Quantum signal processing angles admit closed-form expressions via orthogonal polynomial theory, allowing O(log(1/ε)) gate block-encodings of smooth functions through Hermite expansions and full characterization of SU(1,1)-QSP polynomials by roots.
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New lower-bound techniques based on controllable correlation and entanglement yield non-trivial bounds for Haar-random two-qubit unitaries and the first known bounds for CNOT, DCNOT, sqrt(SWAP), and XX gates, with a tight result for CNOT.
Quasiprobability models in Bayesian networks generalize to produce all non-signalling correlations for a broad class of networks and conjecturally recover the nested Markov model.
Constructs Yangian descendants for the Haldane-Shastry chain via algebraic Bethe ansatz and derives norms and overlaps formulae.
Proposes a CFT analogue of Hodge loci in Calabi-Yau sigma models via non-trivial TDL categories of topological defects, with CM number field embeddings at special points for elliptic curves and K3 surfaces.
Introduces a TAP-motivated framework and constructs explicit parameter-free spectral algorithms that achieve strong detection and weak recovery thresholds in three canonical correlated two-view models with matching lower bounds.
Families of complex tensor trace-invariants with tree-like dominant pairings factorize at large N, allowing computation of typical multipartite Rényi entropies for uniform random states.
An exact spacetime polymer gas representation is derived for finite-temperature Z_N homological codes, providing low-activity bounds on partition functions and an exact duality exchanging electric/magnetic backgrounds.
Derives layer-wise recursions for finite-width tensors under orthogonal initialization that reproduce the observed large-depth stability of nonlinear networks.
Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
Mode stability without symmetry assumptions is proved for self-similar wave map blowups in all dimensions d ≥ 4.
The fractional Massari functional Gamma-converges to the classical Massari functional, preserving minimizers, and yields limiting information for inhomogeneous Allen-Cahn equations together with the new notion of non-local hybrid mean curvature.
The paper proves that 2-group symmetries in 3D defect TQFTs from G-crossed braided fusion categories have no gauging obstructions and that gauging the 0-form G-symmetry on the neutral component produces the equivariantisation, with a reciprocal relation when G is commutative.
Rapid mixing and frustration-freeness in short- and long-range Lindbladians imply polynomial decay of MI and CMI in fixed points, and long-range non-commuting Gibbs states satisfy local Markov property at any temperature.
New unified proof of the Positive Mass Theorem and Riemannian Penrose Inequality for 3D asymptotically flat manifolds with C^{2,α} metrics up to a hypersurface, via approximate monotonicity of a potential-theoretic quantity.
The Quad-C5 graph, built from four overlapping KCBS pentagons, is the maximum-gap contextuality witness on eight vertices and is already contextual for a single qutrit.
Computer-assisted proof shows that the linearized operator around threefold symmetric traveling waves in the Burgers-Hilbert equation has an eigenvalue with negative real part for ω=3 and c≈1.1.
The authors unify the Boussinesq and axisymmetric Euler systems into a parameterized boundary-jet model and prove finite-time blow-up for its closed truncation using a Riccati argument.
A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.
Instanton partition functions on the blow-up are given by chamber-dependent contour integrals over super-partitions selected by stability conditions, yielding explicit wall-crossing formulas that recover the Nakajima-Yoshioka blow-up formula.
A coefficient-based unification of two fluid equations yields exact (1+1)D reductions whose apex dynamics blow up in finite time under stated conditional stability assumptions.
Supplies domination properties of self-adjoint kernels to select Feynman propagators that yield Hadamard states for bosonic, hermitian, Dirac, and Majorana theories.
Explicit spherical solutions to the Dirac equation are given for initial data from hydrogen-like atoms or Minkowski waves that then propagate in de Sitter FLRW spacetime.
