2019/04/24 by Cole Comfort, Comfort, Cole · 1 citation
Computer Science · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Physical sciences #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1904.10614
openalex publication_date 2019/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The real stabilizer fragment of quantum mechanics was shown to have a complete axiomatization in terms of the angle-free fragment of the ZX-calculus. This fragment of the ZX-calculus---although abstractly elegant---is stated in terms of identities, such as spider fusion which generally do not have interpretations as circuit transformations. We complete the category CNOT generated by the controlled not gate and the computational ancillary bits, presented by circuit relations, to the real stabilizer fragment of quantum mechanics. This is performed first, by adding the Hadamard gate and the scalar sqrt 2 as generators. We then construct translations to and from the angle-free fragment of the ZX-calculus, showing that they are inverses. We then discuss how this could potentially lead to a complete axiomatization, in terms of circuit relations, for the approximately universal fragment of quantum mechanics generated by the Toffoli gate, Hadamard gate and computational ancillary bits.