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Quantum Spectral Algorithms for Khovanov Cohomology via Laplacian Formalism and Frobenius Cobordisms

Physics Communication · Vol. 9 No. 2 (2025) · hlm. 114–127

DOI
10.15294/pc.v9i2.30159
ISSN
2528-598X, 2528-5971
Terbit
2025-08-27
Penerbit
Universitas Negeri Semarang
Bahasa
eng

Abstrak

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.

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  • State University of Semarang
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Rekan penulisOrganisasiArtikel bersama
Wahyu HardyantoAfiliasi tidak diketahui3
Ellianawati EllianawatiState University of Semarang3
Isa AkhlisState University of Semarang2
Teguh DarsonoAfiliasi tidak diketahui2
Sulhadi SulhadiAfiliasi tidak diketahui2
Sugiyanto SugiyantoState University of Semarang1
Putut MarwotoState University of Semarang1
Vio Gustian Nur AlamsyahState University of Semarang1
Dicko Alryadi SamudraState University of Semarang1
Arief BudhimanAfiliasi tidak diketahui1
Pratiwi DwijanantiAfiliasi tidak diketahui1
Gilang RamadhanAfiliasi tidak diketahui1
Unes Satuz ZahroAfiliasi tidak diketahui1
Ngurah Made Dharma PutraAfiliasi tidak diketahui1
Nurul ShofiaAfiliasi tidak diketahui1
Destin SuslianaAfiliasi tidak diketahui1
Rizki Firda AmaliaAfiliasi tidak diketahui1
Shiva IrfanaAfiliasi tidak diketahui1
Upik NurbaitiAfiliasi tidak diketahui1
Marosyana Ayu FebrianiAfiliasi tidak diketahui1
Muhammad Fiqhi MahfuddinAfiliasi tidak diketahui1
Teuku FauziAfiliasi tidak diketahui1

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Sumber metadata: OAI-PMH (metadata jurnal) https://journal.unnes.ac.id/journals/pc/oai, pertama di-harvest 6 Nov 2026, terakhir terlihat 8 Nov 2026.
Metadata asli (oai_dc) 
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	<dc:title xml:lang="en">Quantum Spectral Algorithms for Khovanov Cohomology via Laplacian Formalism and Frobenius Cobordisms</dc:title>
	<dc:creator xml:lang="en">Listiyanto</dc:creator>
	<dc:creator xml:lang="en">Celfien Septian Widya Pratama</dc:creator>
	<dc:creator xml:lang="en">Siti Wahyuni</dc:creator>
	<dc:subject xml:lang="en">Knots and Links</dc:subject>
	<dc:subject xml:lang="en">Khovanov Cohomology</dc:subject>
	<dc:subject xml:lang="en">Frobenius Algebra</dc:subject>
	<dc:subject xml:lang="en">Quantum Algorithm</dc:subject>
	<dc:subject xml:lang="en">QSVT</dc:subject>
	<dc:description xml:lang="en">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.</dc:description>
	<dc:publisher xml:lang="en">Universitas Negeri Semarang</dc:publisher>
	<dc:date>2025-08-27</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unnes.ac.id/journals/pc/article/view/30159</dc:identifier>
	<dc:identifier>10.15294/pc.v9i2.30159</dc:identifier>
	<dc:source xml:lang="en">Physics Communication; Vol. 9 No. 2 (2025): August 2025; 114-127</dc:source>
	<dc:source>2528-598X</dc:source>
	<dc:source>2528-5971</dc:source>
	<dc:source>10.15294/pc.v9i2</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://journal.unnes.ac.id/journals/pc/article/view/30159/5958</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2025 Physics Communication</dc:rights>
</oai_dc:dc>