Boson sampling demonstrates quantum advantage through the interference of indistinguishable particles, with output probabilities governed by matrix permanents. Realizing it on deterministic, matter-based platforms requires encoding the bosonic modes in finite-dimensional local Hilbert spaces, which introduces a leakage channel absent in linear optics: multi-particle bunching beyond the local truncation $d$. We develop a unified framework for non-interacting sampling on the irreducible representations of compact Lie groups, in which the transition amplitude is the immanant of a submatrix of the single-particle transition matrix, recovering the permanent in the bosonic case. Within this framework we bound the bunching leakage through a Dyson-series analysis: decomposing the correlated many-body leakage operator into independent random matrices and applying non-commutative concentration inequalities, we prove, in a Gaussian model of the transition matrix, that its spectral norm concentrates at $\tilde{O}(\sqrt{n})$ rather than the $O(n)$ worst-case of prior spin-based emulations; the passage to the physical Haar ensemble is reduced to a single submatrix-comparison input, verified at leading order. Exact numerics across local dimensions $d=2$--$5$ indicate that the bound is tight, the Haar-ensemble norm matching the closed form $\sqrt{d(n-d+1)}$ to sub-percent accuracy. This tightens the required mode number from $m=\Omega(n^4)$ to the near-optimal $m=\tilde{\Omega}(n^{1+2/(d-1)})$; for a spin-1 representation ($d=3$) the overhead falls to $m=\tilde{\Omega}(n^2)$, matching the collision-free threshold. The result is independent of particle statistics and applies across finite-dimensional Lie-symmetric architectures, quantifying the spatial resources needed to preserve sampling hardness.
A recently developed representation-theoretic framework for moments of random passive linear-optical circuits provides a systematic route for searching for regimes that unambiguously combine the absence of exponential concentration and lies beyond known efficient classical simulation methods.
Léo Monbroussou, Hugo Thomas, Hela Mhiri et al.· 1 citation
Entanglement entropy (EE) is commonly studied using real-space bipartitions. We show that, in quantum impurity models, an energy-space bipartition, equivalent to the momentum-space bipartition of the bath, can display universal behavior. Motivated by poor man's scaling, we logarithmically discretize the bath and partition it into high- and low-energy sectors. For models with Fermi-liquid fixed points, including the Anderson model and fully screened or underscreened Kondo models, the low-energy EE flows to constants independent of model parameters. These constants are integer multiples of $\ln 2$ plus corrections that depend only on the logarithmic discretization parameter $\Lambda$. We show that scale invariance of the fixed-point wavefunction in energy space maps to effective translation invariance along a one-dimensional chain, allowing the fixed points to be classified by one-dimensional topological band theory. With low-energy chiral symmetry, each $\ln 2$ contribution originates from a topological edge mode. We also study transitions between distinct Fermi-liquid fixed points using the local-singlet--Kondo-singlet transition in a two-orbital Anderson model driven by an inter-orbital antiferromagnetic coupling. The local-singlet phase has an effectively decoupled impurity and nearly vanishing EE, whereas the Kondo-singlet phase has finite EE larger than $\ln 2$ per spin and orbital. When chiral symmetry holds at low energies, this distinction corresponds to a topological transition of the effective bath chain. At the non-Fermi-liquid critical point, the EE develops an unstable plateau. Its $\Lambda$ dependence resembles that of the overscreened two-channel Kondo model, supporting universality within the same non-Fermi-liquid universality class.
In flat-band systems, quantum metric bounds physical observables like superfluid weight and coherence length, suggesting a single geometric scale for spatial correlations. Here, we show that the RKKY exchange in an isolated filled flat band can violate this expectation. With the intraband channel absent, the exchange proceeds via virtual interband transitions across the gap; the kernel becomes the inverse-gap-weighted trace product of the real-space flat-band projector and empty-band projectors. Because the corresponding momentum-space projectors are analytic, the kernel decays exponentially, with a decay length $\xi_\text{RKKY}$ set by the closest singularities of the analytically continued projectors in the complex momentum plane. Thus, this length depends on both the flat-band geometry and the band gap. Applying this formalism to Chern flat-band systems, we find that for small gaps, $\xi_\text{RKKY}$ depends non-monotonically on the quantum metric length: it first decreases, then increases, revealing that stronger quantum geometry can shorten the magnetic exchange range. Upon restoring dispersion, a nontrivial inversion representation can force the overlap between Bloch states at antipodal Fermi points to vanish under gate tuning, producing a $1/R^3$ RKKY tail instead of the conventional $1/R^2$---a geometric selection effect.
