A framework for semi-universality: Semi-universality of 3-qudit SU(d)-invariant gates

Understand

Quantum circuits with symmetry-respecting gates have attracted broad interest in quantum information science.

• While recent work has developed a theory for circuits with Abelian symmetries, revealing important distinctions between Abelian and non-Abelian cases, a comprehensive framework for non-Abelian symmetries has been lacking.
• In this work, we develop novel techniques and a powerful framework that is particularly useful for understanding circuits with non-Abelian symmetries.
• Using this framework we settle an open question on quantum circuits with SU(d) symmetry.