arXiv:2607.06219v2 Announce Type: replace-cross Abstract: Rising energy demand from data-centre and AI applications has renewed interest in reversible computation, where logic need not dissipate heat at every step if information is uncomputed. Implementations have so far been classical: adiabatic CMOS reduces dissipation by slowing charge motion but is still limited by the threshold physics of transistors. Here we propose classical reversible logic implemented by coherent spin dynamics in a spin quantum-dot array, with inputs and outputs in classical basis states and no algorithmic use of superposition. The same spin stores, transports, and computes, with unitary rotation replacing irreversible switching. The universal building block is an iToffoli gate driven by DC voltage pulses and anisotropic exchange in Ge/Si hole spins. Simulations with experimental parameters reproduce the Toffoli truth table and yield a testable error landscape. Because shuttling transports the bit without measurement, logic and data movement remain reversible until readout. Millivolt pulses on femtofarad gates yield a gate energy below the 4~K Landauer scale, about five (eight) orders of magnitude below a room-temperature CMOS Toffoli with (without) 4 K cooling overhead. The same semiconductor hardware is therefore dual-use, supporting quantum algorithms when superposition is used and classical reversible logic otherwise.

arXiv:2606.31117v2 Announce Type: replace-cross Abstract: We introduce a radical-fragment many-body expansion at the two-body level (MBE2) for quantum chemistry of linear alkanes. Instead of heterolytic bond cleavage with hydrogen capping atoms and electrostatic embedding like in Fragment Molecular Orbital (FMO), we perform homolytic C-C bond cleavage to produce open-shell radical fragments (CH3, CH2) treated with restricted open-shell Hartree-Fock (ROHF) in isolation. The two-body MBE2 assembly formula reconstructs total alkane energies from only four unique fragment calculations regardless of chain length, reducing the maximum qubit requirement. We benchmark this framework against five energy solvers (RHF, CCSD, VQE, ADAPT-VQE, and SQD) across 11 linear alkanes from butane (C4H10) to hexacosane (C26H54). The MBE2 decomposition achieves a 12.3x qubit reduction for C26H54 (from 368 to 30 qubits) and a 12.8x reduction in unique calculations via symmetry exploitation. MBE2-VQE and MBE2-SQD (executed on IBM quantum hardware) closely track their respective classical MBE2 references, demonstrating that fragmentation-based quantum chemistry is viable for scaling quantum solvers to large molecular systems.

arXiv:2605.03910v2 Announce Type: replace-cross Abstract: Interactions between light and mechanics provide a powerful interface between optical and microwave-frequency signals, with applications spanning classical signal processing and quantum technologies. High-performance optomechanical devices require both strong photon-phonon coupling and tolerance to parasitic laser heating. Release-free optomechanical crystals provide improved thermal anchoring compared to suspended nanobeams, but have so far exhibited weaker vacuum optomechanical coupling rates, leaving a trade-off between coupling strength and thermal robustness. Here, we largely close this gap: we design and experimentally demonstrate a release-free silicon optomechanical crystal with a record vacuum optomechanical coupling rate of about $g_\text{OM} / (2 \pi) = 800$ kHz, comparable to suspended state-of-the-art devices. The resulting optomechanical scattering rate $\Gamma_\text{OM}/(2 \pi)= 1.1$ kHz is nearly twice that of previous release-free implementations. This performance is achieved by combining physics-guided human intuition with a multiphysics inverse-design algorithm introduced here for resonant optomechanical structures. Beyond the specific device demonstrated, the inverse-design framework is applicable to co-optimizing optical and mechanical resonances and eigenmodes more broadly. These results strengthen release-free optomechanical crystals as a platform for fast, low-noise classical and quantum optomechanics.

arXiv:2604.17700v2 Announce Type: replace-cross Abstract: We investigate the effect of non-Hermitian Gamma interaction on the phase transitions and magnetic correlations for the transverse field Ising chain. We demonstrate that apart from the gapped antiferromagnetic and paramagnetic phases, there is a gapless phase induced by parity-time symmetry breaking, where the system exhibits long-range and short-range spin-nematic correlations in different regions divided by the quantum critical line determined from the correlation function and the subsystem entanglement entropy. Furthermore, we reveal that the parity-time symmetry breaking leads to the emergence of dynamical spin-nematic correlation, which also suggests a way of characterizing the spin-nematic phase diagram through non-equilibrium dynamics. Our findings show rich quantum phases stem from the competition among the Ising interaction, transverse field and non-Hermitian Gamma interaction, as well as providing a scheme for generating spin-nematic correlation in the spin chain.

arXiv:2601.02199v2 Announce Type: replace-cross Abstract: The interplay between topology and nonlinearity represents a central challenge in modern physics. Here, we investigate this interplay by considering a synthetic Su-Schrieffer-Heeger lattice with all-to-all nonlocal interactions. We find that the distinctive nonlinearity maintains an effective chiral symmetry and leads to a quantized nonlinear winding and Berry phase, as corroborated by the developed Bogoliubov nonlinear adiabatic theory. Increasing nonlinearity drives a sequence of topological transitions signaled by the appearance of characteristic swallowtail band structures at intermediate interaction strengths and band swapping in the strong nonlinear regime. The band swapping results in quantized fractional windings and double-period Bloch oscillations that are closely related to discrete time crystals. Remarkably, even starting from a topologically trivial linear system, nonlocal nonlinearity can induce an emergent topological phase with fractional windings. Experimentally, our model can be realized using photons in a degenerate optical cavity with Rydberg-mediated interactions. Our results establish a rigorous framework and pave the way for exploring nonlinear topological phenomena and their applications in synthetic quantum platforms.

arXiv:2510.05346v4 Announce Type: replace-cross Abstract: We present an exact solution for entanglement entropy for the real-time dynamics following a quench from a thermal pure quantum (TPQ) state in a free-fermion system. In contrast to the usual linear growth and saturation behavior, the entanglement entropy exhibits a characteristic double-plateau structure. We establish this behavior through three complementary approaches: an exact conformal field theory calculation on the Klein bottle, finite-size Gaussian-state simulations, and a quasiparticle picture that becomes quantitatively accurate in the scaling regime.

