Papers

We present an analytical framework for stabilizing second-order correlated tunneling of two spin-orbit-coupled bosons in a periodically driven non-Hermitian double-well potential. By combining Floquet theory with multiple-scale asymptotic analysis, we derive effective second-order dynamics and exact quasienergy spectra in the strongly interacting regime. Our analysis reveals distinct stability mechanisms for three fundamental tunneling channels: interwell spin-conserving, interwell spin-flipping, and intrawell spin-flipping. For balanced gain and loss, we identify discrete, well-defined parameter regions where stable pair tunneling emerges, with the spin-flipping channel exhibiting a characteristic symmetry absent in its spin-conserving counterpart. Under unbalanced gain-loss conditions, stability is achieved only when the gain and loss coefficients satisfy specific parametric relations, enabling dissipation-controlled tunneling. Most notably, stable intrawell spin-flipping, while inherently unstable for an initial Fock state, becomes accessible when the system is prepared in a coherent superposition state, thereby revealing that initial-state coherence can serve as a control parameter for dynamical stability in non-Hermitian systems. These results expand the possibilities for controlling correlated tunneling in many-body systems with engineered dissipation.

We develop a general framework based on the sign patterns of Lyapunov exponents for engineering and characterizing counterintuitive localization properties in one-dimensional non-Hermitian quasiperiodic lattices. On the one hand, for the Anderson localized states in the bulk under the periodic boundary condition, we find that their localization features can be boundary-sensitive, becoming boundary-localized skin modes under the open boundary condition. On the other hand, for non-localized states, the well-known extended-localized duality relation can break down, as their counterparts in the dual model can also be nonlocal. We discuss how these remarkable phenomena can be understood from the perspective of Lyapunov exponents, highlighting the interplay of non-Hermiticiy and quasiperiodicity.

Linear response theory and Green's functions provide a universal framework for understanding dynamical correlations in strongly correlated open quantum systems. While the theoretical foundation for non-Hermitian linear response has been recently established to describe dissipation and fluctuation-dissipation relations (FDR), generalizing these predictions onto practical quantum computers remains a formidable algorithmic challenge due to the intrinsically non-unitary nature of the dynamics. In this work, we present a systematic algorithmic framework that seamlessly transforms non-unitary multi-time correlation functions into a unitary form viable for digital quantum hardware. By mapping the vectorization of the Lindblad master equation into an expanded continuous-variable Liouville space, we employ the Schrödingerization technique to deterministically evaluate the non-Hermitian response. Furthermore, through hardware-aware simulations utilizing a 133-qubit device noise model, we demonstrate that our unitary framework robustly preserves the fundamental spectral information – specifically the phase and oscillatory frequency – against realistic depolarizing channels. By bypassing explicit non-unitary mid-circuit measurements, this approach intrinsically supports the integration of standard quantum error mitigation protocols, providing a scalable algorithmic blueprint for probing open-system universality on near-term hardware.

Quantum emitters near the surface of silver nanoparticles undergo Rabi oscillations in electronic population dynamics due to strong coupling with near-field multipole modes that are not radiative. Low-frequency nanoparticle dipole modes are radiative but do not couple strong enough to quantum emitters. These features limit the observation of strong coupling. Using macroscopic quantum electrodynamics theory within a Lorentzian pseudo-mode approximation for the non-Markovian interaction kernel, we demonstrate that by coating spherical silver nanoparticles with a thin molecular J-aggregate layer, the resulting core-shell plexciton resonance restructures the local electromagnetic vacuum at dipole-mode frequencies to enable Rabi oscillations for quantum emitters that otherwise would only undergo exponential population decay. Specifically, we show for quantum dot emitters in the near field of silver nanospheres of 20 nm radius, that weak-to-strong coupling crossovers can be induced using 2 nm J-aggregate shells. Our work demonstrates the potential of molecular aggregates to enable deep sub-wavelength structuring of the vacuum field for the observation of coherent quantum dynamics in optical nanocavities.

