Complexity of frustration: A new source of non-local non-stabilizerness
Jovan Odavić, Tobias Haug, Gianpaolo Torre, Alioscia Hamma, Fabio Franchini, S. M. Giampaolo
Abstract
We advance the characterization of complexity in quantum many-body systems by examining W <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>W</mml:mi> </mml:math> -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 W <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>W</mml:mi> </mml:math> -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 W <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>W</mml:mi> </mml:math> -states plus an extensive local contribution. Our work reveals that W <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>W</mml:mi> </mml:math> -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.