Tuning the universality class of a quantum process by Trotterization

The quantum contact process is a non-equilibrium model featuring a competition between coherent infection and dissipative recovery. While theoretical studies of the continuous-time version suggest a novel quantum universality class, experimental realizations—often implemented as discrete quantum circuits—have pointed toward the classical directed percolation (DP) class. This paper investigates whether these conflicting results are artifacts of how the continuous process is discretized (Trotterized) for simulation or experimental implementation.

The authors introduce a systematic framework to continuously deform the discretization of the quantum contact process. By varying the Trotter angle—the parameter controlling the step size of the coherent and dissipative operations—they interpolate between the continuous-time limit and the discrete-time experimental implementations. They use matrix product state simulations to monitor the long-time decay of the infection density at the critical point, extracting the critical exponent to identify the universality class. To understand the underlying physics, they analyze the ratio of dark states (zero-energy eigenstates) to bright states, which serve as a proxy for quantum interference effects.

The study reveals that the universality class is not fixed but depends on the discretization parameters. For small Trotter angles, the system exhibits the novel quantum universality class previously predicted for the continuous-time model. As the Trotter angle increases, the system transitions through an intermediate regime consistent with anomalous directed percolation before reaching the classical directed percolation class at larger angles. The authors provide evidence that this shift is driven by the emergence of dark states, which are formed by destructive interference between infection pathways. This confirms that the observed differences in universality are a direct consequence of quantum-mechanical interference effects that are suppressed or modified by the specific discretization scheme used.