Complexity of frustration: A new source of non-local non-stabilizerness

Abstract

We advance the characterization of complexity in quantum many-body systems by examining WW-states embedded in a spin chain. Such states show an amount of non-stabilizerness or “magic”, measured as the Stabilizer Rényi Entropy, that grows logarithmically with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a WW-state, while in the rest of the phase to which the classical point belongs, it is dressed with local quantum correlations. Topological frustrated quantum spin-chains host phases with the desired phenomenology, and we show that their ground state’s Stabilizer Rényi Entropy is the sum of that of the WW-states plus an extensive local contribution. Our work reveals that WW-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems.

Quantifying non-stabilizerness via information scrambling

“…In Ref. [53] lower number of samples comes with doubling the dimension of the Hilbert space. The fact the analytical relationship in Eq.…”