Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems
This addresses the challenge of simulating quantum systems for physics and quantum computing, though it appears incremental as it builds on existing variational methods.
The paper demonstrates that generic high-depth variational quantum circuits can accurately approximate ground states of quantum many-body Hamiltonians, showing success in models like the transverse field Ising and Sachdev-Ye-Kitaev with local extrema near random initial points reaching ground-level energy.
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.