arXiv:2508.02819v3 Announce Type: replace-cross Abstract: We investigate signatures of quantum chaos in the mixed-field quantum Ising model on finite-size Erd\H{o}s-R\'enyi graphs using probes scalable on near-term quantum devices. Upon tuning the graph connectivity, the system exhibits a crossover from a localized regime at low connectivity, through a chaotic regime at intermediate connectivity, to a permutation-symmetric integrable limit near all-to-all connectivity. This crossover has possible implications for the performance and trainability of variational algorithms such as QAOA. We characterize this crossover in finite-size systems using complementary probes. First, deep thermalization of a projected ensemble starting from a product state reveals slow (fast) convergence to the Haar ensemble at extremal (intermediate) connectivities. Second, we analyze eigenstate and eigenvalue correlations using the partial spectral form factor, an experimentally scalable proxy for the spectral form factor with reduced resource overhead, and observe characteristic chaos signatures at intermediate connectivities and distinct deviations at extremal connectivities. Finally, we explore the Krylov complexity of operators, a locality-independent diagnostic that, although not directly experimentally accessible, serves as a tool for quantifying scrambling. We show that it is maximized deep in the chaotic regime, corroborating the signatures observed through the experimentally scalable probes. Our results provide finite-size benchmarks demonstrating robust signatures of chaos in scalable probes and suggest that these diagnostics can be implemented in current quantum platforms to access regimes beyond classical simulation.

arXiv:2504.15264v2 Announce Type: replace-cross Abstract: Extremal problems on set systems with restricted intersections have been an important part of combinatorics in the last 70 years. In this paper, we study the following Ramsey version of these problems. Given a set $L\subseteq \{0,\dots,k-1\}$ and a family $\mathcal{F}$ of $k$-element sets which does not contain a sunflower with $m$ petals whose kernel size is in $L$, how large a subfamily of $\mathcal{F}$ can we find in which no pair has intersection size in $L$? We give matching upper and lower bounds, determining the dependence on $m$ for all $k$ and $L$. This problem also finds applications in quantum computing. As an application of our techniques, we also obtain a variant of F\"uredi's celebrated semilattice lemma, which is a key tool in the powerful delta-system method. We prove that one cannot remove the double-exponential dependency on the uniformity in F\"uredi's result, however, we provide an alternative with significantly better, single-exponential dependency on the parameters, which is still strong enough for most applications of the delta-system method.

arXiv:2607.06837v2 Announce Type: replace Abstract: Currently, remote energy transfer and immunity to dissipation are hot topics in quantum batteries (QBs). In this work, we propose a protocol to realize energy transfer between two remote atoms (a quantum charger and a quantum battery) each coupled to a separate optical cavity with the cavities connected by a fiber. The cavities and fiber are coupled to their individual baths. After optimizing inter-system couplings to achieve an efficient transfer, we uncover the effect of suppressing dissipation by introducing parity deformation of the cavities fields. We also prove that the charger-battery entanglement is a consumable resource for energy storage: it is initially stored until the charger and battery reach energy balance, and then subsequently consumed to maintain the increase in energy stored in the battery. The present scheme is the first execution of energy transfer to a distant battery assisted by entanglement, which may help better understand quantum thermodynamics and open new possibilities toward harnessing decoherence as a resource to improve the charging performance of QBs.

arXiv:2607.05386v2 Announce Type: replace Abstract: Quantum LDPC memories can encode many logical qubits, but that alone does not make them usable: applications need to know where the logical operators are supported, how they are labeled, and how conjugate $X/Z$ partners pair. For hypergraph-product codes this information follows from row reduction over $\mathbb{F}_2$. For Abelian lifted-product codes, which include prominent high-rate constructions, it does not: the entries of the defining seed matrices live in a group algebra rather than a field, so pivots need not be invertible and row reduction can fail. To address this problem, we introduce \emph{logical spectroscopy}. For an odd-order Abelian lift group, the Chinese remainder theorem splits the group algebra into finite fields, one for each Frobenius orbit of characters; we call these orbits packets. Packet by packet, we solve ordinary finite-field linear algebra, lift the answers back to the physical code with the associated packet projectors, and pair $X$ and $Z$ logicals between reciprocal packets by trace duality. The result is a complete conjugate logical basis for a finite Abelian lifted product code that is addressable: every logical coordinate carries canonical packet and K\"unneth-summand labels, deterministic within-block indices, a conjugate partner, and an explicit binary representative. The code's own translation symmetry then acts on these coordinates in closed form. We apply the construction to examples with up to 5000 physical qubits, including high-rate examples whose distance-witness is reported explicitly. We further extend the decomposition to even-order lifts. Logical spectroscopy thus equips Abelian lifted products with an explicit logical coordinate system and an algebraic toolkit for high-rate code search.

arXiv:2607.05112v2 Announce Type: replace Abstract: It is known that a one-dimensional (1D) quantum walk gives a local space-time discretization of the massless Dirac equation with a single quasi-energy cone (no fermion doubling at low energies), keeping the fundamental symmetries (chiral and time-reversal) of the continuum theory. We show that the analogous 2D construction is fundamentally more fragile. Local two-band quantum walks can have an unpaired Dirac cone, but the protecting symmetries then cease to be ordinary on-site symmetries: they become non-symmorphic, involving half-lattice translations, and are broken by generic spatial inhomogeneities. In particular, we demonstrate that the 2D Dirac quantum walk based on the Ho-Chalker network model can be gapped by potential scattering.

arXiv:2607.02280v2 Announce Type: replace Abstract: Braiding statistics, familiar from anyons in fractional quantum Hall systems, are a central manifestation of topology in quantum physics. Ordinary braiding extends naturally to higher-dimensional excitations: a $p$-dimensional excitation and a $q$-dimensional excitation can braid in $d=p+q+2$ spatial dimensions. In this work, we identify a new type of mutual statistics that exists in one lower spatial dimension, $d=p+q+1$. This includes particle-particle statistics in one dimension, particle-loop statistics in two dimensions, and loop-loop or particle-membrane statistics in three dimensions. The corresponding field-theory response is governed by the Bockstein homomorphism, so we call the invariant Bockstein braiding statistics. On lattices, the Bockstein statistics is measured by the Berry phase accumulated in a universal microscopic unitary process built from local excitation operators. We further show that nontrivial Bockstein braiding is the statistical manifestation of a mixed anomaly of the corresponding symmetries. This anomaly rules out a fully symmetric gapped phase, obstructs simultaneous condensation of the two excitations, and implies fractionalization of higher-form symmetries. We illustrate these consequences in a $(1{+}1)$-dimensional spin-$\frac12$ chain, where Bockstein braiding statistics detects the mixed anomaly between $\prod_i X_i$ and $\prod_i \mathrm{CZ}_{i,i+1}$, and in strongly coupled $(3{+}1)$-dimensional continuum gauge theories.

