Papers

Entanglement-based key distribution protocols, such as the Bennett-Brassard-Mermin 1992 (BBM92) protocol and quantum conference key agreement (QCKA), are promising applications of quantum networks. In practical implementations, passive measurement setups are widely adopted because of their simplicity. However, the security analysis of passive protocols with biased basis choice is highly nontrivial, since standard proof techniques for threshold detectors are generally not applicable in this setting. In this work, we establish the security of passive entanglement-based key distribution protocols in the asymptotic regime. Specifically, we prove the security of passive BBM92 with biased basis choice and extend the proof to passive QCKA with an arbitrary number of parties. In addition, we numerically show that the key generation rate of passive BBM92 is almost identical to that of the corresponding active protocol. Our results provide a theoretical foundation for practical passive implementations of entanglement-based key distribution protocols.

Characterizing quantum topological phases requires measuring non-local string order parameters, demanding access to the full system, which is often experimentally unfeasible. In this work, we introduce a data-efficient supervised learning framework that circumvents this limitation by recognizing quantum phases from small subsystems. Our protocol utilizes a quantum kernel constructed from the reduced density matrices of these subsystems, which can be efficiently estimated experimentally. We benchmark our framework with the classification of the phase diagrams of two spin models on one-dimensional lattices, namely the generalized cluster-Ising spin-1/2 chain and the anisotropic Haldane spin-1 chain. Remarkably, our approach achieves high accuracy in phase classification when operations are limited to as few as one to four sites, and it also generalizes to longer chains even when trained on moderate system sizes. These findings demonstrate that local reduced density matrices preserve vital signatures of global topological phases, offering a practical route to characterize rich phase diagrams of quantum many-body systems.

We propose a framework for computing multiphotonic scattering probabilities in a lossless multiport interferometer for arbitrary photon numbers and degrees of indistinguishability. By exploiting a toroidal expansion of multiphotonic states in tensor powers of single-particle states, the framework defines a map from a torus of relative phases to the probability simplex that governs the asymptotic behavior of scattering probabilities in the large-photon limit. Specifically, the probabilities concentrate on the "classically allowed region" defined by the map, and the slowly-varying part of the multiphotonic distribution reproduces a classical measure induced by the map. As a result, we are able to establish a new asymptotic formula for the multiphotonic probabilities in a general scenario of partially indistinguishable photons, while also providing a single-particle picture to explain the asymptotics of known multiphotonic transition amplitudes in the fully indistinguishable case. More broadly, our framework yields new, directly testable consequences in relation to asymptotic photon bunching patterns: it translates features of the classical map – such as caustics and voids – into direct predictions about regions of large or exponentially suppressed photon-distribution probability.

We present a reproducible, parameter-driven software workflow for optimizing approximate mutually unbiased basis (AMUB) configurations in arbitrary dimensions d using a Lie-algebra unitary parameterization. The workflow is designed for portable execution across CPU, Apple MPS, CUDA-capable GPU, and HPC backends, using a Taylor-series matrix exponential layer as an accelerator compatibility pathway. As a dimension-six case study, we optimize unanchored configurations across 100 random seeds for basis counts n = 3, 4, 5, 6 in complex128 and complex64 arithmetic. The workflow recovers exact three-basis configurations, identifies a recurrent four-basis partial-exact hub-and-triangle structure, and finds no near-exact pairs for n = 5 or n = 6 in the reported campaigns under the primary tolerance. As a hardware-execution check, we embed the representative d = 6, n = 4 transition unitaries into three-qubit 8x8 unitaries and execute the resulting circuits on the 156-qubit Heron processor ibm-marrakesh using subspace post-selection. The measured QPU pairwise losses are dominated by a hardware and compilation noise floor of approximately 0.02-0.08, associated with compiled circuits averaging 37 native CZ gates, which obscures the distinction between classically near-exact and defective pairs. The results provide a reproducible computational framework for exploring AMUB landscapes, together with an initial assessment of the challenges involved in executing optimized dimension-six unitaries on current quantum hardware.

