Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2411.07092

Improved entanglement entropy estimates from filtered bitstring probabilities

Kaufman, Avi, Corona, James, Ozzello, Zane, Senseman, Blake, Asaduzzaman, Muhammad, Yannick Meurice

Published Nov 11, 2024• 0 citations
arXivHTMLPDF

Abstract

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 $S^{vN}_A$. We show that in many cases these lower bounds can be improved by removing the bitstrings with a probability lower than some value $p_{min}$ 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 $S^{vN}_A$. 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 $S^{vN}_A$. We briefly discuss practical implementations with QuEra's Aquila device.

DOI
10.48550/arxiv.2411.07092

Related papers

Lower bounds on entanglement entropy without twin copy

Yannick Meurice

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.

arXiv:2404.09935•Physical Review Research•Apr 24, 2025•6 citations

Predicting the von Neumann Entanglement Entropy Using a Graph Neural Network

Anas Saleh

Calculating the von Neumann entanglement entropy from experimental data is challenging due to its dependence on the complete wavefunction, forcing reliance on approximations like classical mutual information (MI). We propose a machine learning approach using a graph neural network for predicting the von Neumann entropy from experimentally accessible bitstrings. We tested this approach on a Rydberg ladder system and achieved a mean absolute error of $3.7 \times 10^{-3}$ when testing it inside of its training range on a dataset with entropy ranging from 0 to 1.9, we also evaluated the mean absolute percentage error on the data that have its entropy larger than 0.01 of the maximum entropy(so we can avoid the areas of our phase space with near zero entropy) and got a relative error of 1.72%, outperforming MI-based bounds. When tested beyond this range, the model still delivers reasonable results. Furthermore, we demonstrate that fine tuning the model with a small dataset significantly improves its performance on data outside its original training range.

arXiv:2503.23635•Mar 31, 2025•0 citations

Predicting the von Neumann entanglement entropy using a graph neural network

Anas Saleh

Abstract Calculating the von Neumann entanglement entropy from experimental data is challenging due to its dependence on the complete wavefunction, forcing reliance on approximations such as classical mutual information (MI). We propose a machine learning approach using a graph neural network to predict the von Neumann entropy directly from experimentally accessible bitstrings. We test this approach on a Rydberg ladder system and achieve a mean absolute error of 3.6 × 10 − 3 when evaluating within the training range on a dataset with entropy values ranging from 0 to 1.9. The model achieves a mean absolute percentage error of 1.44% and outperforms MI-based bounds. When tested beyond the training range, the model maintains reasonable accuracy. Furthermore, we demonstrate that fine-tuning the model with small datasets significantly improves performance on data outside the original training range.

Machine Learning Science and Technology•Aug 5, 2025•0 citations

Multipartite entanglement from ditstrings for 1+1D systems

Zane Ozzello, Yannick Meurice

We show that multipartite entanglement can be used as an efficient way of identifying the critical points of 1+1D systems. We demonstrate this with the quantum Ising model, lattice $λϕ^4$ approximated with qutrits, and arrays of Rydberg atoms. To do so we make use of multipartite compositions of entanglement quantities for different parts combined to form the strong subadditivity, weak monotonicity, and a convex combination of these with conformal properties. These quantities display some remarkable properties. We will demonstrate how the entanglement of individual parts together displays behavior at phase boundaries, but the combination of these in the aforementioned quantities sharpens and localizes this behavior to the boundaries even better. We will show that we can extend a scheme for approximating the entanglement with the mutual information, and that this acts as a lower bound which will also follow the changes in the entanglement for the above quantities, despite the additional contributions of different signs. This mutual information approximation to the identifying quantities can have its lower probabilities removed in a process we call filtering, and despite the combination of terms will respond well to the filtering and offer improvements to the lower bound.

arXiv:2507.14422•Jul 19, 2025•1 citation

An interpretable closed form for entanglement entropy from bitstrings, guided by a graph neural network

Anas Saleh

The empirical bitstring distribution is the most accessible observable on Rydberg-atom arrays, but the bipartite von~Neumann entropy it constrains is far costlier to obtain. We present a six-term linear closed form for the entropy, built on bitstring-derivable physics scalars, and characterize its accuracy, portability, scaling behaviour, and calibration cost. The feature set is selected with guidance from a trained graph neural network: probing the network localizes its entropy prediction to the two-point correlators on the bipartition boundary, and an exhaustive ground-truth search restricted to those boundary correlators isolates the form. It reaches $0.024$~nats mean absolute error in distribution: $6.4$ times the network's error, but in a form a human can read and apply without retraining. Fit once and applied unchanged, it has lower error than the base network on five of six out-of-distribution pools and ties the sixth. An independent density-matrix renormalization-group study to one hundred atoms -- five times the reach of exact diagonalization -- settles the size-extrapolation question: coefficients frozen at small size fail at scale, but the failure is structured. Refit per size the form holds to $25$--$50$~mnat (cross-validated); two of its six slopes follow clean inverse-size laws, one a downward curving growth, and the others are trendless; the fitted laws deploy the form label-free at roughly $40$--$80$~mnat. The result fixes a label-budget rule: at large sizes, a few dozen labels recalibrate the closed form to match a fine-tuned in-distribution ensemble on the same features, while nonlinear ML models pull ahead only given large labelled datasets.

