Related papers: Complexity of frustration: a new source of non-local non-stabilizerness

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

URL: http://arxiv.org/abs/2209.10541v2
Date: Mon, 21 Aug 2023 10:02:30 GMT
Title: Complexity of frustration: a new source of non-local non-stabilizerness
Authors: J. Odavi\'c, T. Haug, G. Torre, A. Hamma, F. Franchini, S. M. Giampaolo
Abstract summary: We advance the characterization of complexity in quantum many-body systems by examining $W$-states embedded in a spin chain. Our work reveals that $W$-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We advance the characterization of complexity in quantum many-body systems by examining $W$-states embedded in a spin chain. Such states show an amount of non-stabilizerness or "magic" (measured as the Stabilizer R\'enyi Entropy -SRE-) that grows logarithmic with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with an extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a $W$-state, while in the rest of the phase to which the classic 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 SRE is the sum of that of the $W$-states plus an extensive local contribution. Our work reveals that $W$-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.

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