Using the bitstring probabilities of ground states of bipartitioned ladders of Rydberg atoms, we calculate the mutual information, which is a lower bound on the corresponding bipartite von Neumann quantum entanglement entropy
SAvN. We show that in many cases these lower bounds can be improved by removing the bitstrings with a probability lower than some value
pmin and renormalizing the remaining probabilities (filtering). We propose a heuristic based on the change of the conditional entropy under filtering that very effectively improves the estimate of
SAvN. We consider various sizes, lattice spacings and bipartitions. Our numerical investigation suggest that the filtered mutual information obtained with samples having just a few thousand bitstrings can provide reasonably close estimates of
SAvN. We briefly discuss practical implementations with QuEra's Aquila device.
We discuss the possibility of estimating experimentally the von Neumann entanglement entropy S A v N of a symmetric bipartite quantum system A B by using the basic measurement counts (bitstrings) for a single copy of a prepared state. Using exact diagonalization and analog simulations performed with the publicly available QuEra facilities for chains and ladders of Rydberg atoms, we calculate the Shannon entropy S A B X associated with the bitstrings of adiabatically prepared ground states and the reduced entropies S A X and S B X obtained from the marginal probabilities in A and B . We then calculate the classical mutual information I A B X = S A X + S B X − S A B X , which is a lower bound on S A v N . We show that for a broad range of lattice spacing and detuning, I A B X is typically 20% below S A v N in regions where S A v N is large and a less close bound in regions where S A v N is low. We argue that this use of the easily available bitstrings provides a robust and efficient way to explore empirically the phase diagram of qubit-based quantum simulators and identify critical regions.
We study bitstring measurements from the publicly available Aquila Rydberg-atom platform using a two-leg ladder that encodes a truncated lattice gauge model as a practical benchmark that can be directly implemented and simulated on current hardware. Our goal is diagnostic: we analyze how errors propagate into bitstring probability distributions and downstream information measures, focusing on ladders with 6, 8, and 10 rungs and
O(103) shots. We introduce cumulative probability distributions as a compact way to compare Aquila data with high-accuracy density matrix renormalization group (DMRG) and exact references, and we use optimally filtered mutual information primarily as a robust device-data diagnostic rather than a direct entanglement estimator. By isolating finite sampling, sorting fidelity, adiabatic ramp-up, Rabi-frequency ramp-down, and readout errors, we find that readout mitigation performs well in controlled DMRG tests. Applying the same procedure on hardware shows accuracy limitations for the leading probabilities estimation, indicating that readout errors are not dominant and that residual error is instead driven by imperfect state preparation.