Control architectures that reduce hardware overhead while maintaining high-fidelity operations are essential for the continued scaling of superconducting quantum processors. Here we experimentally realize a unified control architecture for fluxonium qubits, in which both transverse ($XY$) and longitudinal ($Z$) operations are implemented through a single flux-control channel driven by a single arbitrary waveform generator channel. This architecture imposes competing requirements on the shared control channel, which must simultaneously support low-frequency flux transmission for reset operations while strongly attenuating broadband noise near the qubit transition frequency. We address this challenge through frequency-selective cryogenic filtering together with compensated waveform synthesis that corrects the pulse distortion introduced by the filtered control line. Experimentally, this approach preserves coherence times above 100 $μ$s while enabling active reset with approximately 98% fidelity and 20-ns single-qubit gates with fidelities exceeding 99.99%. We further demonstrate FPGA-native instruction-level waveform synthesis based on reusable pulse primitives for unified flux control. These results establish unified flux control as a scalable architecture for fluxonium qubits that reduces control hardware overhead while preserving high-fidelity operation.

We study rational double points over algebraically closed fields in arbitrary characteristics and completely classify the indecomposable objects in their singularity categories, which correspond to the vertices in their Auslander-Reiten quivers. Along the way, we present an alternative proof determining the configuration of these Auslander-Reiten quivers, and provide methods to handle the homotopy categories of matrix factorizations of isolated hypersurface singularities with computer algebra systems.

Let $E/\mathbb Q$ be an elliptic curve, let $P\in E(\mathbb Q)$ be non-torsion, and let $(D_n)$ be the associated elliptic divisibility sequence. For a fixed prime $ρ$, we study when an arbitrary finite product \[ \prod_{i=1}^k D_{n_i} \] can be a $ρ$-th power in $\mathbb Q^\times$. The main result is that, under the hypothesis that $D_1$ is divisible by $2$ or $3$, such product relations impose rigid restrictions on the large prime divisors of the indices $n_i$. More precisely, for every $B\ge 2$, all sufficiently large prime divisors $\ell$ which occur as simple largest prime divisors of the indices and whose complementary cofactors are $B$-smooth must occur in $ρ$-balanced blocks. Equivalently, the corresponding prime-incidence rows over $\mathbb F_ρ$ have pairwise disjoint supports, are linearly independent, and satisfy the packing bound \[ |Λ^*|\le \lfloor k/ρ\rfloor . \] In particular, if $n_i=\ell_i a_i$, where the $\ell_i$ are sufficiently large primes and the $a_i$ are $B$-smooth, then a $ρ$-th power product relation can hold only if each prime $\ell$ occurs among the $\ell_i$ with multiplicity divisible by $ρ$. The proof combines Silverman's valuation law, a fixed finite-prime-set consequence of Reynolds' finiteness theorem, and the Hasse bound. The case $ρ=2$ gives the corresponding square-product obstruction.

To enable debugging and calibration of real time systems, which are in interaction with the real plant, the software used on those systems often has a huge number of global variables. The huge number of global variables exceed the range addressable relative to the global pointer. Therefore, addressing these variables normally needs two instructions. Other CPU architectures commonly used in the real time control systems domain address these by various near addressing modes. This results in significant code size reductions and performance boost. This paper discusses different variants to add such near addressing features to the RISC-V ISA. The impact on the code size is evaluated with different representative workloads.

Spin layer groups are the crystallographic symmetry groups with a periodic plane, and their symmetry operations are inherited from three-dimensional (3D) spin space groups. However, the direct application of 3D symmetry groups to two-dimensional systems is often inadequate due to anisotropic axes and dimensional reduction. In this work, we systematically classify inequivalent spin layer groups and analytically derive their irreducible corepresentations. This classification establishes a foundational framework for investigating symmetry-protected properties and novel quantum states in low-dimensional magnetic materials.

Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronization of heart cells, the circadian rhythm, or brain waves. It is also used in power system control. The simplest possible model assumes that all oscillators are identical and connected to each other with equal pairwise attraction. In this paper, we give a full geometric description of its global dynamics in terms of Morse theory and dynamical systems. Most of this description is stable in the sense that it is topologically preserved under small perturbations of the parameters.