Artificial intelligence and quantum computing have both seen tremendous progress in recent years, opening up new avenues for accelerating scientific discovery. Classical machine learning has already proven to be useful for addressing challenges in quantum computation; and hardware progress is well underway towards the early fault-tolerant regime. On the other hand, the emerging field of quantum machine learning is aimed at utilizing the strengths of both computational paradigms, via the development of learning algorithms or models that benefit from running on quantum devices or from training on quantum data. We therefore argue that both of these paradigms stand to benefit substantially from each other. Here we review the most salient opportunities for machine learning in quantum computing, hoping to inspire a virtuous cycle through which both fields can mutually benefit.

Quantum algorithms are intrinsically two-boundary processes: an input state is prepared, and an output state or subspace is selected as the computational answer. We formulate this observation as a coherent Quantum Schrödinger Bridge (QSB), a pure-state Hamiltonian counterpart of Schrödinger bridge theory in which the endpoint constraint is imposed on state vectors and the transport cost is the quadratic control action. In this setting Aharonov's two-state vector becomes the natural optimal-control pair: a forward state from the input and a backward state from the target. Pontryagin's principle then yields a universal optimal Hamiltonian whose weak value is purely imaginary in the geodesic gauge. Thus weak values are not an auxiliary interpretation; they are the local response functions that quantify the drift of the pre-selected state toward the post-selected boundary. Applying this framework to unstructured search, periodicity finding, and matrix arithmetic, we reconstruct Grover's algorithm, the quantum Fourier transform underlying Shor's algorithm, and quantum singular value transformation (QSVT). The usual circuit components – oracles, diffusion reflections, controlled phases, and signal-processing rotations – emerge as Lie-algebraic syntheses of the optimal weak-value drift. This perspective unifies distinct algorithmic paradigms into a single geometric principle: algorithm design is the problem of choosing computational boundary conditions and realizing the corresponding optimal flow.

We show that, contrary to conventional understanding, the minimum measurable frequency shift (MMFS) for a single-mode ideal laser is determined by a combination of phase diffusion caused by SE and the shot noise caused by the VM. For all practical sensors, the MMFS is found to be given by the geometric mean of the measurement bandwidth and the Schwalow-Townes Linewidth, multiplied by a factor which can be much larger than unity under certain conditions. We determine the optimal value for the MMFS for three different sensing modalities, an unbalanced Mach-Zehnder Interferometer, a passive Fabry-Perot cavity (FPC), and heterodyning with a reference laser, and identify the conditions needed for reaching the optimal value.

We study the response of axion topological materials under the presence of external static electric and magnetic fields. We focus on the macroscopic quasi-static magnetoelectric response of topological insulators. We use techniques based on surface variables that have been previously employed in soft condensed matter problems for the description of heterogeneous systems composed of multiple homogeneous materials. A complete description of the whole system is written in terms of surface degrees of freedom, which in this case correspond to effective surface charge and surface current densities. We obtain a set of integral equations satisfied by these variables. We present exact analytic solutions for axial-symmetric cases. We develop a numerical method for the solution of the integral equations by means of a boundary finite element method. We apply the numerical method to topological insulators with different geometries such as spheres, hollow spheres and toroidal surfaces. We show that that a variational principle can be used to recover the surface variables equations.

Given two dense multivectors of the Clifford algebra $C\ell(V, Q)$ with $N=2^{p+q}$ coefficients, the fastest known classical algorithms compute their geometric product in $O(N^{\omega/2})$ arithmetic operations, where $\omega$ denotes the matrix multiplication exponent. I show that, under amplitude encoding, a quantum computer executes the geometric product in $O(\operatorname{polylog} N)$ time, using logarithmic space with sublogarithmic circuit depth. This exponential speedup establishes Clifford multiplication as a quantum primitive, providing an efficient computational foundation for quantum geometric algorithms and relativistic simulations.

We investigate Krylov spread complexity for states evolving under time-dependent Hamiltonians. For periodically driven systems, we formulate the problem within Floquet theory and show how the Magnus expansion provides a systematic approximation when the Floquet Hamiltonian is not available in closed form. We then extend this framework beyond periodic driving and demonstrate that, in addition to the globally truncated Magnus expansion, a piecewise Magnus expansion provides a reliable method when the global expansion loses convergence or accuracy. Our results provide practical tools for analyzing complexity growth in a broad class of time-dependent quantum systems.