Models Rozansky-Witten theory of T*X via sheaves of categories from Perf(X×A¹), constructing hybrid Lagrangian objects whose Homs are matrix factorizations.
citing papers explorer
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Analytical Angle-Finding and Series Expansions for Quantum Signal Processing via Orthogonal Polynomial Theory
Quantum signal processing angles admit closed-form expressions via orthogonal polynomial theory, allowing O(log(1/ε)) gate block-encodings of smooth functions through Hermite expansions and full characterization of SU(1,1)-QSP polynomials by roots.
-
Lower bounds on non-local computation from controllable correlation
New lower-bound techniques based on controllable correlation and entanglement yield non-trivial bounds for Haar-random two-qubit unitaries and the first known bounds for CNOT, DCNOT, sqrt(SWAP), and XX gates, with a tight result for CNOT.
-
Bounding Classical and Quantum Correlations in Bayesian Networks with Quasiprobabilities
Quasiprobability models in Bayesian networks generalize to produce all non-signalling correlations for a broad class of networks and conjecturally recover the nested Markov model.
-
Norms, overlaps and Yangian descendants for the Haldane--Shastry spin chain
Constructs Yangian descendants for the Haldane-Shastry chain via algebraic Bethe ansatz and derives norms and overlaps formulae.
-
Hodge Loci and Complex Multiplication via Generalized Symmetries in Calabi-Yau sigma models
Proposes a CFT analogue of Hodge loci in Calabi-Yau sigma models via non-trivial TDL categories of topological defects, with CM number field embeddings at special points for elliptic curves and K3 surfaces.
-
Optimal Spectral Algorithms for Correlated Two-view Models in High Dimensions
Introduces a TAP-motivated framework and constructs explicit parameter-free spectral algorithms that achieve strong detection and weak recovery thresholds in three canonical correlated two-view models with matching lower bounds.
-
Large $N$ factorization of families of tensor trace-invariants
Families of complex tensor trace-invariants with tree-like dominant pairings factorize at large N, allowing computation of typical multipartite Rényi entropies for uniform random states.
-
An exact spacetime polymer gas for finite-temperature $\mathbb Z_N$ homological quantum code
An exact spacetime polymer gas representation is derived for finite-temperature Z_N homological codes, providing low-activity bounds on partition functions and an exact duality exchanging electric/magnetic backgrounds.
-
Criticality and Saturation in Orthogonal Neural Networks
Derives layer-wise recursions for finite-width tensors under orthogonal initialization that reproduce the observed large-depth stability of nonlinear networks.
-
Propagation of chaos for the Boltzmann equation with very soft potentials
Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
-
Mode stability of self-similar wave maps without symmetry in higher dimensions
Mode stability without symmetry assumptions is proved for self-similar wave map blowups in all dimensions d ≥ 4.
-
$\Gamma$-convergence of the non-local Massari functional and applications to inhomogeneous Allen-Cahn equations
The fractional Massari functional Gamma-converges to the classical Massari functional, preserving minimizers, and yields limiting information for inhomogeneous Allen-Cahn equations together with the new notion of non-local hybrid mean curvature.
-
2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging
The paper proves that 2-group symmetries in 3D defect TQFTs from G-crossed braided fusion categories have no gauging obstructions and that gauging the 0-form G-symmetry on the neutral component produces the equivariantisation, with a reciprocal relation when G is commutative.
-
Static features from mixing in short- and long-range Lindbladians: Markov property and correlations
Rapid mixing and frustration-freeness in short- and long-range Lindbladians imply polynomial decay of MI and CMI in fixed points, and long-range non-commuting Gibbs states satisfy local Markov property at any temperature.
-
Riemannian Penrose Inequality for Manifolds with Corners via Non-Linear Potential Theory
New unified proof of the Positive Mass Theorem and Riemannian Penrose Inequality for 3D asymptotically flat manifolds with C^{2,α} metrics up to a hypersurface, via approximate monotonicity of a potential-theoretic quantity.
