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All Journal UPEJ : Unnes Physics Education Journal Physics Communication
Listiyanto
Universitas Negeri Semarang
Education Physics

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Quantum Spectral Algorithms for Khovanov Cohomology via Laplacian Formalism and Frobenius Cobordisms Listiyanto; Celfien Septian Widya Pratama; Siti Wahyuni
Physics Communication Vol. 9 No. 2 (2025): August 2025
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/pc.v9i2.30159

Abstract

We present a comprehensive quantum algorithm for computing Khovanov cohomology, a categorification of the Jones polynomial, together with a clear narrative that connects its motivation, construction, and implementation. By simulating Laplacian operators derived from the Khovanov cochain complex, we estimate cohomological dimensions using quantum phase estimation, thermal sampling, and Quantum Singular Value Transformation (QSVT). The framework explicitly exploits the Frobenius algebra structure and cobordism maps, showing how these topological tools translate naturally into unitary quantum operations. Worked examples for the trefoil knot and Hopf link illustrate each step, from encoding the cube of resolutions to constructing differentials and Laplacians. This narrative approach not only refines and operationalizes the Laplacian method introduced by previous works but also provides a practical roadmap for extending categorified invariants into the realm of quantum algorithms suitable for near-term devices.
Physical Analysis of a Fishing Rod and Development of an Elasticity E-Module as a Supplement for Mechanics Learning Edi Saputra; Wahyu Hardyanto; Listiyanto
Unnes Physics Education Journal Vol. 15 No. 2 (2026)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/upej.v15i2.31899

Abstract

Mechanics instruction at the university level, particularly for students in the Physics and Physics Education study programs, is often hindered by the abstract nature of the content, complex formulas, and unengaging modes of delivery. A preliminary study showed that 83.3% of students found mechanics difficult to understand, partly because of the limited variety of learning media. One interesting topic in mechanics is the dynamics of elastic bodies, including fishing rods. These dynamics involve numerous physical concepts and complex mathematical equations, so an enrichment module is needed to facilitate students’ understanding. This study aimed to develop an elasticity e-module as a supplement for mechanics learning, focusing on the analysis of the curvature of a fishing rod (an elastic rod) and a comparison of the acceleration multiplication factor between elastic and non-elastic rods subjected to a force impulse. This study used a Research and Development (R&D) approach with the 4D development model (Define, Design, Develop, Disseminate). The physical analysis was conducted theoretically and experimentally on tapered elastic rods. In the curvature experiment, the load was varied, whereas in the acceleration experiment, the acceleration response was observed using the accelerometer sensor of a smartphone. The developed e-module was validated by subject-matter and media experts and tested with students as users. The validation results showed that the e-module was categorized as “very feasible” in both content and media aspects. Meanwhile, students’ responses fell into the “very good” category for material presentation (90.53%), language (91.58%), visual display (88.84%), usefulness (91.89%), technical aspects (91.75%), and evaluation (90.53%). Therefore, the elasticity e-module is feasible for use as a supplement in Mechanics courses. 
Co-Authors Celfien Septian Widya Pratama Edi Saputra Wahyu Hardyanto