Quantum Information & Computation
Volume 26
RESEARCH ARTICLE Open access

Clifford Circuits on Qudits of Mixed Dimension

Milo Moses, Jacek Horecki, Konrad Deka, Jan Tułowiecki

Author affiliations
  • Milo Moses1
  • Jacek Horecki2
  • Konrad Deka2
  • Jan Tułowiecki3
  1. Department of Mathematics, UC Santa Barbara, 552 University Rd, Isla Vista, CA, USA; BEITInc., Mogilska 43, Kraków, Poland
  2. BEITInc., Mogilska 43, Kraków, Poland; Institute of Mathematics, Jagiellonian University, ul. Łojasiewicza 6, Kraków, Poland
  3. BEITInc., Mogilska 43, Kraków, Poland; Department of Theoretical Computer Science, Jagiellonian University, ul. Łojasiewicza 6, Kraków, Poland; Doctoral School of Exact and Natural Sciences, Jagiellonian University, ul. Prof. Łojasiewicza 11, I pietro, pok. H-1-02, Kraków, Poland

pp. 180-191 · 10.2478/qic-2026-0009

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Abstract

Associated to every finite abelian group G, there is a generalization of qubit Clifford group associated to G. We demonstrate that every G -Clifford gate can be decomposed into some distinguished elementary types: Fourier transforms, quadratic phase gates, and automorphism gates. Combined with earlier results on classical simulation of normalizer circuits, this implies a generalized Gottesman-Knill-type result. We additionally provide circuits for a universal quantum computing scheme based on local two-qudit G -Clifford gates and magic states.
Open accessCC BY-NC-ND 4.0

Keywords

  • Gottesman-Knill
  • Clifford circuits
  • qudits

Suggested citation

Milo Moses, Jacek Horecki, Konrad Deka, Jan Tułowiecki (2026). Clifford Circuits on Qudits of Mixed Dimension. Quantum Information & Computation, 26(1), 180-191. https://doi.org/10.2478/qic-2026-0009

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