arXiv:2607.01332v2 Announce Type: replace Abstract: In collective dissipative spin systems, the postselection barrier can be partially mitigated; however, a further obstacle may be posed by the finite temporal resolution of detectors. In this work, we investigate how initial-state inhomogeneities can control waiting-time statistics between quantum jumps, thereby mitigating the detector-resolution problem. We consider a collectively monitored spin model with a boundary time-crystalline phase, introducing inhomogeneity by partitioning the ensemble into two subsystems rotated by an angle $\theta$. We find that the measurement-induced phase transition survives under inhomogeneities, with different entanglement scaling regimes. The waiting time increases with $\theta$, scaling as $1/N$ but with a prefactor strongly enhanced by orders of magnitude, and in the anti-aligned limit $\theta = \pi$ it remains finite, fully resolving the resolution barrier. This mitigation, however, comes at a cost: the entanglement saturation time becomes significantly longer, partially reintroducing the postselection barrier. Our results highlight a trade-off between detector resolution and postselection overhead, with direct implications for the experimental observation of measurement-induced phenomena.

arXiv:2606.29235v2 Announce Type: replace Abstract: Pseudo entropy between quantum states at different times is generally complex, yet its imaginary part has lacked a bounded operational meaning. We show that a calibrated replica interferometer converts the pseudo-R\'enyi phase into a directly measurable record of transition orientation. Together with replica visibility, it exactly determines the trace distance between forward and backward ancilla outputs and hence the Helstrom-optimal single-shot success probability. At short times, the symmetrized covariance of the modular and physical Hamiltonians sets the initial distinguishability response. Under any common quantum channel, the corresponding orientation information can only decrease, with equality characterized by Petz recovery. Imaginary pseudo entropy therefore records a reversible distinction between temporal orientations, while coarse graining can make the loss of that record irreversible.

arXiv:2606.16823v2 Announce Type: replace Abstract: Determining non-equilibrium steady states (NESS) of open fermionic systems is a fundamental problem akin to finding ground states of closed systems. To address this, variational quantum algorithms can be used to solve the Lindblad master equation, much like the Schr\"odinger equation, yet ansatz design for NESS remains challenging. Existing approaches rely mostly on hardware-efficient ans\"atze (HEA), which suffer from the barren plateau problem. Here, we introduce a physically motivated ansatz named NE-UCC. Numerical simulations demonstrate that NE-UCC reliably converges to the steady state even in strongly correlated regimes far from equilibrium, reducing the infidelity by up to ten orders of magnitude compared to HEA. Furthermore, NE-UCC facilitates the exploration of excited eigenmodes with specific symmetries.

arXiv:2606.16055v2 Announce Type: replace Abstract: In superconducting circuits, drive-induced unwanted transitions limit the readout power, thereby constraining readout speed and fidelity. When such transitions excite the qubit into leakage states, they produce correlated errors that are particularly harmful for quantum error correction. Native nonlinear qubit-readout resonator coupling is a promising alternative to conventional linear hybridization because it provides intrinsic Purcell protection and stricter selection rules for multiphoton processes. In realistic devices, however, we show that such a coupling alone neither eliminates nor necessarily suppresses drive-induced transitions. Instead, if not appropriately engineered, these couplings often worsen the situation by introducing additional parasitic processes. Moreover, the rates of these unwanted transitions remain sensitive to the choice of readout frequency, regardless of the coupling mechanism. We demonstrate that readout-induced leakage can thus vary by orders of magnitude even when readout frequencies differ by less than ~7%. Our results establish that the benefits of native nonlinear couplings are realized only through informed device design, including the spectral placement of relevant auxiliary modes and elimination of parasitic ones.

arXiv:2606.07734v2 Announce Type: replace Abstract: Producing high-fidelity magic states using the smallest possible number of physical qubits and operations stands as a very important challenge to achieve fault-tolerant quantum computation at scale. Besides emerging proposals for alternative methods such as cultivation, magic state distillation remains essential for achieving very low error rates. Known distillation protocols are usually built through quantum codes derived from triorthogonal matrices. Here, exploiting the specific noise structure present in magic state distillation protocols, we show that classical error-correcting codes offer a simpler framework for deriving these protocols. This formulation is particularly well suited to systematic numerical and analytical studies of distillation protocols involving a fixed number of qubits. Specifically, we use a SAT solver to derive a series of no-go theorems that relate key figures of merit, including the number of qubits and the factory distance. In particular, considering the standard implementation as a circuit of Z-diagonal Pauli product rotations followed by measurements, we show that no $T$-to-$T$ distillation protocol on fewer than eight qubits can exceed distance 3, and no $T$-to-$\mathrm{CC}Z$ protocol distance 2. Our results also include new such distillation protocols with the smallest number of qubits for a given distance in the literature, namely distance 4 and 5 $T$-to-$T$ protocols supported on 10 and 11 qubits, as well as distance 3 and 4 $T$-to-$\mathrm{CC}Z$ distillation protocols supported on 9 and 10 qubits. Finally, going beyond unitary circuits by recycling qubits through mid-circuit measurement and reinitialization, we obtain an implementation of the distance-5 $49T$-to-$1T$ protocol on only 5 active qubits.

arXiv:2606.07275v2 Announce Type: replace Abstract: The characterization of the quantum critical properties of genuine non-Hermitian many-body systems remains ambiguous as neither the state considered nor the definition of expectation values is unique. In this work, we investigate the quantum critical properties of two models of non-Hermitian XY spin chains with magnetic field. Using exact solutions, we systematically investigate the parameter dependence of the energy, the magnetization as well as the long-distance asymptotic behavior of static correlation functions. We compute expectation values within the standard formalism of quantum mechanics as well as within biorthogonal quantum mechanics and take two different states which one might reasonably consider to be the analog of the ground state of a Hermitian model. The critical properties, including such fundamental characteristics as the phase diagram, depend on both the formalism used as well as the state considered. We provide arguments in favor of the use of standard quantum mechanics. Which state to be taken in computations, depends on the (hypothetical) experimental preparation of the system.

arXiv:2605.15233v3 Announce Type: replace Abstract: Public access to pulse-level and control-electronics interfaces in commercial quantum computing has bifurcated. This paper proposes a six-axis rubric for measuring control-plane openness, the layer between gate-level circuit specification and physical control electronics, defined operationally so that the same evidence produces the same grade across vendors. The rubric is validated three ways: a blinded re-grading pass that tests whether the cited evidence and the level definitions alone reproduce the recorded grades, a boundary-case methodology that fixes where each level begins and ends, and a published grading protocol that lets others reproduce and contest any cell. A time-point comparison anchored on the February 2025 removal of pulse-level access from IBM hardware establishes that the rubric measures change rather than describing a snapshot. The rubric is applied to thirteen commercial vendors across superconducting, trapped-ion, neutral-atom, and photonic modalities as of May 1, 2026, and one of the three harms it detects is demonstrated through a reproduction-access audit of five pre-2025 IBM Qiskit Pulse experiments, carried through to a structural port to Rigetti Quil-T. The catalog ships as a machine-readable artifact under CC-BY-4.0 with per-cell source URLs (https://doi.org/10.5281/zenodo.20163276). The readings will go stale; the rubric is the contribution that survives them.

