Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits

Understand

We introduce an exact mapping of Clifford (stabilizer) random tensor networks (RTNs) and monitored quantum circuits, onto a statistical mechanics model.

• With Haar unitaries, the fundamental degrees of freedom ('spins') are permutations because all operators commuting with the action of the unitaries on a tensor product arise from permutations of the tensor factors ('Schur-Weyl duality').
• For unitaries restricted to the smaller Clifford group, the set of commuting operators, the 'commutant', forming the new 'spin' degrees of freedom, will be larger.
• We use the recent full characterization of this commutant by Gross et al., Comm.