Lattice impurities have recently emerged as a platform in which polarons unveil new quantum many-body states absent in free space and can serve to probe strongly correlated matter. In this work, we investigate two-dimensional lattice polarons with strong on-site repulsion and tunable nearest-neighbor interactions using a variational approach including up to one excitation of the medium. We show that extended interactions qualitatively modify the quasiparticle structure beyond the conventional attractive and repulsive polaron picture. A direct analysis of the eigenvalue spectrum reveals the presence of dark impurity states, orthogonal to the bare impurity and therefore spectroscopically dark. These states exhibit nontrivial internal structure, including dipolar symmetries in real space. Our results demonstrate that long-range interactions generate multiple quasiparticle excitations with distinct symmetry properties, highlighting the crucial role of interaction range and lattice geometry. This work opens new avenues for probing hidden quasiparticle states in lattice systems through spectroscopic and wave-function-resolved measurements.

Accurate quantification of intracellular metabolic fluxes is central to systems biology and biotechnology. Flux estimation relies on biochemical network models, with $^{13}$C metabolic flux analysis (MFA) being the state-of-the-art approach. However, isotope labeling data are often insufficient to uniquely support a single network formulation. In such cases, flux estimates become model-dependent, highlighting the need for methods that explicitly account for structural uncertainty. Bayesian model averaging (BMA) provides a principled framework for this purpose, but its application to $^{13}$C-MFA has so far been restricted to uncertainty in reaction bidirectionality within fixed network topologies. We introduce a scalable Bayesian inference framework for $^{13}$C-MFA, Bayesian model set averaging, that applies BMA to encompass uncertainty in reactions and pathways. Our approach combines reversible jump Markov chain Monte Carlo for trans-dimensional exploration of model spaces with diffusive nested sampling for robust estimation of model evidences, enabling averaging over large families of metabolic network models. Using illustrative and application-scale synthetic case studies, we demonstrate that the method yields robust flux estimates, reveals when multiple network configurations are statistically indistinguishable, and recovers data-supported model structures. Importantly, rather than committing to a single model, the framework manages structural uncertainty: under limited data, competing models are retained, whereas increasing data informativeness improved model and flux recovery. The approach scales to billions of model variants, providing a practical foundation for uncertainty- and misspecification-aware quantitative flux inference in $^{13}$C-MFA.

We theoretically investigate a freestanding membrane of infinite-layer nickelate Nd$_{0.85}$Sr$_{0.15}$NiO$_2$ under pressure by constructing a seven-orbital effective model based on first-principles calculations. By performing the fluctuation exchange (FLEX) approximation, we demonstrate that the seven-orbital model explains a monotonic increase in $T_c$ reported in a recent experiment. This enhancement of superconductivity is attributed to the mitigation of excessively strong electron correlations caused by exceptionally low valence of Ni atom. Furthermore, we examine the dynamical stability of the crystal structure under pressure through phonon calculation.

The positional Burrows-Wheeler Transform (PBWT) is commonly used to store haplotype panels compactly in such a way that, given a query haplotype, we can quickly find the set maximal exact matches (SMEMs) between the query and the haplotypes in a panel. There are generally two steps in this process: first we find the maximal substrings of the query that occur in the same positions in haplotypes in the panel and then, for each such substring, report the haplotypes in the panel in which the substring occurs in the same position as in the query. Very recently, Bonizzoni, Gagie and Gao (2026) gave two time-space tradeoffs for the second step: they use either $O ((r + h) \log n)$ bits and $O (\log \log \min (h, \ell) + k)$ time to report $k$ haplotypes in the panel, or $O (r \log h + h \log n)$ bits and $O (k \log \log h)$ time, where $r$ is the number of runs in the panel's PBWT and $h$, $\ell$ and $n = h \ell$ are the panel's height, length and size, respectively. We observe here that if we can batch queries until we have found $r \lg (h) / \lg r$ such substrings and we report an average of at least $\lg (r) / \lg h$ haplotypes in the panel per substring, for example, then for the second step we can easily use $O (r \log h)$ bits and constant time to report each haplotype. Our approach is based on an algorithm for constructing the prefix arrays quickly from the PBWT, which may be of independent interest.

