine the geometrical optics, diffraction, and scattering regimes in the waveguide arrays. We illustrate our results using numerical simulations.

Quantum spin simulations of frustrated lattices remain challenging for both classical and quantum algorithms, particularly in parameter regimes relevant to quantum spin liquid (QSL) phases. In this work, we apply Sample-based Krylov Quantum Diagonalization (SKQD) to estimate the ground state of the antiferromagnetic XXZ Heisenberg model on the $J_1$–$J_2$ square lattice, the Kagome lattice, and a 1D chain, studying system sizes from 12 to 72 spins. In our application of SKQD, we identify a ZZ deformation of $\Delta=2$ as a sufficiently sparse Hamiltonian and introduce two modifications to the SKQD framework tailored to spin models: a canonical bitstring compression scheme that preserves the effectiveness of configuration recovery under spin-flip degeneracy, and the use of multiple Krylov subspaces to improve ground state coverage without any increase in quantum resources. For the 1D chain and Kagome lattice, SKQD achieves sub-percent ground-state energy errors at system sizes up to 24 spins, including a relative error of $0.002\%$ on the 12-site Kagome lattice, surpassing the best prior VQE result of $0.01\%$ on the same system while requiring no variational optimization. SKQD further extends to system sizes well beyond the reach of prior quantum algorithm studies, reaching 72 spins across all three geometries. Beyond 24 spins, accuracy degrades to relative errors of $19\%$–$36\%$ at 72 sites, but the gradual scaling of error with system size suggests these limits are set by available shot budgets and circuit depth rather than fundamental algorithmic constraints. Although classical tensor network methods remain state-of-the-art for these models, this work establishes a new benchmark for quantum simulation of the frustrated Heisenberg model and demonstrates SKQD as a scalable, hardware-compatible approach for studying strongly correlated spin systems.

Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is simple to simulate classically and straightforward to compute analytically, these simplifications are unable to capture the full dynamics of a noisy quantum system. In this work we use advanced hybrid stabilizer-tensor network simulation techniques to simulate coherent quantum crosstalk noise during syndrome extraction on a surface code. We show that the inclusion of coherence increases logical error rates and lowers the code threshold. In addition, we show that the specific distribution of the noise can quantitatively change logical error rates. The methods in this work allow simulation of quantum error correction with noise models previously inaccessible to classical simulation, providing new insights on the effect of crosstalk noise on quantum error correction codes.

This study compares the quantum bit error rate (QBER) performance of BB84, SARG04, and the entanglement-based BBM92 protocol in non-turbulent underwater optical channels. Clear, coastal, and turbid water types are considered under different background-illumination and receiver configurations. For BB84 and SARG04, channel attenuation and background-induced detections determine the quantum gain and QBER. For BBM92, photon loss is included through the two arm detection efficiencies, whereas the polarization state conditioned on two-photon detection is described by local depolarizing Kraus channels. The BBM92 QBER is obtained from the correlations in both measurement bases and from an exact partition of recorded events into true and false coincidences. Stochastic numerical estimates provide consistency checks of the analytical implementation. The results show that water turbidity and optical background reduce the distance below the adopted QBER threshold. They also show that a low conditional BBM92 QBER may coexist with a very small coincidence probability; therefore, the QBER-threshold distance alone does not represent a complete operational or secret-key-rate bound.

We develop an interacting extension of the Double Covariance Model (DCM), a stochastic subquantum framework in which macroscopic quantum dynamics emerge through coarse-graining of correlated microscopic fluctuations. Starting from local stochastic differential equations on subsystem Hilbert spaces, we derive a closed evolution equation for a coarse-grained double covariance operator using multi-scale Itô calculus and sliding-window averaging. The construction explicitly incorporates two separated temporal scales: a fast microscopic fluctuation scale governing subquantum stochastic processes and a slower macroscopic observation scale associated with coarse-grained dynamics. Within the hydrodynamic limit, where the ratio between microscopic correlation time and averaging-window scale vanishes, rapidly fluctuating corrections disappear and the effective dynamics converges to a deterministic macroscopic transport equation. We show that the emergent macroscopic dynamics has the exact Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form: coherent Hamiltonian evolution arises from deterministic subquantum flow, while dissipative channels emerge from quadratic noise correlations. The framework further demonstrates how non-separable interaction Hamiltonians can arise from strictly local, state-dependent stochastic feedback fields. In the fluctuation-free limit, the model reduces naturally to the standard von Neumann equation, providing a unified stochastic foundation for both open and closed quantum dynamics.