The NOON states play a critical role as physical resources in quantum information processing and quantum metrology, yet their preparation efficiency and applicability are often constrained by complicated operational procedures or the requirement for nonlinear interactions. In this paper, we propose an efficient protocol to generate the NOON states within two microwave cavities embedded in a superconducting system, assisted by an auxiliary five-level qudit. The state preparation is accomplished in three steps for an arbitrary photon number $N$ by adjusting only external classical fields, while keeping the qudit-cavity coupling strengths and the qudit level spacings fixed. Based on parameters accessible in superconducting systems, numerical simulations show that the protocol achieves relatively high fidelity for the NOON states preparation even in the presence of parameter fluctuations and decoherence effects. Thus, this protocol may provide a practical approach for preparing the NOON states with current technology. Notably, since nonlinear interactions are not required, the protocol is flexible and has the potential to be applied across various physical systems.

The binomial code is renowned for its parity-mediated loss immunity and loss-error recoverability, while geometric phases are widely recognized for their intrinsic resilience against noise. Capitalizing on their complementary merits, we propose a noise-resilient protocol to realize Nonadiabatic geometric quantum computation with binomial codes in a superconducting system composed of a microwave cavity %off-resonantly dispersively coupled to a %three-level qutrit. The control field %geometric quantum computation is designed by %combining geometric phases, integrating reverse engineering and optimal control. This design provides a customized control protocol featuring strong error-tolerance and inherent noise-resilience. Using experimentally accessible parameters in superconducting systems, numerical simulations show that the protocol yields relatively high average fidelity for geometric quantum gates based on binomial code, even in the presence of parameter fluctuations and decoherence. Thus, this protocol may provide a practical approach for realizing reliable Nonadiabatic geometric quantum computation with binomial codes in current technology.

Dense Lindblad propagation at the Hilbert-space sizes of near-term transmon control ($d = 3$, $9$, $27$) sits in a regime where cache boundaries, launch overhead, and fixed latency decide which hardware is useful, not peak arithmetic rate. This paper characterizes that regime on two x86 CPUs, two NVIDIA GPUs, and a low-cost FPGA. Each implementation is stated as an algorithm in $d$ with an idealized cost built from separately measured ceilings, and the measured gaps are attributed to specific mechanisms: thread fork/join, the strided read of the propagator, PCI Express (PCIe) transfers, and propagator re-upload. An end-to-end gradient-ascent (GRAPE-style) benchmark against released QuTiP 5.2.3 shows that fast propagation does not imply fast control optimization: the C path wins by up to two orders of magnitude at $d = 3$ but loses at $d = 27$, where the dense LU solve inside the Padé propagator build takes over $90\%$ of the cost. The FPGA contributes a deterministic-latency operating point, $95$ cycles per step at a stress-characterized $108$ MHz with zero cycle spread over $1000$ trials, and its Q1.15 fixed-point drift is measured on the device. The results are a map of operating regimes for the measured grid, with the propagator build, not propagation, as the dominant cost at the largest size.

The central theme of my thesis is to explore various simple prototype models that are exactly solvable in the framework of time dependent noncommutative spaces. By adopting the methodology provided by the Lewis Riesenfeld theory, we developed a procedure for obtaining a class of exact solutions for such model systems. We analyzed these solutions by deriving the energy expectation values analytically and representing those energy dynamics graphically. We also examined the explicit existence of a non-zero Berry geometric phase in the noncommutative framework and analyzed the role of noncommutativity in generating a non-trivial Berry phase when the model Hamiltonian and the noncommutative parameters are periodic in time. Overall, my thesis contributes to a deeper understanding of quantum theory in time dependent noncommutative backgrounds and indicates a strong possibility for developing a consistent quantum theory within such frameworks.

