Ghent & Vienna Researchers Stabilize PEPS Gradients With Implicit Methods

Researchers from Ghent University and the University of Vienna are addressing a critical limitation in the optimization of projected entangled-pair states (PEPS), a leading method for simulating complex quantum systems. While automatic differentiation is currently used to calculate energy gradients, the process is computationally expensive and prone to numerical instabilities, hindering reliable results. The team reformulated the gradient computation in terms of a single characteristic equation for the contraction environment, a shift designed to improve scaling with problem size. By choosing a suitable parametrization of this characteristic equation based on the intrinsic symmetries of the contraction environment, instabilities can be removed from the global gradient computation. Finally, the researchers provide…