Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems

TL;DR

This paper demonstrates that high-depth variational quantum circuits can universally and effectively approximate ground states of diverse quantum many-body Hamiltonians, with favorable optimization landscapes and state replication capabilities.

Contribution

It shows that generic high-depth circuits are universally successful in approximating ground states across different models, highlighting their broad applicability in quantum simulations.

Findings

High-depth circuits accurately approximate ground states of different Hamiltonians.

The energy landscape of these circuits facilitates gradient-based optimization.

Circuits can effectively replicate random quantum states.

Abstract

We explore the effectiveness of variational quantum circuits in simulating the ground states of quantum many-body Hamiltonians. We show that generic high-depth circuits, performing a sequence of layer unitaries of the same form, can accurately approximate the desired states. We demonstrate their universal success by using two Hamiltonian systems with very different properties: the transverse field Ising model and the Sachdev-Ye-Kitaev model. The energy landscape of the high-depth circuits has a proper structure for the gradient-based optimization, i.e. the presence of local extrema -- near any random initial points -- reaching the ground level energy. We further test the circuit's capability of replicating random quantum states by minimizing the Euclidean distance.