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quant-ph2026
Spectral gaps and slow modes of Pauli rotations and random quantum circuits
Ziyuan Dong, Xiang Fan
We determine which representation sectors control the slowest convergence of random Pauli rotations and several local random quantum circuits. For , the continuous Pauli wal…
quant-ph2025
Revisiting finite Abelian hidden subgroup problem and its distributed exact quantum algorithm
Ziyuan Dong, Xiang Fan, Tengxun Zhong +1
We revisit the finite Abelian hidden subgroup problem (AHSP) from a mathematical perspective and make the following contributions. First, by employing amplitude amplification, we p…
quant-ph2025
Probabilistic Bounds on the Number of Elements to Generate Finite Nilpotent Groups and Their Applications
Ziyuan Dong, Xiang Fan, Tengxun Zhong +1
This work establishes a new probabilistic bound on the number of elements to generate finite nilpotent groups. Let denote the probability that random elements generate…