Hong-Huai Fang

collaborators

7 papers

quant-ph2026

Einstein Metrics and Quantum Control on Symmetric Tensor Product Quotients

Honghuai Fang

Let $M_{n} = (PU (2)^{n} ⋊ S_{n}) \ PU (2^{n})$ be the space of projective $n$ -qubit unitaries modulo local unitaries and permutations of the qubits. We prove tha…

math.QA2026

Quantum Color Newton Rings

Honghuai Fang

We study integral Newton rings attached to symmetric quantum colors. We show that their boundary values at a deleted node are exactly the elements of Habiro's cyclotomic completion…

math.QA2026

Rectangular Cyclotomic Expansions of Colored HOMFLY-PT Polynomials

Honghuai Fang, Tian Zhou

We prove the rectangular cyclotomic expansion conjecture of Kameyama, Nawata, Tao, and Zhang for reduced colored HOMFLY-PT polynomials of arbitrary zero-framed knots. We also prove…

math.PR2026

Sharp Typical Distance and Exponential Small-Ball Bounds in One-Step-Cliff Nielsen Geometry

Honghuai Fang

Let $D = 2^{n}$ and equip $PU (D)$ with the one-step-cliff Nielsen metric, with quadratic metric coefficients one in Pauli directions of weights one and two and $D^{2}$ in…

quant-ph2026

Variable-Cliff Nielsen Geometry and an Exponent -4/3 Lower Bound for the Infinite-Cliff Diameter

Honghuai Fang

Let $D = 2^{n}$ and $M = 3 n + 9 (2 n)$ . We study the right-invariant one-step-cliff metric $d_{Q}$ on $PU (D)$ , with unit penalty on Pauli weights one and two and penalty $Q…

math.NT2026

Bloch-regulator Principal Parts of Cyclotomic Iwasawa Pseudomeasures

Honghuai Fang, Zekun Chen

Let $p$ be an odd prime and let $K / Q_{p}$ be a finite unramified extension. From a finite presentation by roots of unity of order prime to $p$ , we construct a localized Iwas…

math.GT2026

Cyclotomic Newton Expansions and a Rank-Uniform Integer-Valued Newton Completion

Honghuai Fang, Tian Zhou

Let $J_{r}^{S U (n)} (K; q)$ denote the reduced $S U (n)$ quantum invariant of a zero-framed knot $K$ , colored by the $r$ th symmetric power of the defining representation and normalized to…