arXiv:2604.17369v2 Announce Type: replace Abstract: How many black-box queries to a quantum channel are needed to learn its full classical description? This question lies at the heart of quantum channel tomography (also known as quantum process tomography), a fundamental task in the characterization and validation of quantum hardware. Despite extensive prior work, the optimal query complexity for quantum channel tomography is far from fully understood. In this paper, we study tomography of an unknown quantum channel with input dimension $d_1$, output dimension $d_2$, and Kraus rank at most $r$, to within error $\varepsilon$. We identify the dilation rate $\tau = r d_2 / d_1$ (which always satisfies $\tau\geq 1$ due to the trace preservation of quantum channels) as a key parameter, and establish that the optimal query complexity of channel tomography exhibits distinct scaling laws across three regimes of $\tau$. - In the boundary regime ($\tau = 1$): we show that the query complexity is $\Theta(r d_1 d_2/\varepsilon)$ for Choi trace norm error $\varepsilon$, and is upper bounded by $O(\min\{r d_1^{1.5} d_2/\varepsilon, r d_1 d_2/\varepsilon^2\})$ and lower bounded by $\Omega(r d_1 d_2/\varepsilon)$ for diamond norm error $\varepsilon$. - In the away-from-boundary regime ($\tau \geq 1+\Omega(1)$): we show that the query complexity is $\Theta(r d_1 d_2/\varepsilon^2)$ for both Choi trace norm and diamond norm errors $\varepsilon$. Our results uncover a sharp Heisenberg-to-classical phase transition in the query complexity of quantum channel tomography: at $\tau=1$, the optimal query complexity exhibits Heisenberg scaling $1/\varepsilon$, whereas for $\tau\geq 1+\Omega(1)$, it exhibits classical scaling $1/\varepsilon^2$. In addition, we show that in the near-boundary regime ($1< \tau < 1+o(1)$), the query complexity exhibits a mixture of Heisenberg and classical scaling behaviors.

arXiv:2604.08763v2 Announce Type: replace Abstract: We extend the Weak Adversarial Neural Pushforward Method to the Wigner transport equation governing the phase-space dynamics of quantum systems. The central contribution is a structural observation: integrating the nonlocal pseudo-differential potential operator against plane-wave test functions produces a Dirac delta that exactly inverts the Fourier transform defining the Wigner potential kernel, reducing the operator to a pointwise finite difference of the potential at two shifted arguments. This holds in arbitrary dimension, requires no truncation of the Moyal series, and treats the potential as a black-box function oracle with no derivative information. To handle the negativity of the Wigner quasi-probability distribution, we introduce a signed pushforward architecture that decomposes the solution into two non-negative phase-space distributions mixed with a learnable weight. The resulting method inherits the mesh-free, Jacobian-free, and scalable properties of the original framework while extending it to the quantum setting.

arXiv:2604.02420v2 Announce Type: replace Abstract: We introduce a framework to upper bound the entanglement content of a bipartite quantum state from its spectrum alone. Using linear maps and their inverses, we derive rigorous constraints on the maximal entanglement that can be activated under global unitary transformations. We use as entanglement quantifiers the negativity and the Schmidt number; however, our framework is general and applies to any other entanglement measure. Our approach yields compact analytical sufficient criteria for bounding the entanglement of full-rank states in arbitrary dimensions and reveals new spectral constraints on Schmidt number witnesses.

arXiv:2603.27063v2 Announce Type: replace Abstract: We present a new class of quantum neural networks (QNNs) whose states are solutions of $p$-adic Schr\"{o}dinger equations with a non-local potential that controls the interaction between the neurons. These equations are obtained as Wick rotations of the state equations of $p$-adic cellular neural networks (CNNs). The CNNs are continuous limits of discrete hierarchical neural networks (NNs). The CNNs are bio-inspired by the Wilson-Cowan model, which describes the macroscopic dynamics of large populations of neurons. We provide a detailed study of the discretization of the new $p$-adic Schr\"{o}dinger equations, which allows the construction of new QNNs on simple graphs. We also conduct detailed numerical simulations, offering a clear insight into the functioning of the new QNNs. At a mathematical level, we show the existence of local solutions for the new $p$ -adic Schr\"{o}dinger equations.

arXiv:2603.16492v4 Announce Type: replace Abstract: Quantum state preparation and block encoding are versatile and practical input models for quantum algorithms in scientific computing. The circuit complexity of state preparation and block encoding frequently dominates the end-to-end gate complexity of quantum algorithms. We give algorithms with lower C-NOT counts for both the state preparation and block encoding. For a general $n$-qubit state, we improve the C-NOT count of the Plesch-Brukner algorithm (2011) from $(23/24)\times 2^n$ to $(11/12)\times2^n$. For block encoding, our single-ancilla protocol for $2^{n-1}\times 2^{n-1}$ matrices uses the spectral norm as subnormalization and achieves a C-NOT count leading term $(11/48)\times 4^n$. Further optimization is performed for low-rank matrices, which frequently arise in practical applications. Specifically, we achieve the C-NOT count leading term $(2^{\lceil\log_{2}K\rceil}+(11/12))\times 2^n$ for a rank-$K$ matrix. This is the first quantum algorithm that encodes matrices using the optimal normalization factor while also allowing the C-NOT count to be adjusted according to the matrix rank. Our approach builds upon the recursive Block-ZXZ decomposition from Krol et al. (2024) and introduces a diagonal matrix migration technique based on the commutativity of the diagonal matrix and the uniformly controlled rotation about the $z$-axis to minimize the use of C-NOT gates.

