Graphical Algebraic Geometry creates universal diagrammatic languages for commutative algebras and affine varieties that also characterize the qudit ZH calculus for quantum computation.
Phase-free ZX diagrams are CSS codes (... or how to graphically grok the surface code)
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
fields
quant-ph 5representative citing papers
The qufinite ZXW calculus is complete for the category FHilb of finite-dimensional Hilbert spaces, as any diagram rewrites to a unique normal form.
New search algorithms over stabilizer tableaus and modular assembly techniques yield encoders with up to 43% fewer two-qubit gates and 70% lower depth than prior constructions on tested stabilizer codes including qLDPC and holographic families.
String diagrams formalize constructor theory with locality-composition conflicts, enable wave-based Boolean logic design and optimization, and map Urdu text circuits equivalently to English ones up to gate translation in DisCoCirc.
Projectivizing quantum kinematics produces meromorphic functions characterizing coherent circuits for quantum error correction and magic state distillation.
citing papers explorer
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Graphical Algebraic Geometry: From Ideals and Varieties to Quantum Calculi
Graphical Algebraic Geometry creates universal diagrammatic languages for commutative algebras and affine varieties that also characterize the qudit ZH calculus for quantum computation.
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Completeness of qufinite ZXW calculus, a graphical language for finite-dimensional quantum theory
The qufinite ZXW calculus is complete for the category FHilb of finite-dimensional Hilbert spaces, as any diagram rewrites to a unique normal form.
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Synthesis and Optimization of Encoding Circuits for Fault-Tolerant Quantum Computation
New search algorithms over stabilizer tableaus and modular assembly techniques yield encoders with up to 43% fewer two-qubit gates and 70% lower depth than prior constructions on tested stabilizer codes including qLDPC and holographic families.
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String Diagrams for Quantum Foundations, Computing and Natural Language Processing
String diagrams formalize constructor theory with locality-composition conflicts, enable wave-based Boolean logic design and optimization, and map Urdu text circuits equivalently to English ones up to gate translation in DisCoCirc.
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Meromorphic Quantum Computing
Projectivizing quantum kinematics produces meromorphic functions characterizing coherent circuits for quantum error correction and magic state distillation.