aiqbench analysis
This study demonstrates that iterative quadrature schemes can reduce measurement requirements by over an order of magnitude in noisy quantum simulations while maintaining fidelity to spectral gaps and degeneracies. A modified ansatz further enhances convergence and trainability, offering a practical diagnostic for quantum phase transitions despite the fact that low cost values alone do not guarantee trace distance convergence. These advances provide a more efficient and robust framework for exploring entanglement Hamiltonians in topological phases using current quantum-simulation platforms.
Exploring Variational Entanglement Hamiltonians
arXiv:2505.10530v3 Announce Type: replace Abstract: Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally obtained solutions and compare them to numerically exact calculations in quantum critical systems. We demonstrate that interpreting the cost functional as an integral permits the deployment of iterative quadrature schemes, thereby reducing the required number of measurements by more than an order of magnitude even in the presence of noise. We further show that a modified ansatz captures deviations from the Bisognano-Wichmann form in lattice models, improves convergence, improves trainability and provides a cost-function-level diagnostic for quantum phase transitions. Finally, we establish that a low cost value does not by itself guarantee convergence in trace distance. Nevertheless, it faithfully reproduces degeneracies and spectral gaps, which are essential for applications to topological phases.
Abstract:Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally obtained solutions and compare them to numerically exact calculations in quantum critical systems. We demonstrate that interpreting the cost functional as an integral permits the deployment of iterative quadrature schemes, thereby reducing the required number of measurements by more than an order of magnitude even in the presence of noise. We further show that a modified ansatz captures deviations from the Bisognano-Wichmann form in lattice models, improves convergence, improves trainability and provides a cost-function-level diagnostic for quantum phase transitions. Finally, we establish that a low cost value does not by itself guarantee convergence in trace distance. Nevertheless, it faithfully reproduces degeneracies and spectral gaps, which are essential for applications to topological phases.
Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)
arXiv:2505.10530 [quant-ph]
(or arXiv:2505.10530v3 [quant-ph] for this version)
Full text under the publisher's open licence · 158 words
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