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Paper 1
Untangling Surface Codes: Bridging Braids and Lattice Surgery
Alexandru Paler
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2511.22290
- arXiv
- 2511.22290
We present a systematic method for translating fault-tolerant quantum circuits between their braiding and lattice surgery (LS) representations within the surface code. Our approach employs the ZX calculus to establish an equivalence between these two paradigms, enabling verified, bidirectional conversion of arbitrary surface-code-level circuits. We show that both braiding and LS operations can be uniformly expressed as compositions of multibody measurements and demonstrate that the Raussendorf compression rule encompasses all known braid and bridge optimizations. We also introduce a novel CNOT circuit with LS. Our framework provides a foundation for the automated verification, compilation, and benchmarking of large-scale surface code computations, advancing toward a unified formal language for topological quantum computation.
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Quantum Mechanics reconstruction from invariance of the laws of nature under tensor composition
Florin Moldoveanu
- Year
- 2014
- Journal
- arXiv preprint
- DOI
- arXiv:1407.7610
- arXiv
- 1407.7610
Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are relational, and (4) positivity (the ability to define a physical state). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.
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