Hydrogen-terminated diamond is known for its p-type surface conductivity, which arises from a near-surface hole accumulation layer induced by adsorbed acceptor species. Here, we demonstrate that these surface acceptors also form optically active donor-acceptor pairs (DAP) with substitutional nitrogen donors in diamond. The insertion of a nominally undoped CVD interlayer between a nitrogen-rich HPHT substrate and a hydrogen-terminated surface enables the precise tuning of the donor-acceptor separation with nanometer precision. Radiative DAP recombination appears as bright, spectrally narrow lines whose intensity, energy, and decay dynamics depend systematically on interlayer thickness. Individual lines show single-photon statistics, while ensembles exhibit strong polarization anisotropy reflecting the planar donor-acceptor geometry. These findings reveal an optical counterpart of hydrogen-induced surface transfer doping in diamond and establish a surface-defined, nanometer-tunable platform for engineering DAP-based quantum emitters.

Quantum optimization for computed tomography (CT) reconstruction is constrained by the number of binary variables required for image representation, making direct whole-image quantum reconstruction difficult for large or structurally complex objects. We propose a hybrid region-of-interest (ROI) refinement framework in which a coarse global image is first reconstructed by quantum tomographic reconstruction (QTR) and quantum compressed sensing tomographic reconstruction (QCSTR), filtered backprojection (FBP), or simultaneous algebraic reconstruction technique (SART), and quantum optimization is then applied only to the selected ROI through a residual projection-image formulation. This strategy reduces the effective QUBO size while preserving high-fidelity reconstruction in the target region. Experiments on three discrete phantom samples show that both QTR/QCSTR+QTR/QCSTR and SART+QTR/QCSTR achieve accurate ROI reconstruction for moderate-size cases under a reduced-angle setting. For the largest and most complex sample, the quality of the coarse global estimate becomes critical, and the best result is obtained when a stable classical coarse reconstruction is combined with second-stage ROI-only QTR/QCSTR. Among the tested pipelines, SART+QTR/QCSTR achieves the lowest average ROI RMSE and MAE. The results indicate that the practical advantage of quantum-assisted CT reconstruction lies in reserving quantum optimization for local refinement while using classical reconstruction to stabilize the global background.

Anticoherent spin states have isotropic low-order spin moments and are relevant to direction-independent metrology and quantum reference-frame alignment. In contrast to pure states, for mixed states such isotropy may originate either from genuine quantum correlations or from classical statistical mixing. We introduce an axiomatic framework for mixed-state $t$-anticoherence based on the symmetric qubit embedding. We distinguish total $t$-anticoherence, non-decreasing under SU(2)-covariant channels, from quantum $t$-anticoherence, defined as a resource monotone relative to a chosen total measure and constrained to coincide with it on pure states. This yields a classical contribution as their difference. We construct total measures based on reduced-state purity, Hilbert-Schmidt distance, and cumulative multipoles, and we discuss fidelity-based total candidates. We construct quantum counterparts via convex-roof extensions of pure-state functionals tied to bipartite entanglement in the symmetric sector. We provide explicit mixed-state examples, identify states with maximal quantum anticoherence supported on anticoherent subspaces, study robustness under particle loss for different types of states, and characterize the trade-off between purity and the maximal achievable anticoherence order.