We construct the dynamical symmetry of the quantum Calogero model with particle exchange in a confining Coulomb field. This symmetry is governed by the algebra $so(N+1,2)$, deformed by exchange (Dunkl) operators, with its invariant sector generated by the Dunkl angular momentum tensor and the modified Laplace-Runge-Lenz vector. The equidistant analogue of the Hamiltonian, with a linear spectrum, is expressed in terms of the conformal subalgebra $so(1,2)$. In addition, the wave functions of the Calogero-Coulomb Hamiltonian are classified into infinite-dimensional lowest-weight $so(1,2)$ multiplets.

In the extended Linear-Sigma Model (eLSM), the chiral phase structure of meson states, including pseudoscalars ($J^{pc}=0^{-+}$), scalars ($J^{pc}=0^{++}$), vectors ($J^{pc}=1^{--}$), and axial-vectors ($J^{pc}=1^{++}$), is investigated with the mean-field approximation. A systematic comparison between SU(3) and SU(4) configurations is provided. It has been found that the estimations of meson masses derived from SU(4) eLSM are more congruent with experimental values than those derived from SU(3) eLSM. Consequently, we conclude that an increase in quark degrees of freedom significantly enhances the accuracy of meson mass simulations. We investigate the effect of temperature on the masses of various meson states calculated in the SU(3) and SU(4) eLSM. After establishing all the fitting parameters, the temperature dependence of meson masses shows that although various meson states exhibit unique patterns in their mass changes with temperature, they all seem to share a similar range of dissolution temperatures. This means that the critical temperature that marks the phase transition from hadrons to quarks appears to vary slightly depending on the meson states. In this regard, we find that the quarkonium states, formed by a quark and its antiquark, are largely unaffected by variations in the temperature.

We perform a complete calculation of the next-to-next-to-leading order (NNLO) electroweak fermionic corrections to fermion-pair production processes, where "fermionic" refers to contributions with closed fermion loops. We did this via a semi-numerical technique that uses dispersion relations for the fermion sub-loop in two-loop box and vertex diagrams and dispersion relations and Feynman parameters for vertex diagrams with fermionic triangle sub-loops. UV and IR divergences are treated with suitable subtraction terms. We present numerical results for the cross-sections of $e^+e^-\to μ^+μ^-/u\bar{u}/d\bar{d}$ and differential distributions at representative center-of-mass energies. The NNLO corrections are found to modify the NLO cross-section on the order of 1%.

Only a small fraction of the data generated in state-of-the-art all-atom multi-microsecond molecular dynamics (MD) simulations is typically analyzed. With femtosecond integration steps, microsecond simulations generate billions of time steps containing atomic positions, velocities, and forces, often corresponding to petabytes of data. Since this exceeds practical storage capacities, only a subset of frames is usually written to trajectory files at intervals of 10-100 ps. While sufficient for ensemble averages and slow dynamics, this approach discards information on fast processes such as molecular vibrations, solvent dynamics, short-lived transition states, and transport phenomena that are directly related to macroscopic properties and experimental observables. Here, we introduce a streaming framework for MD simulations that provides direct access to all data generated during a running simulation. Instead of writing high-frequency output to disk, the framework enables user-defined analysis and processing routines to access simulation data in real time. To achieve this, we extend the Interactive Molecular Dynamics (IMD) protocol and implement an enhanced version, termed IMDv3, in the MD packages GROMACS, NAMD, and LAMMPS. We further introduce the Python package imdclient, which receives IMDv3 data streams and exposes them to external applications. To maximize usability, we add an imdclient-based reader to the MDAnalysis package, enabling streamed simulation data to be analyzed alongside conventional trajectory files. Benchmark results show that streaming can improve performance compared to simulations with high-frequency trajectory output. Example applications include live monitoring of custom variables, evaluation of velocity time-correlation functions with fast fluctuations, and real-time analysis of membrane pore currents.