arXiv:2603.04097v2 Announce Type: replace Abstract: Partitioning the photonic environment into resonant and off-resonant modes provides a mechanism for dephasing suppression in photosynthetic energy transfer. Aligning the excitation spectrum with underdamped vibronic resonances in the Fenna-Matthews-Olson (FMO) complex prepares vibronically dressed states with reduced coupling to dissipative fluctuations, inducing a biexponential coherence decay: a rapid initial dephasing ({\tau}fast {\approx} 37fs) followed by persistent inter-band coherences extending beyond 1ps-a > 3x extension of the effective coherence window relative to broadband excitation ({\tau}c = 280fs). This improves forward transfer yields by 39% at 295K. PT-HOPS/SBD simulations establish that dual-band filtering at 750nm and 820nm targets vibronic resonances while bypassing dephasing-dominated noise. This enhancement is robust against static disorder ({\sigma} = 50 cm-1), with an ensemble-averaged increase of {\eta} = 0.39 {\pm} 0.04. These results identify selective vibronic excitation as a foundational design principle for coherence-assisted transport. This framework extends to symbiotic agrivoltaic systems, where organic photovoltaics function as active spectral filters to co-optimize excitonic transport alongside the photosynthetic requirements of underlying crops.

arXiv:2602.22349v2 Announce Type: replace Abstract: We numerically investigate quantum circuit elementary-gate level instantiations of the standard Quantum Phase Estimation (QPE) algorithm for the task of computing the ground-state energy of a quantum magnet; the disordered fully-connected quantum Heisenberg spin glass model. We consider (classical simulations of) QPE circuit computations on relatively small quantum Hamiltonians ($3$ qubits) with up to $10$ phase bits of precision, using up to Trotter order $10$. We systematically study the inputs of QPE, specifically time evolution, Trotter order, Trotter steps, and initial state, and illustrate how these inputs practically determine how QPE operates. From this we outline a coherent set of quantum algorithm input and tuning guidelines. One of the notable properties we characterize is that QPE sampling of the optimal digitized phase converges to a fixed rate. This results in strong diminishing returns of optimal phase sampling rates which can occur when the Trotter error is surprisingly high.

arXiv:2602.03466v5 Announce Type: replace Abstract: Deploying large language models (LLMs) as optimizers for black-box scientific design problems requires efficient test-time refinement under expensive evaluations and without training data. We propose a \emph{memory-augmented test-time optimization} framework that combines episodic memory of high-scoring candidates, score-difference feedback, and restart-from-best sampling to improve iterative search. We evaluate the approach on quantum circuit synthesis, where the objective is to maximize the Meyer--Wallach (MW) global entanglement measure under an exponentially expensive black-box oracle. On 20-qubit circuits, the framework achieves $Q(\psi)=0.99$ without feedback. On the more challenging 25-qubit task, feedback and restart mechanisms enable multiple runs to reach $Q(\psi)=1.0$ within 45 oracle calls, while a budget-matched random hill-climbing baseline stalls below $Q(\psi)\approx0.29$. These results demonstrate that memory and evaluator feedback substantially improve the sample efficiency of LLM-based black-box optimization and establish quantum circuit synthesis as a challenging benchmark for test-time optimization.

arXiv:2601.23084v3 Announce Type: replace Abstract: Quantum devices in the current Noisy Intermediate-Scale Quantum (NISQ) era are inherently affected by noise, which can degrade the predictive performance of quantum machine learning models. In this work, we introduce a new margin-based robustness measure for Quantum Kernel-Assisted Support Vector Machines (QSVMs), termed the cross-kernel margin. This measure quantifies the stability of a classifier learned under a perturbed kernel relative to the ideal feature space. We derive a posteriori stability bounds for the corresponding cross-kernel inverse squared-margin under kernel perturbations using the Tikhonov-stabilised SVM dual formulation. The local depolarising noise model is then applied to this framework to induce perturbations in the kernel. The resulting bounds are numerically checked using simulations across multiple datasets and further tested using kernel matrices obtained from real quantum hardware and a noisy backend simulator. Furthermore, we empirically compare the degradation of test accuracy under local depolarising noise with the commonly used global depolarising noise model in order to motivate its use in our study. Finally, we present empirical results linking margin-based quantities with the generalisation performance of QSVMs, providing additional motivation for our margin-based robustness analysis.

arXiv:2601.19391v3 Announce Type: replace Abstract: Generating long-distance quantum entanglement is crucial for advancing quantum information processing. In this work, we propose a protocol for generating remote magnon-phonon entanglement in a hybrid waveguide-magnomechanical system, where multiple spatially separated magnon modes couple to a common waveguide while interacting with their respective phonon modes. By applying tailored pulsed drives and engineering the magnomechanical interactions, our scheme enables the creation of diverse long-distance and dynamically stable entanglement. Beyond basic magnon-phonon two-mode entanglement, it supports genuine multimode entanglement between a single phonon and multiple magnons, bipartite entanglement between a single magnon and multiple phonons, as well as genuine four-mode entanglement involving two magnons and two phonons. Moreover, we show that dissipative magnon-magnon interactions mediated by traveling photons can generate substantially stronger remote entanglement than coherent couplings. Our work provides an experimentally feasible scheme for the remote generation of magnon-phonon entanglement.

arXiv:2601.18976v2 Announce Type: replace Abstract: We propose a scheme for accumulating entanglement between long-lived qudits provided by central nuclear spins of defect centers. Assuming a generic setting, the electron spin of each node acts as the communication qubit and may be entangled with other nodes, e.g., through a spin-photon interface. The generally available Ising component of the hyperfine interaction is shown to facilitate repeated entanglement transfer onto memory qudits of arbitrary dimension $d\le 2I+1$ with $I$ the nuclear spin quantum number. When $d$ is set to an integer power of two, maximal entanglement can be generated deterministically and without intermittent driving of nuclear spins. The scheme is applicable to several candidate systems, including the $^{73}$Ge germanium vacancy in diamond.

arXiv:2601.10034v2 Announce Type: replace Abstract: Decision making often exhibits context dependence that challenges classical probability theory. This paper develops a quantum-like extension of the Tug-of-War (QTOW) decision-making model to clarify when such context dependence can be represented by a single minimal internal state. The QTOW construction uses a qutrit internal state, conservation-preserving updates, and measurement-induced disturbance to model decision, learning, and probing operations within one coherent state space. Within this minimal representation, KCBS-type probing contexts can be constructed, yielding a witness of non-contextual classical non-embeddability. The main claim is not that quantum theory is uniquely or assumption-freely derived from decision making. Rather, a classical reconstruction of the same operation family requires additional contextual memory, history dependence, or an enlarged hidden-state representation. Thus, contextual probability appears as a resource signature of minimal decision dynamics, while quantum probability provides a compact, memory-efficient realization of this structure.

