arXiv subjects

Fred Sun

Publications and source records attributed to Fred Sun.

3 recordsLinked to original sources

arXiv2026

A Fully Quantum Algorithm for Image Edge Detection

This work introduces a novel quantum algorithm for gradient-based edge detection that operates entirely within the quantum circuit model. Grayscale images are encoded using the Novel Enhanced Quantum Representation (NEQR), allowing exact arithmetic on pixel intensities. Directional gradients are computed by generating superpositions of neighboring pixels via cyclic shift operations and performing subtraction with an exact quantum arithmetic circuit. To refine accuracy, we introduce a direction-aware shifting mechanism that aligns edges with the darker side of intensity transitions. Our novel Quantum Partitioning Algorithm enables efficient in-place thresholding of edge candidates. This work exhibits polynomial-time improvements and optimizes the ancilla count compared to previous NEQR-based quantum edge detection algorithms. These results demonstrate a resource-efficient and fully quantum approach to edge detection, highlighting a practical quantum advantage in image processing.

quant-ph↗

arXiv2026

A Polylogarithmic-Depth Quantum Multiplier

We present a quantum algorithm for multiplying two $n$-bit integers with overall circuit depth and $T$-depth both bounded by $O(\log^{2} n)$, while using $O(n^{2})$ gates and ancillary qubits. Our construction generates partial products via indicator-controlled copying and adds them using a binary adder tree, enabling parallel accumulation with logarithmic depth overhead per level. To the best of our knowledge, our design has the lowest $T$-depth among all multiplication algorithms using the Clifford + $T$ model. By optimizing both circuit depth and $T$-depth, our construction advances the practical feasibility of large-scale fault-tolerant quantum algorithms.

quant-ph↗

arXiv2026

Electronic Structure of Multilayer Graphene with Arbitrary Stackings

Stacking geometry in multilayer graphene (MLG) provides an interesting degree of freedom to engineer its electronic structure near the Fermi level, wherein the linear bands in single layer graphene could retain or evolve into parabolic or flat bands. Using a tight-binding model, we carried out a detailed analytical analysis of the electronic band structures for arbitrarily stacked MLGs. We show that their low energy band dispersions near the Fermi level may be deduced from its substacks in isolation. The analytical solutions of the momenta with zero eigenvalue for an AA stacking allows us to generalize the results of the zero energy momenta for arbitrarily stacked MLGs. Moreover, we find that an interplay of parallel and rhombohedral stackings allows for flat band engineering and enhancement in arbitrarily stacked MLGs. The existence of flat bands in MLGs might offer another interesting platform for exploring the superconductivity in graphene systems beyond the twisted bilayer graphene.

cond-mat.mes-hall↗