-
The Quad-$C_5$ Graph: Maximum Contextuality Gap on Eight Vertices
The Quad-C5 graph, built from four overlapping KCBS pentagons, is the maximum-gap contextuality witness on eight vertices and is already contextual for a single qutrit.
-
Linear instability of a Burgers--Hilbert traveling wave
Computer-assisted proof shows that the linearized operator around threefold symmetric traveling waves in the Burgers-Hilbert equation has an eigenvalue with negative real part for ω=3 and c≈1.1.
-
A unified Boussinesq--Euler formulation and finite-time blow-up for a Hou--Luo type boundary-jet system
The authors unify the Boussinesq and axisymmetric Euler systems into a parameterized boundary-jet model and prove finite-time blow-up for its closed truncation using a Riccati argument.
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On the Quantisation of Linear Gauge Theories on Lorentzian Manifolds: Maxwell's Theory via Complete Gauge Fixing
A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.
-
Wall-crossing of Instantons on the Blow-up
Instanton partition functions on the blow-up are given by chamber-dependent contour integrals over super-partitions selected by stability conditions, yielding explicit wall-crossing formulas that recover the Nakajima-Yoshioka blow-up formula.
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2D inviscid Boussinesq equations and 3D axisymmetric Euler equations: (1) A unification ($Em$), (2) Finite-time blow-up of two unified $(1+1)$D systems rigorously derived from ($Em$)
A coefficient-based unification of two fluid equations yields exact (1+1)D reductions whose apex dynamics blow up in finite time under stated conditional stability assumptions.
-
On the construction of Hadamard states from Feynman propagators
Supplies domination properties of self-adjoint kernels to select Feynman propagators that yield Hadamard states for bosonic, hermitian, Dirac, and Majorana theories.
-
Propagation of Dirac spherical waves in the expanding universe
Explicit spherical solutions to the Dirac equation are given for initial data from hydrogen-like atoms or Minkowski waves that then propagate in de Sitter FLRW spacetime.
-
Modeling Rozansky-Witten Theory with Sheaves of Categories
Models Rozansky-Witten theory of T*X via sheaves of categories from Perf(X×A¹), constructing hybrid Lagrangian objects whose Homs are matrix factorizations.
-
Mass-$p$-Capacity Inequalities in Asymptotically Flat Half-Spaces
Establishes monotone quantities and sharp mass-p-capacity inequalities for p-capacitary functions in 3D AF half-spaces with nonnegative scalar and boundary mean curvature, equality on Schwarzschild half-spaces.
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Bayesian Inference with Shaped Deep Non-linear MLPs
In the LP/N = Θ(1) regime, Bayesian predictive posteriors for deep MLPs equal those of data-dependent kernels to first order, with a criterion identifying data processes that benefit from larger effective depth.
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From Finite-Node Conifold Geometry to BPS Structures III: Mediated Triangle Transport and Graded Interaction Data
Mediated triangle transport yields graded interaction polynomials I_Σ^gr from conifold state data, extending binary support structures for BPS and stability theory.
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Emergent fracton strings from covariant bi-form gauge field theory
A rank-4 tensor gauge theory yields emergent fracton strings with a new generalised dipole conservation law for closed strings and reduces to linearised area-metric gravity in a suitable limit.
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Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions
A 3D QFT is defined with infinite-dimensional topological-holomorphic symmetry from a centrally extended affine graded Lie algebra, yielding a raviolo vertex algebra for its local operators after radial quantization.
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Different types of torsion and their effect on the dynamics of fields
In VEP formalism the off-shell spin connection admits a one-parameter family of conformal transformations interpolating between Nieh-Yan and conformally invariant torsion; dynamically generated torsion lacks well-defined conformal properties and affects fermions and conformal scalars.
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The butterflies' effects
Spectral butterflies form in parameter-dependent Schrödinger operators on weighted Delone sets and reflect fractal self-similar structures, with the framework extending across dimensions and to non-Abelian groups.
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Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.