arXiv:2601.02471v2 Announce Type: replace Abstract: Time-translation symmetry strongly constrains physical dynamics, yet systematic characterization for continuous-variable systems lags behind its discrete-variable counterpart. We close this gap by providing a rigorous classification of Gaussian quantum operations that are covariant under time translations, termed Gaussian covariant operations. We show that several key results known for discrete-variable covariant operations break down in the Gaussian optical setting: discrepancies arise in physical and thermodynamic implementation, in the extensivity of asymmetry, and in catalytic advantages. Our results provide comprehensive mathematical and operational toolkits for Gaussian covariant operations, including a peculiar pair of asymmetry measures that are completely non-extensive. Our findings also reveal surprising consequences of the interplay among symmetry, Gaussianity, and thermodynamic constraints, suggesting that real-world scenarios with multiple constraints have a rich structure not accessible from examining individual constraints separately.

arXiv:2512.20613v2 Announce Type: replace Abstract: To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ans\"{a}tze. We perform variational energy minimization with respect to a quantum annealing Hamiltonian and utilize randomness by embedding the approaches in the metaheuristic iterated local search (ILS). The resulting quantum-inspired ILS algorithms are benchmarked on maximum cut problems of up to 50000 variables. We show that they can outperform traditional (M)PS methods, classical ILS, the quantum approximate optimization algorithm and other variational quantum-inspired solvers.

arXiv:2511.20569v2 Announce Type: replace Abstract: Fast charging of quantum batteries requires amplification of the energy transferred to a storage mode without uncontrolled gain or phenomenological non-Hermitian dynamics. Inspired by broken/unbroken dynamical regimes, we introduce a reservoir-engineered quantum battery in which a two-photon-driven charger and a battery mode are coupled through a lossy dissipative mediator. Eliminating the fast mediator yields a reduced two-mode Lindblad model with a complex dissipative coupling and renormalized damping rates. Its drift matrix has a pump-induced stability threshold: below threshold the seeded response is bounded, whereas above threshold a weak seed excites a growing mode and the battery occupation increases exponentially. Compared with a coherent beam-splitter charger--battery benchmark at equal effective coupling, the dissipative architecture reaches this broken regime at a lower pump amplitude. For the parameters studied here, this corresponds to about \(61\%\) less critical pump power and opens a pump-power window in which dissipative charging is exponential while the coherent benchmark remains below threshold. In the broken dissipative regime, the growth is dominated by a seed-selected coherent battery displacement rather than incoherent fluctuation buildup, so a large fraction of the stored energy is directly extractable by a displacement operation. The broken-regime boundary is a dynamical stability threshold, not generally an exceptional point, and the full three-mode Lindblad model confirms the reduced description in the fast-mediator regime. Our results give a completely positive route to pump-efficient, low-threshold, and coherently addressable quantum energy storage using engineered reservoirs.

arXiv:2511.12138v2 Announce Type: replace Abstract: High-Q optical microresonators combine low losses and high optical energy concentration in a small effective mode volume, making them an attractive platform for optical sensors. While light is confined in the microresonator by total internal reflection, a portion of the optical field, known as the evanescent field, extends outside. This makes the mode's resonant frequency sensitive to changes in the surrounding environment. In this work, we explore the quantum sensitivity limits of this type of sensors. We show that using the intracavity squeezing of the light in the microresonator, it is possible to suppress the influence of the optical losses and cancel the undesirable self phase modulation effect, originating from the cubic non-linearity of the microresonators media. As a result, the sensitivity surpassing the shot noise limit can be achieved. An additional sensitivity gain can be obtained by preparing the input light in a squeezed quantum state.

arXiv:2510.17974v2 Announce Type: replace Abstract: $W$ states are a central class of multipartite entangled states with applications in quantum information processing, yet their scalable and deterministic preparation remains challenging. Here we propose a protocol based on {\it topological ring frustration}, where an antiferromagnetic ring with an odd number of sites hosts a delocalized excitation corresponding to a $W$ state. We implement this protocol on a Rydberg atom array -- a programmable quantum simulator -- generating $W$ states of up to 11 atoms. Our results demonstrate a fidelity of $\mathcal{F} \approx 0.77$, and numerical simulations indicate scalability to larger system sizes accessible with near-term hardware improvements. To enable certification of these many-body entangled states, we introduce a novel and efficient Bayesian tomography method that, leveraging on classical simulations, enables their certification with a cost that avoids the exponential scaling of full tomography. These results establish topological frustration as a practical mechanism for engineering multipartite entanglement and provide a scalable route toward the certification of correlated quantum many-body states in quantum simulators.

arXiv:2509.17876v2 Announce Type: replace Abstract: Recently, several researchers proposed portfolio optimization as a potential use case for quantum optimization. However, the literature is lacking an extensive benchmark quantifying the potential of quantum computers for portfolio optimization. In this work, we contribute to closing this gap. We provide a computational study, comparing quantum approaches against state-of-the-art classical methods on a meaningful, real-world instance set. In particular, we compare quantum annealing and the quantum approximate optimization algorithm against classical mixed-integer programming, simulated annealing, steepest descent local search, tabu search and a problem-tailored heuristic. We consider a volatility-minimizing variant of portfolio optimization which we show to be more difficult to solve for classical optimizers than return-maximizing or multi-objective formulations. Our benchmark data set comprises 250 instances with up to 1,000 assets from actual stock data. Due to hardware limitation, quantum methods could only be tested for instances with at most 30 assets. The results show that all instances can be solved to proven optimality by mixed-integer programming in the order of seconds. Moreover, the problem-tailored heuristic consistently outperforms quantum approaches in terms of solution quality for fixed runtime. Thus, we conclude that there is only very limited room for a potential quantum advantage for the considered variant of portfolio optimization.

arXiv:2507.06954v2 Announce Type: replace Abstract: Spontaneous collapse models provide a possible, testable solution to the quantum measurement problem. While experiments are providing increasingly stronger bounds on their parameters, a full-fledged relativistic extension is still missing. Previous attempts have encountered different obstacles, such as violation of microcausality, infinite energy rate, and particle production from vacuum. Here, we propose a generalization of the collapse master equation that is characterized by a local field collapse operator and a non-Markovian noise with a Lorentz invariant correlation. Our construction is able to overcome previously encountered problems and has the desirable properties in the non relativistic limit. A specific choice of the noise correlation function is also introduced and discussed.

