AYZL's Shelves

Welcome to AYZL's library

Works

The Strohmer–Beaver conjecture at odd integer density — Revised manuscript · 13 September 2026 · 19 pages. Hexagonal optimality for Gaussian Gabor frames at densities 3, 5, 7, …, with sharp lower and upper frame bounds and exact equality cases.
On Localization of Infinite Matrices — Research manuscript · supervised by Dr. Tim Wertz. Off-diagonal decay through inversion, functional calculus, and stable factorizations; centered finite windows give constructions for bi-infinite matrices.
Parameter Continuity Bounds for Rényi Entropies — Research manuscript. Escort variance controls changes in Rényi order, with a sharp local classical constant at order one and fixed-marginal sandwiched conditional quantum bounds independent of the conditioning dimension on the stated order intervals.
O(n²) LCU sampling overhead bound — Research note · 10 October 2026 · 6 pages. Fourier-symbol design bounds the relative loss in success probability by O(n²) when Haar-random collective rotations replace a permutation-invariant unitary and acceptance is confined to a fixed Hamming-weight sector.
Optimal query complexity for fractional quantum evolution — Preprint · with Adam Wesołowski, Jayne Thompson, Mile Gu, and Lirandë Pira · 1 October 2026 · arXiv:2610.01940. Matching worst-case query bounds for coherent fractional powers of unknown unitaries, with controlled access to the unitary and its inverse, a promised branch gap, and exponents bounded away from 0 and 1.
The Cost of Removing Tunability in Quantum Data Re-Uploading — Preprint · with Lirandë Pira · arXiv:2606.25598. Approximation resources and structural obstructions in quantum circuits with fixed data encodings.
Harmonic Geometry of Re-uploading Quantum Models — Research notes. Localized Fourier correlations, exact harmonic-energy laws, and finite-feature approximation for specified circuit ensembles. The latest theorem concerns a fixed two-qubit model; broader learning questions remain open.
A formal proof for odd-integer Gaussian Gabor frames — Lean 4 proof archive · concise-paper snapshot. Formal source, verification records, and a reproduction guide, with the earlier 14-page manuscript.
Quantum Proof Factory — Research software · AI4Math. Independent proof attempts, synthesis, adversarial review, and persistent research records. The workflow supports human review; it does not automatically certify theorems or execute Lean.
Pinching — Expository note · quantum information. How block projections remove coherence between sectors, and the operator inequalities behind the pinching map.
行云 — poem · 2026
三个梦和一首巴赫烟斗小曲 — three dreams and a poem · 2026
人类时间 — essay · 2026
天空中的鱼 — essay · 2026

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Anthony Yuezhang Liu — a personal index of mathematics and literature