The Aharonov-Bohm (AB) effect remains a cornerstone of fundamental and applied physics. In this work, we utilize the AB caging effect originated from an effective magnetic field induced by multiorbital interactions, creating an all flat band (FB) lattice system. Normally, FB states are known for being compact in space and having a zero tail; therefore, their mobility in a linear environment is generally understood as impossible. We propose a Floquet driving protocol in an all-FB photonic system to fully control the dynamics of localized photonic states. The modulation of the Hamiltonian along the propagation coordinate allows the translation of compact states in the direction of constructive interference, resulting in an effective stroboscopic quantum walk-like effect. We find that the traveling states exist in chiral pairs. We experimentally implement the Floquet driven protocol using femtosecond laser written photonic waveguides and demonstrate directional control of the propagation, determined by the relative phase of the input condition.

A binary $(n,m)$ quantum random access code (QRAC) compresses an $n$-bit classical string into an $m$-qubit quantum state, from which a decoder attempts to recover a randomly selected target bit. Of particular interest is the optimal average probability of success, $P^{Q,\mathrm{avg},\mathrm{opt}}_{n,m}$, which was numerically conjectured to satisfy the bound $P^{Q,\mathrm{avg},\mathrm{opt}}_{n,m}\leq \frac{1}{2}+\frac{1}{2}\sqrt{\frac{m}{n}}$. Recent constructions of $(n,n-1)$ QRACs by Suzuki and $(n,n-2)$ QRACs by Akibue et al. meet this bound exactly, raising the question of their strict optimality. In this work, we settle this question by proving the conjectured upper bound for $m\in\{n-1,n-2\}$, thereby precisely determining $P^{Q,\mathrm{avg},\mathrm{opt}}_{n,n-1}$ and $P^{Q,\mathrm{avg},\mathrm{opt}}_{n,n-2}$. The proof utilizes a translation recently studied by Lin and de Wolf from local to global reconstruction via pretty good measurement, along with dimensional and positive-semidefinite constraints on an induced channel.

Quantum networks are advancing towards larger and more operational infrastructures, yet their evaluation remains fragmented across heterogeneous physical platforms, simulators, protocols, and architectural abstractions. Current digital-twin studies for quantum networks mainly realise isolated capabilities or application-specific solutions rather than reusable system-level twins. This paper argues that Model-Driven Engineering (MDE) can provide a systematic basis for integrating and evolving these heterogeneous artefacts. It derives requirements for design-time evaluation and runtime synchronisation, and proposes a progression of architectures from code-driven and domain-model-driven solutions to point-to-point and hub-and-spoke integration. A conceptual implementation case study illustrates this using SysML v2, QKD kit, an EMF-based controller, and SeQUeNCe. The work provides a foundation for adaptable and interoperable digital twins for quantum networks.

Dense representation of an $n$-qubit pure state requires $2^n$ complex amplitudes, precluding dense classical materialization at large $n$. We develop Gram-certified resource continuation for structured quantum-representation workloads and ask when a solution obtained under a lower-cost resource model remains a justified initialization for a richer one. For coarse and fine state ensembles connected by a declared isometry, fine, coarse, and cross complex amplitude overlaps form a positive-semidefinite block Gram matrix. A signed operator of dimension at most twice the sample count has the nonzero signed spectrum of the fine density minus the lifted coarse density, yielding trace- and operator-norm diagnostics without constructing either density operator. We prove that a coarse weighted spectral flag with objective suboptimality $\delta_c$ has fine-level suboptimality at most $\delta_c+2\varepsilon$, where $\varepsilon$ is the empirical trace distance; the factor two is attainable. We distinguish encoder change from exact feasible-family prolongation, give a gap-dependent subspace-stability test, and show that continuation cannot overcome a final Schmidt-rank ceiling. In deterministic synthetic controls over an 8-to-40-qubit ladder, exact ancilla lifts agree to numerical precision. Transferred initialization reduces final-rung block updates from 30 to 20, but the complete cascade costs $4.80$–$5.43$ times a direct final-rung solve, without material objective improvement. Reordering eight Bell pairs reduces the maximum matrix-product-state bond from 256 to 2. Thus continuation is justified only when cross-rung mismatch, feasible-family inclusion, topology, and total work jointly satisfy prespecified audits. These noise-free classical results neither establish generic 40-qubit simulability nor claim hardware performance or quantum advantage.

