All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks

Abstract Variational algorithms require architectures that naturally constrain the optimization space to run efficiently. Geometric quantum machine learning achieves this goal by encoding group structure into parameterized quantum circuits to include the symmetries of a problem as an inductive bias. However, constructing such circuits is challenging as a concrete guiding principle has yet to emerge. In this paper, we propose the use of spin networks , a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ansätze—circuits possessing spin-rotation symmetry. By changing to the basis that block diagonalizes the SU(2) group action, these networks…

• UD
  U.S. Department of Energy

  Awards: -AC02-05CH11231, 05CH11231, AC02-05CH11231, DE-AC02, DE-AC02-05CH11231, DE-AC02-
• NR
  National Research Foundation of Korea

  Awards: RS-2025-18362970, RS-2025-02316431, RS-2025-16066935
• OO
  Office of Science

  Awards: AC02-05CH11231, -AC02-05CH11231, DE-AC02