Completeness of qufinite ZXW calculus, a graphical language for mixed-dimensional quantum computing
2023
academicJournal
Zugriff:
Finite-dimensional quantum theory serves as the theoretical foundation for quantum information and computation based on 2-dimensional qubits, d-dimensional qudits, and their interactions. The qufinite ZX calculus has been used as a framework for mixed-dimensional quantum computing; however, it lacked the crucial property of completeness, which ensures that the calculus incorporates a set of rules rich enough to prove any equation. The ZXW calculus is a complete language for qudit quantum computing with applications previously unreachable solely with the ZX or ZW calculus. In this paper, we introduce the qufinite ZXW calculus, a unification of all qudit ZXW calculi in a single framework for mixed-dimensional quantum computing. We provide a set of rewrite rules and a unique normal form that make the calculus complete for finite-dimensional quantum theory. This work paves the way for the optimization of mixed dimensional circuits and tensor networks appearing in different areas of quantum computing including quantum chemistry, compilation, and quantum many-body systems. ; Comment: 36 pages
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Completeness of qufinite ZXW calculus, a graphical language for mixed-dimensional quantum computing
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Autor/in / Beteiligte Person: | Wang, Quanlong ; Poór, Boldizsár |
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Veröffentlichung: | 2023 |
Medientyp: | academicJournal |
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