Quantum technologies are maturing into systems that classical engineering must build, verify and maintain. The model-driven community has begun to respond with quantum-aware pipelines and languages, and the domain models these produce must be synchronised with the heterogeneous models created and owned by other communities. We argue that existing synchronisation approaches are insufficient for engineered quantum systems. A quantum system description captures superposition and entanglement, which a model transformation could remove undetected, while every structural check passes. To address this, we present the Quantum Systems Model Management (QSysMM) Framework, which guides the construction and synchronisation of the models of a quantum system into a digital single source of truth. The framework features four concerns: ontological, abstraction, composition and exposure, each given the treatment that engineered quantum systems require. Within this framework, we propose a Quantum Systems Modelling Language (QSysML) on the SysML v2 technology stack, and we close with a proposal that matures this synchronisation core into full model management for quantum systems.

The tripartite quantum Rabi model couples two qubits to a bosonic mode through a collective spin-oscillator interaction, providing a simple setting for studying two-qubit entanglement. In the zero-detuning limit, the triplet part of the spectrum splits into branches with zero and maximal entanglement, while the antisymmetric singlet ladder remains exactly decoupled. Within the triplet sector, finite detuning turns the crossings between these branches into avoided crossings and redistributes this entanglement. We identify an eigenbranch whose entanglement grows from nearly zero to a nearly maximal value through such avoided-crossing mixing. The weak-coupling level ordering yields a simple analytic criterion for whether this eigenbranch has a separable weak-coupling endpoint. A three-state effective model explains how the Bell-state component becomes dominant as the coupling increases. We further use a finite-time linear ramp of the collective coupling to benchmark the final coupling and ramp time required for high Bell-state fidelity. These results show how collective spin-oscillator coupling reorganizes spectral entanglement and connects static branch structure to finite-time Bell-state preparation.

This work proposes Rank-Refined Quantum-Behaved Particle Swarm Optimization (RR-QPSO) for high-dimensional parameter search in Quantum Molecular Generation (QMG). RR-QPSO targets the optimization bottleneck caused by expensive objective evaluations, where each candidate parameter vector requires stochastic circuit sampling, bitstring decoding, and molecular evaluation. The method provides a population-based alternative to Bayesian optimization (BO), combining Sobol-based initialization, a rank-refined mean-best update, and fitness-guided refinement based on validity and uniqueness. Experiments use the 9-heavy-atom QMG benchmark with a 134-parameter, 20-qubit CUDA-Q circuit and particle evaluations parallelized across 8 NVIDIA V100 GPUs. With M=64 particles and T=150 iterations, RR-QPSO reaches VxU = 0.930; increasing the swarm size to M=128 further improves the product to 0.942, compared with 0.902 for BO under the same protocol. A multi-objective extension targeting HBA=4 and HBD=3 further shows that RR-QPSO can guide molecular properties while preserving a higher validity–uniqueness product than BO. These results suggest that optimizer-level design can improve QMG without modifying the chemistry-inspired circuit or molecular decoding pipeline.

The limit states of canonical ensembles of a large number of interacting bosons at a given temperature, which are confined by harmonic forces, are studied in the framework of the resolvent algebra. It is shown that the limits satisfy the KMS condition or are ground states, regardless of the type of interaction. In case of attractive forces, where the ensembles collapse, observables that become meaningless in the limit disappear from the limit representations. For repulsive forces, this can also happen if condensates with an infinite number of particles in the same state (proper condensates) appear in the limit. The resulting structures and their interpretation are illustrated by a simple model. The study of vanishing harmonic forces (thermodynamic limit) involves changes of the dynamics. It is conveniently based on derivations acting on the algebra. They are given by the commutator of the Hamiltonians with the elements of the algebra. To ensure that the images remain in the algebra, the interaction must be regularized. This is accomplished in a manner that has only a minor impact on the dynamics and may be of broader interest. With this input a relation between the strength of the confining harmonic forces and the number of particles in the ensembles is derived from the condition that the limit states are to be stationary (invariant) under the adjoint action of the unconfined, spatially homogeneous limit dynamics. This relation encompasses the conditions that are frequently used in studies of Bose-Einstein condensates.

