Variational preparation of entangled states on quantum computers

We propose a variational approach for preparing entangled quantum states on quantum computers. The methodology involves training a unitary operation to match with a target unitary using the Fubini-Study distance as a cost function. We employ various gradient-based optimization techniques to enhance performance, including Adam and quantum natural gradient. Our investigation showcases the versatility of different ansatzes featuring a hypergraph structure, enabling the preparation of diverse entanglement target states such as GHZ, W, and absolutely maximally entangled states. Remarkably, the circuit depth scales efficiently with the number of layers and does not depend on the number of qubits. Moreover, we explore the impacts of barren plateaus, readout noise, and error mitigation techniques on the proposed approach. Through our analysis, we demonstrate the effectiveness of the variational algorithm in maximizing the efficiency of quantum state preparation, leveraging low-depth quantum circuits.