Effect of nilpotent Jordan sectors on Lee–Yang zeros in integrable quantum circuits

Determine how nilpotent sectors and polynomial depth factors associated with Jordan blocks modify the trajectories and accumulation sets of Lee–Yang zeros for the complexified gate parameters of quantum circuits assembled from the integrable R-matrices.

Background

The paper proposes assembling the integrable R-matrices into quantum-circuit architectures and studying their conserved quantities through compatible inhomogeneous transfer matrices. Because the generic operators are non-unitary, such architectures require a distinction between stochastic updates and quantum operations.

Within this proposed circuit setting, the paper identifies an unresolved question concerning Lee–Yang zeros. Specifically, it asks how nilpotent sectors and the polynomial-in-depth contributions generated by Jordan blocks affect the motion and limiting accumulation sets of zeros in complexified gate-parameter space.