Quantum correlations are central resources for quantum information processing, yet their ability to manipulate dynamical transmission processes remains largely unexplored. Here, we investigate this ability through backflow, a uniquely interference phenomenon in which local probability flow propagates opposite to the momentum direction. We report the first nonlocal manipulation of backflow in double-slit interference using polarization-path-entangled photons. By performing local measurements on one photon, we remotely engineer the relative amplitude and phase of the two paths associated with its partner, manipulating the emergence, spatial distribution, and propagation dynamics of backflow without directly accessing the interfering system. Combining weak measurements to extract the transverse momentum and reconstruct Bohmian trajectories, we provide a direct visualization of the manipulation process with single-pixel spatial resolution. Furthermore, using Werner states with tunable correlation strengths, we reveal a distance-dependent resource requirement for nonlocal backflow manipulation: the minimum correlation strength required to induce backflow increases with propagation distance, progressing from entanglement to EPR-steering and ultimately Bell nonlocality. Our results show quantum correlations as operational resources for manipulating transmission dynamics and open new avenues for non-contact manipulation of fragile or inaccessible systems.

This work presents a matrix product state (MPS) simulation framework for adaptive non-local observable variational quantum circuits (ANO-VQCs) in image super-resolution (SR) beyond the practical limits of statevector simulation. Runtime benchmarks on a single NVIDIA RTX 4070 GPU show that, under the tested shallow-circuit setting, MPS completes ANO-VQC forward feature extraction for individual inputs up to 16 x 16 pixels (256 qubits), whereas statevector simulation encounters a memory bottleneck at 6 x 6 inputs (36 qubits) and exact tensor-network (Exact TN) contraction becomes computationally impractical beyond 12 x 12 inputs (144 qubits). For a fixed 7 x 7 input (49 qubits), a bond-dimension sweep over depths L = 1 to L = 4 shows that the required MPS bond dimension increases with circuit depth. Using Exact TN contraction as the reference, the bond dimension required for near-exact agreement increases from chi = 2 at L = 1 to chi = 16 at L = 4. Finally, 7 x 7 to 28 x 28 Fashion-MNIST SR training with chi = 16 shows that the shallow L = 1 model achieves the lowest loss, lowest LPIPS, and highest PSNR and SSIM among the tested depths. These results highlight MPS as a scalable and controllable simulation backend for ANO-VQC image SR and as a practical tool for studying large-scale quantum algorithms.

Combinatorial optimization problems are central to many applications but can be challenging to solve. Quantum approaches such as the Quantum Approximate Optimization Algorithm (QAOA) offer new tools with which to tackle such problems. However, QAOA circuits inherit the interaction structure of the target Hamiltonian, often resulting in deep circuits when compiled onto hardware with limited connectivity. Efficient transpilation is therefore critical to their practical performance. In this work, we propose a transpilation scheme for circuits consisting of blocks of commuting two-qubit gates on two-dimensional lattices. Unlike standard approaches based on random initial mappings and fixed routing, our method alternates between constructing problem-dependent SWAP-layer sequences and updating the qubit layout. By adapting the routing to the required interactions, this yields significantly shorter circuits for graphs with few edges. We benchmark our approach on QAOA instances for Maximum Cut (MC) on Random Regular graphs and Maximum Independent Set (MIS) on Erdős-Rényi graphs. Compared to standard methods, we reduce circuit depth and gate count by about a factor of two, enabling experiments with up to $80$ qubits and improving approximation ratios by up to $6.6\%$ for MC and $9.3\%$ for MIS.

