“QSEP-CIRCUIT, as defined in a recent paper by Patrick Hayden, Kevin Milner, and Mark Wilde ( in the computer science department here at McGill, is the problem of determining whether or not a quantum state given as a circuit is separable or not. The problem has been shown to be in QIP(2), and to be NP-hard and QSZK-hard, which lends credence to the idea that the problem is QMA-hard. The goal of this talk is to provide background for and explain in detail what QSEP-CIRCUIT and QMA are, explain why we care whether or not QSEP-CIRCUIT is QMA-hard, and hopefully showcase quantum information theory as an exciting and dynamic field. No background knowledge will be assumed."