Variational Entanglement Detection

Variational Entanglement Detection is a variational quantum algorithm which uses criteria based on positive maps as a bridge and works as follows. Given an unknown target bipartite quantum state, it firstly decomposes the chosen positive map into a linear combination of NISQ implementable quantum operations. Then, it variationally estimates the minimal eigenvalue of the final state, obtained by executing these quantum operations on the target state and averaging the output states. Deterministic and probabilistic methods are proposed to compute the average. At last, it asserts that the target state is entangled if the optimized minimal eigenvalue is negative. VLNE builds upon a linear decomposition of the transpose map into Pauli terms and the recently proposed trace distance estimation algorithm. It variationally estimates the well-known logarithmic negativity entanglement measure and could be applied to quantify entanglement on near-term quantum devices.