An Error Suppressing Encoding for Positional Disorder in Rydberg Atom Analog Quantum Simulation

Rydberg atom platforms are promising for analog quantum simulation because of their inherent long-range interactions and extended coherence times. However, experimental results often fall short of theoretical predictions, primarily due to the positional disorder of atoms, which limits precise control of interaction strengths. Given the challenges in physically reducing positional disorders, we propose an error-suppressing encoding to mitigate their impact. In this paper, we introduce an experiment-ready encoding scheme for Rydberg atom platforms aimed at simulating a family of XXZ Heisenberg models. Our scheme constructs a "super atom" encoding, where each logical atom is represented by m physical atoms within the Rydberg blockade regime. Intuitively, this method effectively averages out the positional disorders of individual atoms. We conduct theoretical analysis and numerical simulation, observing a reduction of error by a factor of $1/\sqrt{m}$, therefore an increase in effective simulation time by $\sqrt{m}$ within the same error margin. Our results demonstrate a pathway to practical encoding strategies for suppressing specific physical errors in analog quantum simulation.