Symbolic integration over the Haar measure of compact groups is a computational cornerstone in quantum information science and random matrix theory. We present \texttt{IntegrateUnitary.jl}, a comprehensive Julia package for computing exact expectations of polynomial functions over a wide range of compact groups ($U(d)$, $O(d)$, $Sp(d)$, and $SU(d)$ for balanced polynomials), circular and Gaussian ensembles, Ginibre ensembles, permutation groups, random pure states, and unitary $t$-designs. The package provides a fully open-source implementation of the Weingarten calculus and Wick contractions with broad symbolic-$d$ support for entry-wise and trace-polynomial integrals, while selected workflows currently require concrete integer dimensions (including higher pure trace moments $|\mathrm{tr}(U)|^{2k}$ for $k > 1$ and HCIZ with \texttt{SymbolicMatrix} inputs, and direct matrix-valued integration of \texttt{SymbolicMatrix}/\texttt{SymbolicMatrixProduct} expressions), automatic asymptotic expansions, a high-level symbolic trace interface that reconstructs Weingarten graphs from index-free expressions, and a bridge to \texttt{ITensors.jl} for tensor network averaging. We discuss the underlying algorithms, including the Murnaghan-Nakayama rule and symplectic-orthogonal duality, and demonstrate that the package efficiently handles high-degree moments and quantum information metrics.

We scrutinize properties of electrical charges bounded to visible and dark matter sectors, in the vicinity of a magnetic poles of both sectors. It turns out that the considered system has an angular momentum despite the charges are at rest. On the other hand, investigation the behavior of electric charges of visible and hidden sectors held at rest outside a magnetically charged black hole, discloses that even if the electric charge are regarded as perturbations on a spherically symmetric magnetic static black hole in dark photon theory, at large distances it looks like a stationary axisymmetric magnetically charged black hole.

Pulsar halos are produced by electrons and positrons diffusing in the interstellar medium around their parent pulsar wind nebulae. Recent observations by HAWC and LHAASO have revealed asymmetric morphologies in the halos surrounding Geminga and Monogem. The anisotropic diffusion model provides a natural explanation for such asymmetries, where the morphology is determined by the viewing angle of the mean magnetic field, the Alfvénic Mach number ($M_{\rm A}$), and the pulsar distance. In this work, we model the measured morphologies based on this framework and constrain the properties of interstellar magnetic turbulence. We find that the mean magnetic field orientations within the two halos are different, implying that they reside in different magnetic coherence regions, whereas the Alfvénic Mach numbers are relatively close ($M_{\rm A}\sim 0.2$). The results suggest a local magnetic field coherence length of approximately 100pc. Our study demonstrates that the morphology of pulsar halos serves as a powerful diagnostic tool for the properties of interstellar magnetic fields, highlighting the need for more accurate morphological measurements and sophisticated diffusion modeling in future studies.

For the adiabatic version of Grover's quantum search algorithm as proposed by Roland and Cerf, we study the impact of decoherence caused by a rather general coupling to some environment. For quite generic conditions, we find that the quantum Zeno effect poses strong limitations on the performance (quantum speed-up) since the environment effectively measures the state of the system permanently and thereby inhibits or slows down quantum transitions. Generalizing our results, we find that similar restrictions should apply universally to adiabatic quantum algorithms and quantum annealing schemes which are based on analogous isolated Landau-Zener type transitions at avoided level crossings (similar to first-order phase transitions). As a possible resort, more gradual changes of the quantum state (as in second-order phase transitions) or suitable error-correcting schemes such as the spin-echo method may alleviate this problem.

Quoridor is an award-winning abstract strategy game designed by Mirko Marchesi and published in 1997. Similar games include Maze Attack, Blockade (also known as Cul-de-sac), and Pinko Pallino. In line with chess, checkers, Go, and other classic combinatorial games, Quoridor is a turn-based, deterministic, perfect-information game played on a square grid. We show that it is PSPACE-complete to determine whether a given player has a winning strategy in a given Quoridor position on a board with size $n \times n$. We prove this by reduction from Gpos(POS CNF), a Boolean formula game originally defined in 1978 by T. Schaefer.

This paper studies the Manickam-Miklós-Singhi (MMS) property for graphs and hypergraphs. Using the structural characterisation of the $2$-uniform case, we construct new families of regular graphs with the MMS property. We then analyse the Erdős--Rényi random graph model $\mathbf{G}(n,p)$ and identify regimes in which the MMS property holds with high probability. Finally, we extend the matching-based sufficient condition to higher uniformities via pseudo-matchings and introduce a blowout construction that produces higher-uniformity hypergraphs with the MMS property from lower-uniformity examples.

