Groups of diagonal gates in the Clifford hierarchy

DOI10.1134/s0040577924120018MaRDI QIDQ6663783

Shunlong Luo, Lingxuan Feng

Publication date: 15 January 2025

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Clifford groupstabilizer formalismdiagonal gatesClifford hierarchy\(T\)-gate

Mathematics Subject Classification ID

Clifford algebras, spinors (15A66) Quantum gates (81P65) Computational stability and error-correcting codes for quantum computation and communication processing (81P73) Applications of Clifford algebras to physics, etc. (15A67)

Cites Work

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• Canonical forms for single-qutrit Clifford+\(T\) operators
• Optimal diagonal qutrit gates for creating Wigner negativity
• A normal form for single-qudit Clifford+\(T\) operators
• Order 3 symmetry in the Clifford hierarchy
• Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets
• Universal quantum computation with ideal Clifford gates and noisy ancillas
• UNITARY OPERATOR BASES
• The resource theory of stabilizer quantum computation
• Symmetric informationally complete–positive operator valued measures and the extended Clifford group
• SIC POVMs and Clifford groups in prime dimensions
• Hecke operators and distributing points on the sphere I
• Efficient discrete approximations of quantum gates
• Floating point representations in quantum circuit synthesis
• T-Count Optimization and Reed–Muller Codes
• Hierarchies of resources for measurement-based quantum computation
• Optimality of T-gate for generating magic resource

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