Many-Body Quantum Magic

Magic (non-stabilizerness) is a necessary but "expensive" kind of "fuel" to drive universal fault-tolerant quantum computation. To properly study and characterize the origin "complexity" in computation as well physics, it crucial develop rigorous understanding quantification magic. Previous studies magic mostly focused on small systems largely relied discrete Wigner formalism (which only behaved odd prime power dimensions). Here we present an initiatory genuinely many-body states that may be strongly entangled, with focus important case many qubits, at quantitative level. We first address basic question how "magical" state can be, show maximum $n$-qubit essentially $n$, simultaneously for range "good" measures. then that, fact, almost all pure have nearly $n$. In quest explicit, scalable cases highly entangled whose understood, connect hypergraph second-order nonlinearity their underlying Boolean functions. Next, go investigate practical physical contexts. consider variant MBQC where client restricted Pauli measurements, which feature initial "resource" state. $n$ magic, or indeed states, cannot supply nontrivial speedups over classical computers. example analyzing "natural" condensed matter interest. apply function techniques derive explicit bounds certain representative 2D SPT comment possible further connections between complexity phases matter.