We use a three-dimensional model to calculate steady-state climates at various intervals in Earth's future, across a parameter space of increasing insolation and decreasing CO$_2$ mixing ratio. Comparison with prior results shows an overestimation of warming by one-dimensional models when solar constant is increased and CO$_2$ mixing ratio is fixed. We consider two future trajectories as limiting cases: strong weathering, in which surface temperature remains constant but CO$_2$ is drawn down; and weak weathering, in which CO$_2$ remains constant and surface temperature increases. Under strong weathering, we find the conventional 10 ppm CO$_2$ starvation limit for C4 photosynthesis that occurs at 1.35 Gyr; however, we suggest that crassulacean acid metabolism (CAM) photosynthesis could persist below this limit and note that aquatic macrophytes can utilize dissolved bicarbonate if atmospheric CO$_2$ is low. If we take the CO$_2$ starvation limit at 1 ppm instead, then the vegetative biosphere could continue until 1.84 Gyr. Thermal limits apply instead under weak weathering, in which Earth would be too hot for most land plants at 1.68 Gyr (>323 K) and too hot for all land plants (>338 K) at 1.87 Gyr. These lifetimes approach the moist and runaway greenhouse limits for Earth. We discuss other possible mechanisms for extending the lifetime of Earth's biosphere, noting that both technological intervention and evolutionary processes could enable life to adapt to a brightening sun.

We prove an analog of Aldous' spectral gap conjecture in the generalized symmetric groups $G\wr S_n$ where $G$ is an arbitrary finite group. Moreover, we show that Caputo's extension of the conjecture to hypergraphs transfers to these groups whenever it holds in the ordinary symmetric group.

In this work, a comprehensive analysis for processes related to $b\to c\bar{u}q~(q=d, s)$ transitions are carried out, including new physics contributions. In light of a recent tension between branching fractions for $B_{(s)}\to D_{(s)}^{(*)}M$ ($M$ represents a meson) decays in the QCD factorization approach and relevant experimental results, phenomenological constraints on complex-valued Wilson coeffients are discussed. Analyzed observables contain direct CP asymmetry ($A_{\text{CP}}$) in $B^-\to D^0π^-$ decays and $γ/ϕ_3$, one of the angles in the unitarity triangle, combined with others from $τ_{B^+}/τ_{B_d}$, $ΔΓ_{q}/Γ_q$, and $A_{\rm SL}^{q}~(q=d, s)$. We constrain the complex Wilson coefficients at $1σ$ and $2σ$ levels under color-singlet and color-rearranged scenarios. These constraints yield correlated predictions for $ΔΓ_d/Γ_d$, $A_{\rm SL}^d$ and $A_{\text{CP}}$.

Among the thriving quantum computation and quantum simulation platforms based on arrays of Rydberg atoms, those using circular Rydberg atoms are particularly promising. These atoms uniquely combine the strong dipole-dipole interactions typical of Rydberg states with long lifetimes. However, low-angular-momentum ($\ell$) laser-accessible Rydberg levels have been so far mostly used, because circular Rydberg atoms have no optical transitions, hindering their individual detection and manipulation. We remove this limitation with a hybrid platform, combining an array of logical laser-trapped circular Rydberg atoms of rubidium with an auxiliary array of Rb ancilla atoms transiently excited to a low-$\ell$ Rydberg level. We perform a quantum non-demolition detection of the logical qubit with the ancilla, through the blockade of the ancilla optical excitation induced by a Förster resonance. Conversely, we locally manipulate the logical qubit through the excitation of the ancilla. This dual-Rydberg platform is highly promising for quantum computation and simulation. It adds to the circular-atom toolbox the mid-circuit measurements, essential for error correction. More strikingly, it gives access to time correlations in long-term quantum simulations, uniquely accessible to circular Rydberg atoms.

We consider an infinite graph with the vertex set $\mathbb{Z}^2$ and edges connecting the vertices iff the Euclidean distance between the respective points is an integer, and the points do not lie on the same horizontal or vertical. Equivalently, there must exist a Pythagorean triangle with the hypotenuse corresponding to the graph edge and the legs parallel to the axes. We prove that the diameter of this graph is $3$, but surprisingly it appears that the nodes at the maximal (graph) distance of $3$ apart seem to be only those that are geometrically very close to each other. It also appears that the paths of length $2$ connecting geometrically close nodes may need to go through geometrically very distant points. We prove a general relation that generates infinite series of length-$2$ paths, and present the results of our computer experiments. We conclude the paper with a general conjecture about the length-$2$ and length-$3$ paths. We have posed this conjecture to several of the current leading AI models. Remarkably, none of them managed to make any significant progress in proving it.