Multimode squeezing is a key resource for continuous-variable quantum technologies, but its spatial range in bosonic lattices is usually tied to dispersive propagation. Here we show that parametric pairing can create an exactly flat Bogoliubov band spanned by compact Bogoliubov generators, while producing phase-sensitive anomalous correlations and sub-vacuum collective-mode squeezing that extend far beyond their finite support. Each compact generator mixes annihilation and creation operators, thereby encoding the Bogoliubov squeezing structure, and neighboring translated generators can have nonzero commutator overlap. Enforcing canonical bosonic commutation relations therefore requires spatially extended linear combinations of these translated compact generators, which define the canonical Bogoliubov modes. The squeezing transformation of these modes varies with momentum and is quantified by the squeezing-sector symplectic quantum metric. A complex-momentum singularity of the analytically continued canonical Bogoliubov modes sets both the anomalous-correlation decay length and the momentum-space width of this metric, defining an intrinsic quantum-geometric length scale. This singularity can be tuned continuously while preserving exact flatness, thereby controlling the spatial range of correlations and squeezing. Away from exact flatness, long-distance correlations persist through multiple decay channels, while modes localized by defects and dimerized boundaries provide complementary probes of the underlying quantum geometry. In the weak-damping limit, the same quantum-geometric length scale can be extracted from frequency-filtered two-port correlations. Our results establish the quantum geometry of canonical Bogoliubov modes as a mechanism for spatially extended quantum resources arising from compact Bogoliubov generators.
Sonu Verma, Sangmo Cheon, M. Hwang et al.· 0 citations
We study the reflected entropy and the Markov gap for modes of a free bosonic field shared by inertial observers (Alice, Charlie) and a uniformly accelerated one (Bob), for a bipartite Bell state and the tripartite Werner (W) and Greenberger--Horne--Zeilinger (GHZ) states. The bosonic Bogoliubov transformation spans an infinite-dimensional Fock space with an unbounded squeezing parameter unlike the fermionic case. By identifying a conserved charge, we block-diagonalize the reduced density matrices into exact two-dimensional sectors, yielding closed or semi-analytic forms for all three states. Although bosonic entanglement is known to vanish asymptotically, the Alice--Bob reflected entropy instead saturates at a nonzero floor, retaining the surviving classical correlation, and converges to the value Alice shares with Bob's causally disconnected partner. Crucially, only the inter-wedge reflected entropy diverges, linearly in the squeezing parameter---the sharp distinction from the fermionic case, where it stays bounded---while the Markov gaps saturate. The construction transfers verbatim to a Schwarzschild black hole, where the saturation values become mass-independent constants.
Integration and sampling in high dimensions are among central challenges in modern science and technology, underlying applications ranging from quantum many-body physics to Bayesian inference and artificial intelligence. Although conventional Monte Carlo methods are formally scalable, their efficiency deteriorates rapidly in the presence of strong correlations or sharp features in high-dimensional configuration space. Here we introduce a new framework, termed the Schr"odinger Generator, for integration and sampling based on the explicit optimization of coordinate transformations. The method decomposes the total Jacobian into two complementary components, including an adaptive map that minimizes estimator variance by learning the marginal structure in each dimension, and a normalizing-flow-based transformation that captures non-factorizable correlations in the target distribution. A final resampling step guarantees unbiased sampling even when the learned transformation is imperfect. We demonstrate stable and scalable performance for nuclear quantum many-body states in dimensions exceeding 600. Short-range correlations among nucleons in finite nucleus are faithfully reproduced. The framework offers a physically transparent approach to high-dimensional stochastic integration and sampling, opening new possibilities for simulations of complex quantum systems.
Ling Jiang, Fu Ma, Pei Li et al.· 0 citations
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