Magic of quantum hypergraph states

Understand

Magic, or nonstabilizerness, characterizes the deviation of a quantum state from the set of stabilizer states and plays a fundamental role from quantum state complexity to universal fault-tolerant quantum computing.

• However, analytical or even numerical characterizations of magic are very challenging, especially in the multi-qubit system, even with a moderate qubit number.
• Here we systemically and analytically investigate the magic resource of archetypal multipartite quantum states -- quantum hypergraph states, which can be generated by multi-qubit Controlled-phase gates encoded by hypergraphs.
• We first give the magic formula in terms of the stabilizer R$\mathrm{\acute{e}}$nyi-$\alpha$ entropies for general quantum hypergraph states and prove the magic can not reach the maximal value, if the average degree of the corresponding hypergraph is constant.