This paper establishes log-concavity of the ground state for a large family of discrete, 1-dimensional Schrödinger operators, extending the analysis of the Hamming weight with a spike problem to more…

This paper presents two quantum algorithms for solving linear systems with normalized solution $|x angle$ to accuracy $ε$, independent of the condition number $κ$.

The paper introduces an operator calculus for population-based optimization methods, establishing a modular Lyapunov principle for their convergence analysis.

The authors introduce a quantum empirical operator and use it to prove a universal achievability result for composite quantum hypothesis testing.

An algorithm is given to estimate quantum state eigenvalues with fewer copies using a new tomography guarantee.

The paper introduces the quantum instrument monad, a noncommutative generalization of the state monad for modeling computational effects in quantum systems.

This paper introduces Twisted Schrödinger Bridge Matching (TSBM), a new diffusion-based method for handling continuous- and discrete-time potentials in the Schrödinger bridge problem with improved per…

The paper introduces a Jacobian-based spectral audit to evaluate neural operators, demonstrating that standard prediction error metrics fail to capture crucial local dynamical structures and operator…

This paper analyzes the statistical and computational limits of learning bounded linear operators between Sobolev spaces from noisy data, and constructs a finite-resolution blockwise least-squares est…

The paper constructs a family of simple quantum states (pseudoentangled states) generated by constant-depth circuits that exhibit non-trivial entanglement structure, demonstrating that entanglement st…

This paper develops a formal semantics and verification methods for a core continuous-variable quantum programming language, using closed positive quadratic forms as semantic predicates.

The paper reformulates nonreversible perturbations of Fokker--Planck dynamics as gauge fields, providing a unified operator viewpoint to analyze relaxation processes and develop methods for learning o…

This paper shows that shallow circuits cannot prepare near-optimal states for random quantum $p$-spin glasses, and proves depth lower bounds for such preparations.