Haonan Zhang

collaborators

7 papers

math.AP2026

Tightness of and counterexamples to several quantum estimates

Haonan Zhang, Joseph Slote, Alexander Volberg

We prove here several tightness results for such quantum inequalities as the comparison of operator norm and product norm of $d$ -local hamiltonians, Bohnenblust--Hille inequality f…

cs.CC2026

The Boolean surface area of polynomial threshold functions

Fan Chang, Joseph Slote, Alexander Volberg +1

Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work o…

math.NT2026

Fourier growth of degree $2$ polynomials

Lars Becker, Joseph Slote, Alexander Volberg +1

We prove bounds for the absolute sum of all level- $k$ Fourier coefficients for $(- 1)^{p (x)}$ , where polynomial $p : F_{2}^{n} \to F_{2}$ is of degree $1$ or degree $2$ .

quant-ph2026

Approximating the operator norm of local Hamiltonians via few quantum states

Lars Becker, Joseph Slote, Alexander Volberg +1

Consider a Hermitian operator $A$ acting on a complex Hilbert space of dimension $2^{n}$ . We show that when $A$ has small degree in the Pauli expansion, or in other words, $A$ is a l…

math.CA2025

A dimension-free discrete Remez-type inequality on the polytorus

Joseph Slote, Alexander Volberg, Haonan Zhang

Consider $f : I^c ◯_{K}^{n} \to C$ a function from the $n$ -fold product of multiplicative cyclic groups of order $K$ . Any such $f$ may be extended via its Fourier expansion to an a…

math.FA2024

Bohnenblust--Hille inequality for cyclic groups