arXiv:2507.04500v3 Announce Type: replace Abstract: We present a two-step protocol for quantum measurement tomography that is light on classical co-processing cost and still achieves optimal sample complexity. Given measurement data from a known probe state ensemble, we first apply least-squares estimation to produce an unconstrained approximation of the POVM, and then project this estimate onto the set of valid quantum measurements. For a POVM with $L$ outcomes acting on a $d$-dimensional system, we show that the protocol requires $\mathcal{O}\left((d^3+d^2L)/\epsilon^2\right)$ samples to achieve error $\epsilon$ in worst-case distance, and $\mathcal{O}(d^2 L/\epsilon^2)$ samples in average-case distance. We further establish two matching sample complexity lower bounds of $\Omega((d^3 + d^2 L) /\epsilon^2)$ and $\Omega(d^2 L/\epsilon^2)$ for any non-adaptive, single-copy POVM tomography protocol. Hence, our projected least squares POVM tomography is sample-optimal in both the dimension and the number of outcomes for both distances. Our method admits an analytic form when using global or local 2-designs as probe ensembles and enables rigorous non-asymptotic error guarantees. Finally, we also complement our findings with empirical performance studies carried out on a noisy superconducting quantum computer with flux-tunable transmon qubits.

arXiv:2506.22346v3 Announce Type: replace Abstract: Accurate and efficient simulation of open quantum systems remains a significant challenge, particularly for Non-Markovian dynamics. We demonstrate the profound utility of expressing the environmental correlation function as a sum of damped sinusoidals within master equations. While not strictly required, this decomposition offers substantial benefits, crucially reducing the cost of Lamb-shift and decay rates calculations without sacrificing accuracy. Furthermore, this approach enables straightforward calculation of Lamb-shift corrections, bypassing the need for complex principal value integration. We show that these Lamb-shift effects are demonstrably non-negligible in heat transport scenarios, and are needed for an accurate description. Unlike in the Gorini-Kossakowski-Lindblad-Sudarshan(GKLS) master equation, the non-commuting nature of the Lamb-shift with the Hamiltonian in non-Markovian descriptions, coupled with GKLS's inaccuracies at early times, brings the necessity of Non-Markovian descriptions for finite-time thermodynamics. In the weak coupling regime, our Master Equation formulations with exponential decomposition achieve accuracy comparable to numerically exact methods. This methodology significantly simplifies and accelerates the simulation of non-Markovian dynamics in open quantum systems, offering a more reliable and computationally tractable alternative akin to a Global Master Equation.

arXiv:2506.18061v2 Announce Type: replace Abstract: Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate bicycle (BB) codes, achieve dramatic reductions in qubit overhead, yet their logical operations remain a key challenge under planar hardware constraints. Here, we introduce code craft, a framework for designing fault-tolerant logical operations on planar BB codes within a translationally invariant, two-dimensional qubit lattice. By systematically deforming codes through local modifications-stretching, cutting, and painting-we enable the manipulation of logical qubits using strictly planar operations. We establish fault tolerance through numerical optimization of code distances and show that logical operations, including controlled-NOT gates, state transfers, and Pauli measurements, can be efficiently implemented within this framework to assemble an individually addressable logical qubit network. Universal quantum computation can then be realized by coupling just one BB-code logical qubit to a surface-code block. By combining the high encoding efficiency of qLDPC codes with geometric locality, our approach offers a practical and resource-efficient path to fault-tolerant quantum computation.

arXiv:2503.13775v3 Announce Type: replace Abstract: This review surveys recent progress in III--V semiconductor quantum dots (QDs) as a platform for quantum repeaters. We start by discussing the state of the art in QD-based non-classical light sources. Specifically, we report on on single-photon and entangled-pair sources operating across near-infrared and telecom wavelengths, with emphasis on the key metrics-multi-photon suppression g2(0), photon indistinguishability, extraction efficiency, and spin coherence time-while discussing frequency conversion, excitation schemes, cavity engineering, remote indistinguishability, and spin coherence. We then examine the two principal repeater architectures. For all-photonic repeaters we review linear cluster- and graph-state generation using QD spins, recent experimental milestones, and the critical role of spin dephasing time. For memory-based repeaters we focus on heterogeneous implementations combining deterministic QD photon sources with room-temperature alkali-vapor memories, providing rate benchmarking against other platforms, discussion of storage protocols, wavelength compatibility, and early demonstrations. Enabling technologies such as cryogenic cooling, on-chip photonic integration, network synchronization and multiplexing are also presented. The review highlights the strength of QD-based architectures and identifies the remaining milestones required for their deployment in practical fiber-based quantum networks.

arXiv:2412.19918v5 Announce Type: replace Abstract: We revisit the Bohr model through Brownian motion of the electron and the principles of stochastic optimal control. The electron is assumed to have a definite but random position, represented by a single real-valued stochastic process in physical space whose probability density obeys the Fokker-Planck equation. Because Brownian paths are not differentiable, the process carries two mean drifts, one for each direction of time. We treat the forward drift as the control field, while the backward drift is fixed by the density of the same process. The running cost combines the two drifts into a time-symmetric kinetic term, and through the backward drift it inherits a dependence on the density, so the value becomes a functional on density space. Bellman's dynamic-programming principle requires the control to minimize the expected action from every intermediate time and density onward. The drift therefore emerges as a feedback law on position and density, rather than from the global stationarity of a stochastic action. The resulting law-dependent HJB-Fokker-Planck system reduces to the Schr\"odinger equation. For stationary hydrogen states the theory yields explicit drift fields in spherical coordinates and reproduces the standard radial and angular kinetic-energy averages of the quantum operator formalism. Direct trajectory-level simulations show the coordinate distributions converging to the Born marginals and the time-averaged energies reproducing the quantum expectation values. For the 2p eigenstates with magnetic quantum number $m=\pm1$, a phase-driven azimuthal drift makes the simulated trajectories circulate at the analytically predicted rate, and the angular momentum accumulated from the raw trajectory increments converges to exactly $L_z=m\hbar$. The angular-momentum quantization postulated in the Bohr model thus reappears as a property of the simulated stochastic motion.

arXiv:2305.02439v2 Announce Type: replace Abstract: Estimation of the expectation value of observables is a key subroutine in quantum computing and is also the bottleneck of the performance of many near-term quantum algorithms. Many methods have been proposed to reduce the number of measurements needed for this task by designing measurement schemes that decide the measurements to perform; however, these schemes are usually constructed from hand-crafted heuristics, which limits the measurement efficiency they can achieve. In this paper, we propose a framework for learning measurement schemes directly from the observable, using machine learning techniques including stochastic gradient descent and a two time-scale update rule. As a concrete realization of this framework, we introduce Composite-Locally Biased Classical Shadow (C-LBCS), which learns a mixture of locally-biased classical shadows and their mixing weights end-to-end. We numerically demonstrate C-LBCS on molecular systems up to $\mathrm{CO}_2$ (30 qubits) and show that C-LBCS outperforms the previous state-of-the-art methods despite its simplicity. We believe our approach opens up a reliable and scalable path toward efficient observable estimation on large quantum systems.