We develop a family of semi-device-independent (SDI) entanglement-assisted prepare-measure (PM) communication games involving two parties, within the $n\rightarrow l$ random-access code (RAC) framework where the sender Alice holds a n-bit string and communicates $l<n$ bits or qubits to the receiver Bob. In contrast to the standard quantum PMRAC, here the parties share a prior entanglement, and Alice applies quantum operations on her sub-system to encode her inputs and sends to Bob. We first consider the $4\rightarrow l$ entanglement-assisted PMRAC with $l=1$ and $2$ and derive the optimal quantum success probabilities using an elegant analytical technique. We demonstrate quantum supremacy over both classical RACs and conventional quantum PMRACs. Moreover, we exhibit that the optimal quantum advantage allows one to certify Alice's unitary operations. We then derive an upper bound on the quantum success probabilities for $5\rightarrow l$ entanglement-assisted PMRAC with $l=1,2$ and $3$. Further, we extend the demonstration of quantum advantage for $n\rightarrow n-2$ case where n is arbitrary.

Hybrid Schrodinger-Feynman (HSF) simulation offers an attractive memory-path tradeoff for exact quantum-circuit emulation, but its practical runtime is often dominated by exponential path growth from cross-boundary two-qubit gates. Existing GPU and FPGA quantum simulators are largely optimized for full-state Schrodinger execution and therefore do not align well with HSF's path-centric workflow. This paper presents HSF-S, a compiler-accelerator co-designed framework for exact HSF-based quantum circuit emulation. HSF-S lowers input circuits to an HSF-compatible basis, formulates a rank-aware effective path-cost model, and applies dependency-preserving reordering together with discounted-gain SWAP insertion to suppress recurring cross-boundary interactions while preserving exact circuit semantics. A regression-free selector guarantees that the compiled circuit never increases effective path cost relative to the naive lowered baseline. We further design a dedicated HSF-S accelerator and execution flow, and integrate them into a stand-alone processor for efficient per-path dual-slice evaluation and final accumulation without materializing the full state vector. Across 56 benchmark circuits, HSF-S matches reference amplitudes to within floating-point precision, reduces effective path cost by up to 90.0%, and substantially improves practical tractability, including representative timeout-to-sub-second reductions under a 1-hour budget. On the resulting compiled workloads, the HSF-S processor prototype delivers up to 4.34x additional speedup.

Recent progress in quantum physics and quantum technologies is driving quantum computing from the noisy intermediate-scale (NISQ) era toward fault-tolerant operation. High-precision control of two-qubit gates is among the most critical requirements in this transition and hinges on accurate two-qubit calibration. For controlled-phase and CZ-style operations, the residual conditional phase (the nonlocal ZZ-type deviation after local compensation) is weakly resolved at leading order in average infidelity and randomized benchmarking, and repeated Ramsey amplification does not reliably isolate it from ordinary target detuning, SPAM errors, and contrast loss in long sequences. We introduce branch-resolved Pauli-block spectroscopy to estimate the per-cycle residual ZZ-rotation angle theta_c with its sign, from which the controlled-phase residual follows by a fixed convention. The protocol repeats a fixed probe for N cycles, measures the closed Pauli block IX, IY, ZX, and ZY, and forms branch coherences C+ and C- conditioned on the control qubit; theta_c splits the two branch phase slopes in opposite directions, while local target phase beta_c shifts them together. An echoed-cycle variant suppresses removable local terms while preserving the nonlocal contribution. Numerical simulations with injected theta_c, detuning, damping, and SPAM confirm unbiased signed readout where scalar-sector alternatives fail and distinguish opposite-sign errors at equal infidelity. On one superconducting cloud qubit-coupler pair, a pulse-level calibration closed loop shows near-linear injection, preserved branch contrast, and tracking of the native residual conditional phase through one iteration. The approach yields a low-overhead, signed per-cycle estimate of residual conditional phase that standard fidelity benchmarks underresolve at leading order.