We investigate the effect of nonrelativistic motion on the emission dynamics of a dipole emitter moving next to a reflecting interface. Within the formalism of macroscopic QED, we obtain a general equation of motion for the dipole amplitude in terms of the dyadic Green's function, yielding a dynamical extension of the Drexhage effect. At short dipole-surface distances, the dipole can be described as a parametric oscillator featuring time-dependent dampings and Lamb shifts, both arising from the self-induced modulation of the surrounding electromagnetic environment. Importantly, these time-dependent parameters do not always average out, leading to amplification of the dipole amplitude and the radiated intensity when considering certain sinusoidal trajectories with specific modulation amplitudes and frequencies. We derive threshold modulation amplitudes as function of the relative permittivities at the interface. Qualitatively, in the vicinity of certain epsilon-near-zero materials, amplification is possible purely by modulation of the damping. Our findings open up avenues for the dynamic control of light-matter interaction in nanophotonic environments.

We present a new p-adic version of the Jackiw-Rebbi model. In the new model, the real numeric line is replaced by a p-adic line (the field of p-adic numbers Q_{p}), and the Dirac Hamiltonian is replaced by a non-local operator acting on complex-valued functions defined on Q_{p}. These Hamiltonians admit localized wavefunctions and allow long-range interactions, so spooky action at a distance is allowed. These features are not present in the original model. The new model gives the same predictions as the standard one. The p-adic line serves as a discrete model for the physical space; in this type of space, non-locality emerges naturally.

We introduce a first-principles-guided framework for predicting statistical TLS distributions from mobile impurities in disordered materials. Machine-learned interatomic potentials, with DFT and minimum-action-path validation, connect impurity landscapes to tunnel-splitting and asymmetry distributions, TLS densities, and dielectric loss. Applied to amorphous Nb$_2$O$_{5-\delta}$ and Ta$_2$O$_{5-\delta}$, the framework implicates interstitial hydrogen as a source of microwave loss. Loss tangents match Nb-pentoxide measurements at inferred H concentrations, while weaker H uptake in Ta reproduces the Nb/Ta TLS contrast.

We use a Quantum Extreme Learning Machine for characterizing and estimating parameters of quantum dynamics generated by a tunable collision model. The input to the learning protocol consists of quantum states produced by successive system environment interactions, while the reservoir is implemented as a disordered many body quantum system evolving under a fixed Hamiltonian. We systematically explore how extending the QELM feature space, through the inclusion of temporal information and additional observables, affects estimation performance. Our results demonstrate that temporal extensions of the feature vector consistently and significantly enhance estimation accuracy relative to the baseline protocol. Notably, incorporating memory from earlier time steps yields the most substantial and robust improvements, whereas extensions based solely on additional observables offer only marginal gains. Crucially, the advantage conferred by temporal memory becomes increasingly pronounced as the dynamics become more strongly non Markovian, indicating that environmental memory effects serve as a constructive resource for learning.

Early demonstrations of fault tolerant quantum systems have paved the way for logical-level compilation. For fault-tolerant applications to succeed, execution must finish with a low total program error rate (i.e., a low program failure rate). In this work, we study a promising candidate for future fault-tolerant architectures with low spatial overhead: the Gross code. Compilation for the Gross code entails compiling to Pauli Based Computation and then reducing the rotations and measurements to the Bicycle ISA. Depending on the configuration of modules and the placement of code modules on hardware, one can reduce the amount of resulting Bicycle instructions to produce a lower overall error rate. We find that NISQ-based, and existing FTQC mappers are insufficient for mapping logical qubits on Gross code architectures because 1. they do not account for the two-level nature of the logical qubit mapping problem, which separates into code modules with distinct measurements, and 2. they naively account only for length two interactions, whereas Pauli-Products are up to length $n$, where $n$ is the number of logical qubits in the circuit. For these reasons, we introduce a two-stage pipeline that first uses hypergraph partitioning to create in-module clusters, and then executes a priority-based algorithm to efficiently assign clusters onto hardware. We find that our mapping policy reduces the error contribution from inter-module measurements, the largest source of error in the Gross Code, by up to $\sim36\%$ in the best case, with an average reduction of $\sim13\%$. On average, we reduce the failure rates from inter-module measurements by $\sim22\%$ with localized factory availability, and by $\sim17\%$ on grid architectures, allowing hardware developers to be less constrained in developing scalable fault tolerant systems due to software driven reductions in program failure rates.