In this paper, we present a quantum implicit-explicit (IMEX) scheme for multiscale ordinary and partial differential equations whose discretization parameters are independent of the scaling parameter $\varepsilon$. A key ingredient of our approach is a continuous-time formulation of classical IMEX schemes, which decouples the evolution time of the quantum algorithm from the physical time of the differential equation and is therefore particularly useful in multiscale settings. Building on this idea, we employ the Schrödingerization framework [Phys. Rev. Lett. 133 (2024), 230602] to implement IMEX schemes on quantum computers. Compared to previous HHL type quantum AP scheme [J. Comput. Phys. 471 (2022), 111641], this new method requires narrower – an extra logarithmic factor – auxiliary register numerical examples on linear heat and multiscale telegraph equations demonstrate the independence in $\varepsilon$ of the method.

We present a conditional construction of candidate CSL-type collapse-noise correlators inspired by Generalized Trace Dynamics (GTD). The construction is not a parameter-free derivation from the minimal GTD Grassmann algebra. It rests on a chain of explicit structural postulates, listed in Section 1; within that auxiliary structure the spectral form and amplitude follow by computation rather than by phenomenological fitting. The resulting narrow-band spectrum at the Hubble scale lies outside the bands of current CSL bounds, so the framework is not in tension with existing high-frequency data. We compute the two-point function of a candidate collapse-noise operator associated with the GTD aikyon decomposition $q_i = q_B + a_0\beta_i q_F$. In the minimal Grassmann algebra, $q_F$ appears only multiplied by Grassmann generators $\beta_i$, the reduction of $\mathrm{Tr}(q_F^\dagger\Gamma^\mu q_F)$ to ghost-mode operators is obstructed by the nilpotent $\delta\beta = \beta_2 - \beta_1$, and the pure-fermion coefficient $\beta_1\beta_2$ has no ordinary sign, modulus, or inverse. We therefore introduce an auxiliary canonical fermionic Fock-space sector for $q_F$, equivalently replacing the nilpotent pure-fermion coefficient by an ordinary effective scalar body parameter. This replacement is an independent structural postulate, not a consequence of the original minimal action. Under this auxiliary postulate, together with a scalar bilinear $J = \mathrm{Tr}(q_F^\dagger q_F)$ as bath operator, positive-norm canonical quantization, and an effective sign choice $\sigma = \pm1$ for the scalarized pure-fermion sector, elementary Wick contraction gives a Wightman line at $|\omega| = 2\omega_0$ with amplitude $A_J = (\hbar/2m_R\omega_0 L_{\mathrm{aik}}^2)^2\cdot N\cdot D$. The cosmological identification $\omega_0 \sim H_0$ places the line at twice the Hubble scale. [truncated]

Temporal cavity solitons generated in monochromatically driven dispersive Kerr resonators offer an attractive avenue for on-chip optical frequency comb generation. Key to many of their applications is to understand how noise – both technical and quantum – affects the soliton states, which has accordingly been extensively investigated. Here, we report on a comprehensive theoretical study that elucidates how technical and quantum fluctuations impact a new type of soliton structure that has very recently been predicted and observed in dispersive Kerr resonators under conditions of bichromatic driving: the pure-Kerr parametrically driven cavity soliton (PDCS). We examine how classical laser phase noise transfers from the two pump fields onto the soliton frequency comb, and we calculate the solitons' fundamental quantum-limited timing jitter and two-mode squeezing spectra. In each case, we find that PDCSs can out-perform conventional cavity solitons with comparable characteristics, even when driven by two uncorrelated lasers. Our results demonstrate that pure-Kerr PDCSs can offer unprecedented performance in noise-sensitive photonic applications and as a quantum resource

We present a comparative study of the permutation matrix representation (PMR) method for Hamiltonian simulation alongside other leading quantum algorithms. Our analysis focuses on resource costs for simulating both time-independent and time-dependent Hamiltonians. For the time-independent case, we benchmark PMR against quantum signal processing (QSP) and qubitization, using the Rydberg interaction Hamiltonian as a representative example. For the time-dependent case, we compare the time-dependent extension of PMR with the quantum highly oscillatory protocol (qHOP), applied to a Floquet-driven transverse field Ising model in arbitrary spatial dimensions. In both regimes, we find that PMR offers complementary advantages in resource requirements and exhibits favorable scaling with certain system parameters, suggesting that it may provide practical benefits on resource-constrained quantum hardware.