Quantum algorithms that sample basis states and diagonalize a Hamiltonian in their span depend on repairing noisy measurement outcomes, using a constraint native to the target problem$\unicode{x2014}$typically particle-number symmetry. Many eigenvalue problems possess no such constraint. Here we show that the constraint can instead be engineered into the sampling representation. Using dual-rail encoding, $|0\rangle\to|01\rangle$ and $|1\rangle\to|10\rangle$, we implement sampling operations in encoded form, making code-space violations local recovery signals for self-consistent, reference-based repair. On transverse- and mixed-field Ising models of up to 36 spin sites, which lack a $U(1)$ symmetry usable for recovery, code-space recovery reached lower Ritz energies than diagonalization over the full observed support of matched unencoded samples while using 38-84% fewer basis states, despite a twofold qubit overhead. The margin was largest for the two-dimensional and 36-site systems and was already present in the first recovery iteration. Recoverable structure can be engineered rather than inherited.

We study a quadratic open SSH chain with a single-site loss and show that the many-body fermionic Lindblad problem admits an exact reduction to a finite non-Hermitian one-body matrix with a rank-one imaginary impurity. Its rapidities generate the complete Liouvillian spectrum and reveal three mechanisms governing the slowest relaxation. At weak loss, decay is selected by the clean local spectral weight at the lossy site, yielding the generic law $\Delta_{\mathcal L}\sim\gamma N^{-3}$ and, in the topological regime, exponentially smaller edge-controlled gaps. At intermediate loss, a centered bulk-loss geometry reaches an exact exceptional point on the real-$\gamma$ axis. Symmetry-related rapidity pairs coalesce simultaneously, including the pair at the lower rapidity edge. Exact real-space dynamics at this lower-edge exceptional point exhibits a polynomially enhanced exponential tail, whereas a matched high-energy control with the same parity-even one-body decay edge but no lower-edge defectiveness remains nearly exponential. At strong loss, one ultrafast defect mode separates from an active slow sector governed by a cut-chain Zeno problem, giving $\Delta_{\mathcal L}\sim\gamma^{-1}$ up to a geometry-dependent prefactor. The full finite fermionic Liouvillian spectrum, including its operator-parity sectors and subset-sum structure, is statistics-specific. By contrast, the elementary one-body decay spectrum and the three associated mechanisms are governed by a finite-dimensional linear drift matrix, so their spectral and dynamical signatures can also be accessed in bosonic and classical-wave platforms engineered to realize the same effective matrix. These results establish how topology, defect geometry, and local dissipation jointly organize long-time relaxation in an open dimerized lattice.

Anyons in $2+1$ dimensions are not only characterized by exotic braiding statistics but also by intricate fusion properties. Two anyons may fuse into multiple topological charge sectors, and associativity of fusing three anyons to produce a fixed charge sector is governed by $F$-symbols. While braiding invariants, such as the modular data, are typically complex valued, a complete description of general anyon models requires understanding the arithmetic properties of its fusion associativity data as well. The $F$-symbols for many of the most common $2+1$d topological orders, including all Abelian anyon models as well as Fibonacci and Ising anyons, can be made real valued. We show this phenomenon is not universal by exhibiting braided fusion categories whose $F$-symbols cannot be made real. We call such $F$-symbols "inherently complex." The examples we study lack a charge-conjugation symmetry and our results are therefore consistent with the converse of a statement proved in a companion work linking real $F$-symbols in braided fusion categories with the existence of a suitable charge-conjugation symmetry. We analyse the smallest-rank braided fusion categories we know of with inherently complex $F$-symbols: ${\rm Rep}(\mathbb{Z}_7\rtimes\mathbb{Z}_3)$ and ${\rm Rep}(\mathbb{Z}_5\rtimes\mathbb{Z}_4)$. Consequently, the corresponding $\mathcal Z({\rm Rep}(\mathbb{Z}_7\rtimes\mathbb{Z}_3))$ and $\mathcal Z({\rm Rep}(\mathbb{Z}_5\rtimes\mathbb{Z}_4))$ anyon models also have inherently complex $F$-symbols. Our presentation connects these examples with recent results on classifying anyons beyond modular data.