This work unlocks the manufacturing of nanophotonic quantum systems that exploit the unique material properties of single-crystal diamond (SCD). We achieve this by introducing a semiconductor-compatible process for the direct bonding of multiple high-quality, ultrathin diamond films onto a carrier wafer, enabling the subsequent parallel nanofabrication of optoelectronic integrated circuits. Central to this approach is a new diamond surface-preparation method that avoids boiling tri-acid mixtures while producing exceptionally clean 20 um thin single crystals. These platelets are bonded side-by-side to 100 mm silica wafers and exhibit a record shear strength of 45.1 MPa for (100)-oriented diamond, surpassing all previously reported bonding attempts. Evidence indicates that the bonding is dominated by van der Waals interactions, likely arising from mismatched protonation mechanisms between Si-OH and C-OH surface terminations, rather than from covalent-bond-driven mechanisms. Despite this non-molecular nature, the heterostructures remain stable through liquid immersions and standard nanofabrication steps. Because the method depends primarily on surface cleanliness and roughness rather than specific chemistries, it is broadly transferable across wafer materials. This capability to parallel-bond ultrathin SCD films onto large-area substrates provides a scalable route to high-performance platforms spanning nanophotonic quantum technologies, high-power electronics, MEMS, and biotechnology.

We demonstrate a new magneto-optical trap (MOT) configuration using a simple pair of crossed wires rotated at 45 deg and an appropriate bias field to generate a MOT of >10^8 atoms. The same pair of wires, with slightly adjusted control parameters, is then used to magnetically trap the atoms and cool them via forced evaporative cooling into a Bose-Einstein condensate (BEC) with >10^4 atoms. We present the theoretical framework for generating a quadrupole field using a pair of crossed wires with arbitrary rotation angle, along with the atom chip design and fabrication. Finally, we describe the experimental protocols required for BEC production using only a single crossed-wire atom chip.

Quantum reservoir computing (QRC) is a hardware-implementation-friendly quantum neural network scheme with minimal physical system requirements and a proven advantage over classical counterparts. We use an extension of the positive-P phase space method to efficiently simulate a bosonic, linear silicon-chip based QRC system excited with a single nonclassical state, a "kitten" state. In combination with input-encoding coherent states, our method allows to obtain exact results for all correlation functions without Hilbert space cutoff. Surprisingly, we find that such a setting - where the only "quantumness” derives from a single input mode, is sufficient to obtain significant (over 9-fold) reduction of classification error over the classical counterpart. Our work provides a promising direction toward efficient quantum computation with accessible optical hardware.

This article presents a mathematical analysis and numerical strategies for solving the optimization problem of minimizing the quadratic function $J(P) = \text{Tr}(BP)- \frac{1}{2} \text{Tr}(A P A P)$, where $A,B \in \mathbb R^{M \times M}_{\rm sym}$, with $A \succeq 0$, over the Grassmann manifold ${\rm Gr}(m,\mathbb R^M)$. While this problem is non-convex and typically admits non-global local minima - posing challenges for Riemannian optimization and self-consistent field (SCF) algorithms - we identify cases where the global minimizer can be obtained by solving an auxiliary convex problem. When this approach is not directly applicable, the solution to the auxiliary problem still serves as an effective initialization for Riemannian optimization methods and SCF algorithms, significantly improving their performance. This work is motivated by applications in quantum embedding methods, particularly in the construction of bath orbitals, where such optimization problems naturally arise.

The role of quantum entanglement in thermodynamical systems remains elusive. Does entanglement result in thermodynamic advantages or does it impose fundamental limitations? Here, we unambiguously quantify the amount of heat and work in a quantum system that is due to the presence of entanglement. This is achieved by constraining the system's non-equilibrium dynamics to separable states, thereby isolating the impact entanglement has on thermodynamic effects. Unlike thermodynamic entanglement measures, which signify a loose connection between entanglement and thermodynamic properties, imposing a constraint constitutes an active intervention into a system – answering how much of a system's thermodynamics is caused by (not correlated with) its quantumness. We benchmark our theory by applying the constrained dynamics to several multipartite systems, including quantum batteries and quantum refrigerators.

