On the Hardness of Measuring Magic

Abstract: Quantum computers promise to solve computational problems significantly faster than classical computers. These 'speed-ups' are achieved by utilizing a resource known as magic. Measuring the amount of magic used by a device allows us to quantify its potential computational power. Without this property, quantum computers are no faster than classical computers. Whether magic can be accurately measured on large-scale quantum computers has remained an open problem. To address this question, we introduce Pauli instability as a measure of magic and experimentally measure it on the IBM Eagle quantum processor. We prove that measuring large (i.e., extensive) quantities of magic is intractable. Our results suggest that one may only measure magic when a quantum computer does not provide a speed-up. We support our conclusions with both theoretical and experimental evidence. Our work illustrates the capabilities and limitations of quantum technology in measuring one of the most important resources in quantum computation.