arXiv:2302.00821v3 Announce Type: replace Abstract: Existing approaches to emulating quantum computing algorithms using classical electronic hardware are limited by exponential scaling limitations in space, such as circuit size, or time, such as runtime or bandwidth. We introduce a scheme for representing quantum information using analog signals that lessens the bandwidth limitation problem seen in existing approaches [1, 2] by taking full advantage of the ability of analog signals to encode information using RMS voltage as well as frequency and phase. We introduce the mathematical framework for this representation, which separates the information relevant for measurement in the computational basis from information that is not relevant to it. We introduce circuits that take advantage of this separation of concerns to achieve simplifications, for working with quantum information in this representation. We argue that it is comparatively very inexpensive (as low as ~$5.00 / qubit) to outmatch the computing capabilities of existing FPGA based emulators [3], though scaling beyond tens of qubits is still impractical due to constraints of analog hardware module precision. However, our approach opens the door to a new avenue by which classical emulators can hope to improve: by improving on analog electronic circuit performance.

arXiv:2607.08684v1 Announce Type: cross Abstract: Bulk reconstruction is a central problem in AdS/CFT, and entanglement wedge reconstruction is its subregion version. We argue that this subregion statement should be separated from the stronger holographic quantum error correction interpretation, in which one region-independent logical bulk operator has code-preserving representatives in several boundary regions. A simple locality argument shows that such a common reconstruction must commute with the code-preserving local algebras in the complementary regions. This is the mechanism realized in HaPPY-type codes: the erased regions are blind to a protected logical algebra. An ordinary finite $N$ holographic CFT does not have such a protected invisible sector for supergravity fields. Its low-energy local observables, in particular, suitably smeared stress tensors, detect the physical support and gravitational dressing of ordinary bulk operators, up to possible center or superselection data. Thus, there is no such holographic quantum error correction and the $N=\infty$ agreement of global and subregion HKLL formulae is a free-theory statement. What remains is entanglement wedge reconstruction without holographic quantum error correction, or subregion complementarity: each boundary region has its own code-preserving low-energy algebra and its own region-adapted bulk interpretation, rather than a shared logical operator.

arXiv:2607.08589v1 Announce Type: cross Abstract: We study the critical properties of random quantum circuits with a $U(1)$ symmetry subject to local projective measurements that explicitly break this symmetry. We find that, at the measurement-induced phase transition, symmetry-breaking measurements act as a relevant perturbation at large scales, leading to the same universal critical properties as the corresponding monitored random circuit with non-symmetric unitary dynamics. In particular, we consider monitored $U(1)$-symmetric Haar-random circuits in the limit of large local Hilbert-space dimension, where the trajectory-averaged entanglement entropy can be exactly obtained in terms of a classical statistical mechanics model. In this model, the charge associated with the conservation law follows a symmetric simple exclusion process, in which symmetry-breaking measurements correspond to disordered defects that create and destroy charges. We prove that the charge correlation length remains finite for any measurement rate, ruling out a charge-sharpening transition, in contrast to the case of symmetry-preserving measurements. We further support our predictions at finite local Hilbert-space dimension through numerical finite-size scaling analyses of the entanglement transition in monitored $U(1)$-symmetric Haar and stabilizer random circuits.

arXiv:2607.08583v1 Announce Type: cross Abstract: We develop a general framework for the statistics of mixed-dimensional excitations subject to intertwined conservation laws, extending the familiar Fermi statistics with conserved particle number. We define statistics microscopically through a \emph{hopping-operator algebra}: a local operator subalgebra (LOsA) generated by operators that locally move or deform excitations while preserving the conservation law. Nontrivial statistics arise when this subalgebra is nontrivial. We first focus on LOsAs that encode \emph{pointed} conservation laws. These give rise to invertible excitations, whose fusion rules are exactly those of the symmetry defects of a higher group $\cG$. For such $\cG$-conserved excitations in $d$-dimensional space, we show that the corresponding LOsA -- and hence the statistics it defines -- is classified by a cohomology class $[\omega] \in H^{d+2}(B\cG;\R/\Z)$, where changing $[\omega]$ by a coboundary corresponds merely to a rephasing of the local operators. We further provide a holographic realization: excitations with this prescribed conservation law and statistics live on the boundary of a $\cG$ higher-group gauge theory in $(d+1)$-dimensional space, twisted by $[\omega]$. More generally, non-pointed conservation laws and the associated statistics of non-invertible excitations are defined by a pair: a LOsA together with its excitation-complex representation. This is equivalent to the pair consisting of a LOsA and its Hilbert-space representation, which is the data defining a generalized symmetry. Consequently, non-pointed conservation laws and their statistics in $d$-dimensional space are classified by fusion $d$-categories, just as generalized symmetries are. The higher-group results above are the fully-pointed special cases of this more general classification.

arXiv:2607.08568v1 Announce Type: cross Abstract: Renormalization provides a framework for relating microscopic models of physical systems to effective descriptions at larger length scales. This procedure is studied for the boundary states of non-chiral two-dimensional topologically ordered models. The initial data consist of renormalization fixed points built from representations of finite-dimensional $C^*$-Hopf algebras, which are then perturbed by uniform on-site noise quantum channels and repeatedly coarse-grained. The resulting flows admit an intrinsic algebraic description in terms of completely positive maps on the $C^*$-Hopf algebra or, equivalently, positive linear functionals on its enveloping $C^*$-Hopf algebra. Their iteration is governed by convolution powers, and convergent trajectories yield new matrix product density operator fixed points, described by finite $*$-quantum hypergroups. This provides a concrete physical interpretation of such structures. For finite group algebras and their duals, we provide explicit classifications via Goursat's lemma for groups. Finally, we formulate and prove a quantum generalization of Goursat's lemma for finite-dimensional $C^*$-Hopf algebras, a result of independent interest, which gives an explicit structural description of all convergent renormalization trajectories.

arXiv:2607.08421v1 Announce Type: cross Abstract: We measure the spatial pattern associated with the superradiant emission from a cloud of cold 87Rb atoms using Fourier imaging. We observe a highly directional, ring-shaped emission structure, which corresponds to a single collective jump operator associated to the most superradiant mode of the ensemble. Using spatial filtering, we isolate this channel and find the typical superradiant burst with superlinear scaling of the intensity with atom number. We compare our results to two models that describe the competition between the various decay channels, finding good agreement. Our work shows that the collective jump operators introduced by Carmichael et al. [Optics Communications 179, 417 (2000)] can be measured and manipulated.