The dynamical generation of quantum resources, such as many-body entanglement, Bell correlations or spin squeezing, can be achieved via one-axis twisting (OAT) dynamics, which require all-to-all couplings. However, current digital and analog quantum simulation platforms natively provide short-range or power-law couplings that decay too quickly for this purpose. We demonstrate that two spin-$\tfrac12$ chain models – a staggered nearest-neighbor XXX chain and a long-range XXZ chain – develop an effective OAT nonlinearity when projected onto the symmetric sector. We show that these dynamics generate metrologically useful spin-squeezed states and Greenberger-Horne-Zeilinger coherences that ensure violation of many-body Bell inequalities. We confirm the accuracy of this mapping by comparing it to the exact dynamics and demonstrate that the generated correlations can be read out using a single probe qubit. The resulting dynamics can be simulated with analog and digital quantum simulators.

The most widely used approach for simulating the dynamics of time-dependent Hamiltonians via quantum computation depends on the quantum-classical hybrid variational quantum time evolution algorithm, in which ordinary differential equations of the variational coefficients for determining time evolution are solved via classical simulations with a time discretization method. We here present a full-quantum approach, in which ordinary differential equations of the variational coefficients are transformed into static linear equations via the Chebyshev spectral discretization method and then solved via the quantum singular value transformation algorithm. Our full quantum algorithm avoids classical feedback, achieves exponential convergence for smooth Hamiltonians, and yields a quantum circuit depth that is independent of the number of time steps. We demonstrate two implementation strategies, with a global formulation designed for fault-tolerant architectures and a sequential formulation tailored to near-term devices, and validate the approach through numerical simulations of proton-hydrogen charge-transfer dynamics, a prototypical time-dependent quantum chemistry problem. This work establishes a systematic pathway from quantum-classical hybrid variational quantum algorithms to full-quantum solvers for general time-dependent Hamiltonians, particularly those whose dynamics admit compact variational descriptions, opening a route toward full quantum computational advantages in time-dependent simulations.

We investigate the dissipative adaptation hypothesis in a quantum regime using a system-reservoir approach. This hypothesis proposes that self-organization arises from a system's ability to dissipate the work transiently absorbed from an external drive. We analyze the quantum dynamics of a driven open system described by a time-dependent spin-boson Hamiltonian modeling a particle in a metastable double-well potential with controllable asymmetry. We explore how the work provided by the dynamic potential is related to the transition probability between the two ground states of the double well. These studies motivate further investigations of the driven spin-boson model toward an understanding of the system's evolution and its thermodynamic implications.

In this work, we study a particular class of Bell inequalities involving only direct equality-comparisons of outcomes. In the bipartite case, the scenario can be interpreted as a natural generalization of full-correlator in- equalities (XOR games) beyond binary outputs. We define the sub-polytope of the local polytope corresponding to this scenario and solve it for several bipartite and multipartite scenarios by leveraging some structural prop- erties. In doing so, we obtain thousands of new tight inequalities, many of which are also facets of the standard local polytope. We also define unanimous Bell inequalities, a particular case of the previous class applied to the multipartite setting in which only full-equality events (all outcomes equal) are considered. We show that such inequalities can always be written as deterministic nonlocal games, and we give a simple multipartite unanimous family and prove its local bound. We show that most of these inequalities admit quantum violations, and we also display aspects of their importance for nonlocality. For instance, we identify examples where such inequalities can act as dimension witnesses, outcome witnesses, witnesses of genuine multipartite nonlocality, as well as being relevant to CHSH. These results show that these simple and elegant inequalities by themselves provide a powerful tool for discovering new Bell inequalities and device-independent witnesses.

Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of unitary evolutions. Characterizing channels that do not admit such a decomposition is in general a hard problem with significant implications for noise mitigation in quantum technologies and for fundamental problems in quantum information theory. Here we establish a link between mixed-unitarity of unital channels and the (quantum) nature of the memory effects in non-Markovian dynamics. Translating the problem into the language of process tensors, this connection yields a hierarchy of semidefinite programs that provides numerically efficient witnesses for non-mixed-unitary behavior, outperforming existing criteria. We demonstrate the power of this approach through illustrative examples of unital channels in dimensions three and four, and show how the method can detect non-mixed-unitary behavior based on incomplete channel tomography.

