#nearestneighbor

Quantum-graph neural networks

Quantum simulators use AI to improve precision: Innovative GNN Approach Finds Control Flaws

AI is predicted to develop quantum simulators, which can tackle quantum many-body problems that supercomputers cannot. A scalable Hamiltonian learning system using graph Neural Networks (GNNs) may offer real-time feedback control in quantum systems like Rydberg-atom arrays and overcome experimental restrictions.

Simulating complex quantum systems, especially those with long-range entanglement, can solve physics problems and disclose distinct matter phases. This promise requires these simulations to correctly govern their nanoscale physical qualities.

Challenge: Atom Array Imperfections

Rydberg atom arrays support quantum computing.

Simulations are difficult due to the imprecision of optical tweezers employed to catch atoms. These minor positional uncertainties disrupt the system's Hamiltonian, which represents its energy and interactions, limiting control and predictability. Quantum characterisation and verification, notably Hamiltonian learning, are needed to fix these issues. The experimental Hamiltonian is determined from data. Current methods often fail when faced with many parameters, unfamiliar terminologies, experimental limits, or the need for speedy execution.

A Scalable GNN-Based Learning Solution

This new study presents a scalable Hamiltonian learning strategy to solve these challenges. The primary innovation is using Graph Neural Networks (GNNs), a family of machine learning models that excel with graph-structured data. Quantum simulator measurements can be naturally represented as a graph, with edges representing two-body correlators like spin-spin correlations and nodes containing on-site information like local magnetisation.

The researchers trained the GNN using large datasets of ground-state snapshots of the transverse-field Ising model (TFIM), a common model natively implemented in Rydberg-atom arrays. These snapshots were created using the powerful numerical method for simulating quantum many-body systems, the Density Matrix Renormalisation Group (DMRG) algorithm. The GNN input data was correlation functions recreated from these simulated snapshots.

Foundational Theory and Key Results

This paper shows a bijective link between correlation functions and interaction parameters in the Hamiltonian, contributing to theory. This theorem logically proves that nearest-neighbor (NN) spin correlation functions alone can uniquely estimate NN relative distances between atoms, laying the groundwork for the learning process. This is generalised by density functional theory's Hohenberg-Kohn theorem.

The analysis yielded many key findings that enhance the GNN:

Great Extrapolation: The GNN predicted Hamiltonian parameters for systems much larger and varied in shape than those taught. Moreover, precise correlators trained on three small cluster sizes accurately predicted elements of larger systems.

Best Training Info:

Correlation functions matter NN and NNN spin correlation functions provided the most useful inputs for the GNN. Multi-Basis Measurements: By merging Z- and X-base measurements, the GNN improved its performance for experimental “snapshot” data, countering finite projective measurement errors.

Training the GNN with samples from various transverse field () values, particularly those near or above the magnetic phase transition, greatly improved its performance. The GNN has more signals to work with in this regime since correlation functions are more unpredictable.

It's noteworthy that local magnetisation didn't provide much extra information and could even be set to identification without affecting performance.

Architectural advantages: The GNN layer's graph preprocessing was crucial. This feature allowed the network to account for “edge effects” in the system, resulting in more accurate predictions across cluster sizes than a multi-layer perceptron (MLP) model. NNN edges in the input graph improved optimisation performance as “skip connections” for information flow without feature values.

Exact simulations yield almost faultless results, but real-world trials yield statistically confusing “snapshot” data. The study found that more than 10,000 projective measurements were needed to estimate spin-spin correlators to forecast NN relative distances from snapshot data with an average difference below 10%. Taking additional photos improved performance routinely.

Future implications: Adaptive Control

This research advances analogue quantum simulators. Even with defective experimental data, the GNN's rapid and exact Hamiltonian parameter inference has significant consequences:

Feedback Control: The GNN's speed and precision may provide real-time feedback control of Rydberg-atom array optical tweezer locations. This would allow experimentalists to actively address positional errors, making quantum simulations more exact and feasible. This precision is needed to study disorder-sensitive quantum phenomena like quantum spin liquids.

Beyond Known Hamiltonians: The GNN might be trained on a wider range of Hamiltonians to directly identify unknown noise from measurement data.

Wide Applicability: The network's extrapolation ability suggests it can solve challenges beyond Hamiltonian learning. We may use advanced statistical methods like truncating empirical covariance matrices or obtaining photos from random computational bases to test the GNN on snapshot data.