Resource Theories and Quantum “Magic”

Abstract

Quantum computing requires physical resources to achieve an advantage over classical computation. Among these resources, quantum entanglement is often emphasized; however, it is now known that entanglement alone does not guarantee computational advantage—circuits composed solely of Clifford gates can produce highly entangled states yet remain efficiently simulable on classical computers (nature.com). Another essential ingredient is the so-called “quantum magic,” a term referring to non-stabilizer resources or non-Clifford operations needed to attain universal quantum computation and surpass classical efficiency (nature.com). This work addresses the resource theory of quantum magic, reviewing the main measures of “magic” (such as mana and robustness of magic) and their relation to non-Clifford operations; discussing Clifford+T circuit synthesis and the challenges of resource conversion (including the role of quantum catalysts); and exploring links between quantum magic, the attainment of quantum advantage, and the complexity of quantum states. The theoretical foundations and recent results are presented and discussed, showing how quantum magic emerges as a key component for universal, fault-tolerant quantum computation.