quant-pharXiv:2606.22713•Jun 23, 2026•0 citations

Improved entanglement entropy estimates from filtered bitstring probabilities

Avi Kaufman, James Corona, Zane Ozzello +3 more

Physical Review A•Sep 5, 2025•2 citations
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 SAvNS^{vN}_ASAvN​. We show that in many cases these lower bounds can be improved by removing the bitstrings with a probability lower than some value pminp_{min}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 SAvNS^{vN}_ASAvN​. 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 SAvNS^{vN}_ASAvN​. 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.
Calculating the von Neumann entanglement entropy from experimental data is challenging due to its dependence on the complete wavefunction, forcing reliance on approximations like classical mutual information (MI). We propose a machine learning approach using a graph neural network for predicting the von Neumann entropy from experimentally accessible bitstrings. We tested this approach on a Rydberg ladder system and achieved a mean absolute error of 3.7×10−33.7 \times 10^{-3}3.7×10−3 when testing it inside of its training range on a dataset with entropy ranging from 0 to 1.9, we also evaluated the mean absolute percentage error on the data that have its entropy larger than 0.01 of the maximum entropy(so we can avoid the areas of our phase space with near zero entropy) and got a relative error of 1.72%, outperforming MI-based bounds. When tested beyond this range, the model still delivers reasonable results. Furthermore, we demonstrate that fine tuning the model with a small dataset significantly improves its performance on data outside its original training range.
Abstract Calculating the von Neumann entanglement entropy from experimental data is challenging due to its dependence on the complete wavefunction, forcing reliance on approximations such as classical mutual information (MI). We propose a machine learning approach using a graph neural network to predict the von Neumann entropy directly from experimentally accessible bitstrings. We test this approach on a Rydberg ladder system and achieve a mean absolute error of 3.6 × 10 − 3 when evaluating within the training range on a dataset with entropy values ranging from 0 to 1.9. The model achieves a mean absolute percentage error of 1.44% and outperforms MI-based bounds. When tested beyond the training range, the model maintains reasonable accuracy. Furthermore, we demonstrate that fine-tuning the model with small datasets significantly improves performance on data outside the original training range.
We show that multipartite entanglement can be used as an efficient way of identifying the critical points of 1+1D systems. We demonstrate this with the quantum Ising model, lattice λϕ4λϕ^4λϕ4 approximated with qutrits, and arrays of Rydberg atoms. To do so we make use of multipartite compositions of entanglement quantities for different parts combined to form the strong subadditivity, weak monotonicity, and a convex combination of these with conformal properties. These quantities display some remarkable properties. We will demonstrate how the entanglement of individual parts together displays behavior at phase boundaries, but the combination of these in the aforementioned quantities sharpens and localizes this behavior to the boundaries even better. We will show that we can extend a scheme for approximating the entanglement with the mutual information, and that this acts as a lower bound which will also follow the changes in the entanglement for the above quantities, despite the additional contributions of different signs. This mutual information approximation to the identifying quantities can have its lower probabilities removed in a process we call filtering, and despite the combination of terms will respond well to the filtering and offer improvements to the lower bound.
The empirical bitstring distribution is the most accessible observable on Rydberg-atom arrays, but the bipartite von~Neumann entropy it constrains is far costlier to obtain. We present a six-term linear closed form for the entropy, built on bitstring-derivable physics scalars, and characterize its accuracy, portability, scaling behaviour, and calibration cost. The feature set is selected with guidance from a trained graph neural network: probing the network localizes its entropy prediction to the two-point correlators on the bipartition boundary, and an exhaustive ground-truth search restricted to those boundary correlators isolates the form. It reaches 0.0240.0240.024~nats mean absolute error in distribution: 6.46.46.4 times the network's error, but in a form a human can read and apply without retraining. Fit once and applied unchanged, it has lower error than the base network on five of six out-of-distribution pools and ties the sixth. An independent density-matrix renormalization-group study to one hundred atoms -- five times the reach of exact diagonalization -- settles the size-extrapolation question: coefficients frozen at small size fail at scale, but the failure is structured. Refit per size the form holds to 252525--505050~mnat (cross-validated); two of its six slopes follow clean inverse-size laws, one a downward curving growth, and the others are trendless; the fitted laws deploy the form label-free at roughly 404040--808080~mnat. The result fixes a label-budget rule: at large sizes, a few dozen labels recalibrate the closed form to match a fine-tuned in-distribution ensemble on the same features, while nonlinear ML models pull ahead only given large labelled datasets.