Luttinger's theorem constrains the particle density of interacting fermions through global properties of the single-particle Green's function, and its violation signals a breakdown of the identification between the quantized Hall response and the Green-function-based Ishikawa-Matsuyama invariant. This phenomenon becomes especially compelling in strongly correlated topological phases, such as fractional Chern insulators, where fractionalized quasiparticles lack an adiabatic connection to electrons, raising the question of how Green's-function-based topological invariants manifest in such phases. Using exact diagonalization of the fermionic Harper-Hofstadter-Hubbard model, we compute bulk single-particle Green's functions deep inside a fractional Chern insulating phase and directly evaluate the Luttinger count, its possible correction (the Luttinger integral), and the Ishikawa-Matsuyama invariant $N_3[\mathrm{G}]$. We demonstrate a clear violation of Luttinger's theorem and show that the fractional nature of the many-body Chern number is encoded in the Středa response of the Luttinger integral, while the integer invariant $N_3[\mathrm{G}]$ arises from the Středa response of the Luttinger count. We also analytically prove that $N_3[\mathrm{G}]$ is fully determined by the Luttinger count together with the Chern number of the occupied Bloch band, upon neglecting Bloch-band mixing. Finally, we propose an experimental protocol to extract all Green-function-based topological invariants from local density-of-states measurements, experimentally accessible in fractional quantum Hall systems.

We study a doubly minimized variant of the lautum information - a reversed analogue of the mutual information - defined as the minimum relative entropy between any product state and a fixed bipartite quantum state; we refer to this measure as the tumula information. In addition, we introduce the corresponding Petz Renyi version, which we call the doubly minimized Petz Renyi lautum information (PRLI). We derive several general properties of these correlation measures and provide an operational interpretation in the context of hypothesis testing. Specifically, we show that the reverse direct exponent of certain binary quantum state discrimination problems is quantified by the doubly minimized PRLI of order $\alpha\in (0,1/2)$, and that the Sanov exponent is determined by the tumula information. Furthermore, we investigate the extension of the tumula information to channels and compare its properties with previous results on the channel umlaut information [Girardi et al., arXiv:2503.21479].

We present a controllable quantum spin-chain model that reproduces the Page curve (the rise-and-fall of bipartite entanglement expected in black-hole evaporation), using only local interactions and a kinematic reduction of the subsystem size. Two transverse-field Ising chains are coupled to form a pure bipartite state; Hawking-like evaporation is implemented by dynamically shrinking the 'system' chain and enlarging the 'environment' chain, while unitary real-time evolution is simulated with matrix product state (MPS) tensor networks. The characteristic Page curve profile emerges robustly under this controlled subsystem resizing and notably persists even when the explicit Hamiltonian coupling across the boundary is set to zero, demonstrating that shrinking Hilbert-space dimension alone can generate Page curve behaviour. We show that the detailed shape of the curve depends on the internal information dynamics: operation at criticality yields a smooth profile, whereas moving away from criticality distorts entanglement growth and decay. These results position locally interacting spin chains as a realistic platform for probing black-hole-inspired information dynamics on current quantum hardware.

Many-body systems with strong interactions often exhibit macroscopic behavior markedly absent in single-particle or noninteracting limits. Such emergent phenomena are well exemplified in lattice Hubbard models, where the interplay between interactions, geometric frustration, and magnetic flux gives rise to rich physics. Superconducting qubits naturally enable analog quantum simulation of Bose-Hubbard models, while offering tunable parameters, site-resolved control, and rapid experimental repetition rates. Here, we study a superconducting-qubit device that realizes the Bose-Hubbard model on a triangular-ladder lattice. By tuning the magnitude and sign of couplings, we engineer a synthetic magnetic flux to characterize the resulting half-filling ground state for various parameter regimes. We measure observables analogous to current-current correlators and bond kinetic energies, finding signatures consistent with chiral superfluids, Meissner superfluids, and bond-ordered insulators. Our results establish superconducting circuits as a platform for robustly probing quantum phases of matter in frustrated Bose-Hubbard systems, even in strongly correlated and gapless regimes.