Dark modes arise when destructive interference prevents selected bosonic degrees of freedom from coupling to environmental channels. We formulate a Hamiltonian criterion for identifying such modes in multimode bosonic systems by separating two requirements: the candidate mode must be invisible to the direct system–environment coupling, and its generated operator space must remain invariant under the intrinsic system dynamics. For linear environment coupling and quadratic system Hamiltonians, the criterion is reduced to the the familiar null-space and invariant-subspace conditions of passive linear dark-mode theory. We then extend the analysis to nonlinear scenarios. For a two-photon conversion channel coupled to an auxiliary environmental mode, interference among nonlinear conversion pathways can reduce the environment coupling to a single collective two-photon channel, leaving a complementary bosonic mode decoupled from the environment. We show that preserving this mode under nonlinear intrinsic dynamics generally requires more than conventional Kerr-type quartic interactions: correlated four-boson conversion processes are needed to cancel mixed nonlinear conversion between the dark and environment-coupled collective modes. Finally, we show that the Bogoliubov dark mode of a parametrically driven optomechanical satisfies the same Hamiltonian criterion through an active canonical transformation. These results provide a unified Hamiltonian framework for identifying and engineering dark modes in linear, nonlinear, and driven bosonic systems.

We present a unified, geometry-resolved framework for analyzing absorption, resonance fluorescence, entanglement negativity, and phase-space quasiprobability in Doppler-broadened four-level atomic vapor. Using a density-matrix formalism with thermal velocity averaging and exact dressed-state diagonalization, we show that these observables constitute complementary projections of a common coherence-driven phase-space structure governed by multiphoton interference. Central to this framework is the Stratonovich-Weyl (SW) Wigner function, which provides a unified phase-space representation incorporating both populations and coherences. Direct comparison reveals a near one-to-one correspondence between SW quasiprobability distributions and entanglement landscapes, with geometry-dependent features, including hyperbolic dispersion asymptotes and split resonance ridges, consistently preserved. Furthermore, isolating the Doppler-odd component yields an eigenvalue-free proxy that captures the coherence geometry underlying entanglement negativity, providing a non-invasive quantum correlation witness. At the same time, resonance fluorescence emerges as a thermally robust observable: unlike susceptibility-based absorption, its additive pole weighting preserves sharp Autler-Townes spectral features under strong driving. This robustness enables fluorescence to accurately track bright dressed states and entanglement extrema despite severe Doppler dephasing, establishing its dual role as a sensitive electrometry probe and correlation witness. By combining a coherence-resolved description with a Doppler-sensitive phase-space representation, the proposed framework offers an experimentally accessible, eigenvalue-free approach to quantum state characterization, enabling Doppler-resilient fluorescence-based quantum sensing and precision field electrometry in warm atomic media.

Color codes are promising alternatives to surface codes for universal fault-tolerant quantum computing due to their simpler lattice-surgery protocols and the transversal implementation of logical Clifford gates. However, their practical deployment has been limited by slower decoding algorithms and worse logical failure rates and thresholds compared to surface codes. Although AI-based logical-flip decoders have recently been proposed to address these challenges, no clear framework currently exists for implementing such decoders within the parallel block-wise decoding schemes in both space and time required for large-scale fault-tolerant computation. AI-based pre-decoders offer a scalable alternative due to their local nature. By performing spacelike corrections on physical qubits and timelike corrections on stabilizer measurements, pre-decoders are naturally compatible with parallel block-wise decoding schemes and lattice-surgery protocols. In this work, we introduce AI-based pre-decoders for triangular color codes. We present a novel neural-network architecture for their implementation and develop methods to simplify the complex training data generated by color-code syndrome-extraction circuits containing feedforward operations. Remarkably, we find that both logical failure rates (LERs) and runtimes improve relative to raw Chromobius decoding as the code distance increases. For example, at code distance d=31 and physical error rate $p=0.3\%$, our pre-decoder + Chromobius pipeline improves the logical failure rate by a factor of 347x while reducing runtime by 7.33x compared to raw Chromobius decoding alone. These results demonstrate that AI-based pre-decoding can substantially narrow the performance gap between color codes and surface codes, bringing color codes closer to practical large-scale fault-tolerant quantum computation.