Author

Zi-Yi Yang

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Preprint Sep 2026

Quantum Query Complexity of Finding a Tarski Fixed Point on a High-Dimensional Grid

The Knaster-Tarski fixed-point theorem states that every monotone function over a complete lattice has a fixed point. Beyond its fundamental role in order theory, the theorem and its algorithmic variants have found broad applications in areas such as economics, game theory, and programming languages. While the query co...

Tong-Yang Li, Wei-Ran Ma, Zi-Yi Yang et al. · 3 citations · ⚡1

Preprint Oct 2026

Bootstrapping Classical and Quantum Query Lower Bounds for Finding Tarski Fixed Points

The Tarski fixed-point problem asks for a fixed point of a monotone map on a $k$-dimensional grid lattice of width $n$ and has applications in game theory, economics, and verification. Substantial gaps remain between the known upper and lower bounds on its quantum query complexity. We prove two hardness bootstrapping t...

Tong-Yang Li, Wei-Ran Ma, Zi-Yi Yang et al. · 1 citation

Jul 2026

Quantum Algorithm for Elliptic Curve Discrete Logarithms with Space-Efficient Point Addition

A new space-efficient reversible modular inversion circuit is presented, which addresses the dominant space bottleneck in affine-coordinate point addition and provides a space-efficient controlled affine point-addition circuit and a complete implementation of Shor's algorithm for ECDLP.

Han Luo, Zi-Yi Yang, Jingquan Luo et al. · arXiv.org · 1 citation