We present a computational survey of Kochen-Specker (KS) uncolorability in three-dimensional Hilbert space across coordinate alphabets drawn from quadratic, cyclotomic, golden-ratio, and cubic Pisot number fields, principally the two-symbol family A = {0, +-1, +-x}. In every tested alphabet, KS sets arise only when x supports a cancellation identity: an algebraic relation making dot products vanish exactly. Three mechanisms occur: modulus-2 cancellation (|x|^2 = 2, with the integer case 1+1=2 as the degenerate additive instance), phase cancellation (a vanishing sum of unit-modulus terms, as in 1 + omega + omega^2 = 0), and minimal-polynomial cancellation, in which the defining relation of a cubic algebraic unit supplies the vanishing sum directly, as in the supergolden ratio psi^3 = psi^2 + 1. Generators with |x|^2 >= 3 that are not roots of unity produce orthogonal triples but not KS-uncolorability in our survey. This pattern explains why constructions cluster into at least eight discrete algebraic islands among the tested fields, two of them cubic. Two yield potentially new KS graph types: the Heegner-7 ring Z[(1+sqrt(-7))/2] (43 vectors) and the golden ratio field Q(phi) (52 vectors, revealed only by cross-product completion); Z[sqrt(-2)] gives a new realization of a known Peres-type graph. Using SAT-based bipartite KS-uncolorability we verify and extend the input counts of Trandafir and Cabello across all six non-cubic islands. The two-mechanism pattern reported in versions 1-8 of this paper is refuted by the supergolden island, which motivates the third mechanism; whether the three-mechanism classification is complete remains open.

Quantum transfer learning combines pretrained classical deep learning models with quantum circuits to reuse expressive feature representations while limiting the number of trainable parameters. In this work, we introduce a family of compact quantum transfer learning architectures that attach variational quantum classifiers to frozen convolutional backbones for image classification. We instantiate and evaluate several classical-quantum hybrid models implemented in PennyLane and Qiskit, and systematically compare them with a classical transfer-learning baseline across heterogeneous image datasets. To ensure a realistic assessment, we evaluate all approaches under both ideal simulation and noisy emulation using noise models calibrated from IBM quantum hardware specifications, as well as on real IBM quantum hardware. Experimental results show that the proposed quantum transfer learning architectures achieve competitive and, in several cases, superior accuracy while consistently reducing training time and energy consumption relative to the classical baseline. Among the evaluated approaches, PennyLane-based implementations provide the most favorable trade-off between accuracy and computational efficiency, suggesting that hybrid quantum transfer learning can offer practical benefits in realistic NISQ era settings when feature extraction remains classical.

The resource theory for nonnegativity of quantum amplitudes distinguishes completely positive completely positive (CPCP) quantum channels from the larger class of completely positive doubly nonnegative (CPDNN) quantum channels. Johnston and Sikora showed that all qubit-to-qubit quantum channels that are CPDNN are also CPCP. However, they left open the question of whether a qutrit-to-qubit quantum channel exists that is CPDNN but not CPCP. We prove that no such channel exists and, more generally, that every CPDNN quantum channel with qubit output is CPCP. Thus the doubly nonnegative relaxation is exact for all qubit-output quantum channels. Our argument yields an explicit structural picture in which, after a canonical permutation of the Choi matrix, every qubit-output CPDNN channel is determined by a nonnegative vector and a nonnegative matrix, subject to a single positive-semidefinite block constraint. This gives a complete binary-output normal form, an explicit formula for the action of the channel, and quantitative population-coherence tradeoff inequalities governing the unique output off-diagonal mode. In this sense, qubit output is the nontrivial binary regime in which trace preservation and double nonnegativity collapse the free-channel cone to a fully describable geometry.