Zero-noise extrapolation provides a practical means of suppressing gate errors in current noisy intermediate-scale quantum hardware. The accuracy of the zero-noise estimate depends sensitively on the fidelity of the assumed noise model to the actual error scaling. This work introduces a hybrid Gaussian-exponential extrapolation scheme tailored for quantum circuits with periodic structure, which are ubiquitous in quantum algorithms. Under Pauli diagonal errors, by constructing and analyzing an approximate Markov process for the transfer of Pauli operators, we prove a central limit theorem: the noise amplification factor weakly approaches a log-normal distribution, which motivates augmenting the standard exponential model with Gaussian variance corrections. The resulting model requires no prior noise characterization and applies directly to arbitrary periodic circuits. Performance is assessed on Trotterized Ising dynamics, random circuits, and Grover search algorithm using Qiskit noise simulators. For moderate to large circuit depths, the hybrid model yields measurable reductions in bias relative to previous extrapolation variants, indicating its utility for error mitigation on near-term quantum hardware.

We investigate constrained quantum motion on curves and surfaces using connection factorization methods. We show that Laplace operators admit an exact half-connection factorization generated by connection one-forms. The first-order part of the Laplacian is identified with the Darboux rotational connection of the orthogonal frame. Elimination of this rotational connection naturally produces quadratic geometric invariants analogous to supersymmetric Riccati potentials. Using orthonormal moving frames, we derive effective geometric contributions for planar curves, spatial curves, and embedded surfaces. We further analyze Dirac reductions using structure equations and show that for Fermi-type reductions the scalar Jensen–Koppe–da Costa contribution is cancelled in the reduced Dirac sector, leaving a residual first-order spinorial derivative structure. The resulting framework suggests the existence of hidden nilpotent covariant differential complexes naturally generated by geometric connection structures.

States of sufficiently low purity are separable and cannot be entangled by unital (purity-non-generating) operations. Since high-purity states are experimentally demanding, it is natural to ask how much purity a state must possess to enable entanglement generation. Absolutely separable states remain separable under all deterministic unital channels, and so cannot deterministically generate entanglement in this setting. We show, however, that some absolutely separable states can generate entanglement via probabilistic protocols that do not produce purity. This motivates the study of states that fail to generate entanglement with any non-zero probability, which we call completely absolutely separable; we give a full characterization of this class. Along the way, we derive a novel sufficient condition for separability that depends only on the largest and smallest eigenvalues, along with the smallest local dimension and is independent of all previously known spectral separability criteria.

This work investigates the deformed-derivative formalism introduced by Borges, with emphasis on the relation between the linear operator $D_{(q)}$ and its nonlinear dual counterpart $D^{(q)}$. Directly inserting the dual derivative into the kinetic term leads to a nonlinear Schrödinger equation and obscures the usual interpretation of superposition and probability. We show that this nonlinearity can be removed by a simultaneous transformation of the coordinate and of the wave function. The transformed problem is an ordinary linear Schrödinger equation in a deformed coordinate, and its representation in the physical coordinate is equivalent to a Hermitian position-dependent-mass (PDM) Hamiltonian. In this formulation, the deformation parameter $q$ determines both the effective mass profile and the associated metric. The formalism is applied to the free particle, the infinite square well, the rectangular barrier, and the harmonic oscillator in the weak-deformation regime. Comparison with the nonadditive-translation approach of Costa Filho et al. shows that the Borges dual-$q$ framework provides an alternative route to the same effective geometric structure. For $q<1$, the effective confinement length is reduced, which raises the bound-state spectrum and enhances tunneling; for $q>1$, the effective length is increased, which lowers the spectrum and suppresses tunneling relative to the undeformed limit $q=1$.