This paper studies conditional allocation between a growth/technology ETF basket, denoted by $G$, and a defensive income/value-oriented ETF basket, denoted by $D$. The objective is not to discover a new standalone alpha factor, but to examine whether known style exposures can be dynamically allocated using macro-market timing signals. Fama-French five-factor plus momentum attribution shows that the relative portfolio $G-D$ is a recognizable style portfolio: its market beta is 0.273, its HML beta is -0.552, its momentum beta is 0.117, and its annualized alpha is 1.95\% with a Newey-West t-statistic of only 0.81. The empirical object is therefore interpreted as a growth-versus-defensive style allocation problem rather than a new return anomaly. The allocation framework replaces discrete regime labels and if-then trading rules with a continuous smooth score. The score combines rate relief, SPY drawdown depth, high-VIX stress relief, and a growth-crowding penalty. Interaction terms are smoothed with softplus functions, the total score is mapped to G/D weights through a hyperbolic tangent function, and realized weights are smoothed with EWMA. In the main aligned comparison window from June 28, 2017 to May 15, 2026, with 10bp transaction costs, the selected smooth-score policy uses a 50\% maximum active tilt and obtains a 19.24\% CAGR, a Sharpe ratio of 1.01, and a maximum drawdown of -31.63\%. It improves over 50/50 G/D, matched TNX-only, matched core-only, SPY, and volatility-matched 100\% G benchmarks. It does not, however, exceed 100\% G or the best high-G static portfolios in raw CAGR. Walk-forward and post-2022 validations provide additional evidence of drawdown reduction and risk-adjusted allocation value. Overall, the evidence supports continuous, interpretable style timing, while also showing that high static growth exposure remains a strong benchmark.

We prove a variety of results about subgroups of Thompson's group $V$. First we prove that every action graph of a finitely generated subgroup of $V$ acting on an orbit in Cantor space is quasi-isometric to a tree. Then we prove that for a broad class of groups of homeomorphisms of the real line, for example Thompson's group $F$, any action on the Cantor space via an embedding into Thompson's group $V$ must be semiconjugate to the standard action on the line. Finally, we use this to establish that many such groups cannot embed into $V$; in particular the Stein group $F_{2,3}$ cannot embed in $V$, answering a question of the third author.

We study deformed neutron halo nuclei in the mass region $40 < A < 90$ and their soft electric dipole ($E1$) excitations based on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). Three candidates, $^{43}$Si, $^{69}$Ti, and $^{75}$Cr, are selected for detailed analysis. Unique features are identified in the decoupled densities of possible $s$- and $p$-wave deformed halo nuclei in this mass region, which are influenced by large high-$l$ configurations. It is shown that the dipole response is a highly sensitive observable to detect the halo component of the single-particle wave function in deformed halo nucleus, and it helps identify the configuration and the magnitude of deformation for halo nuclei in the $40 < A < 90$ mass region. Experimental confirmation of the dipole strength in the low-energy region is highly desirable to explore possible deformed halo candidates in the medium-heavy mass region.

We recalculate the contributions of individual six loop graphs to the $β$-function for a three dimensional scalar theory with an arbitrary sextic scalar potential. Previously this was calculated by Hager who specialised to a theory with maximal $O(N)$ symmetry. Our results differ in some contributions to the overall $β$-function but agree with a recent calculation \cite{Kompaniets2}. At large $N$ three eight loop diagrams which are relevant are calculated. At the $O(N)$ fixed point some critical exponents are determined to $\rm O(\varepsilon^3)$. Imposing that the $β$-function satisfies a gradient flow equation is shown to require linear relations between some $β$-function coefficients. The curvature for the associated metric is also determined. Detailed results for the Feynman integrals are described in the appendices.

Quantum computation is not many classical computations running in parallel, but controlled interference in Hilbert space. Amplitude is spread, problem structure is folded into phases, and measurement detects the invariant made visible by recombination. What is exposed is usually not a branchwise table of values, but a structure-matched statistic such as a parity, period, symmetry class, or marked subspace. Quantum advantage comes from matching the relevant structure to an efficient interference pattern, under the constraints of measurement contexts, thermodynamic irreversibility, and contextuality.