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Entanglement complexity of quantum states, dynamics and quantum computation

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Figure 2 ·1: (Color online) Average entanglement spectrum of highly excited eigenstates for a system of size L = 16, averaged over 10 real-izations of disorder (plotted in logarithmic scale)
Figure 2 ·3: (Color online) The order parameter for the random-sign RK-type wave functions
Table 3.1: Summary of the main results presented in this chapter.
Figure 3 ·1: (Color online) Comparison between ESS and energy level spacing statistics after a quantum quench at t 0 = 1000 starting from a random product state in systems that are Anderson localized (a-b), nonintegrable and featuring ETH (c-d), featuring
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Outline

Entanglement spectrum statistics Complexity of Entanglement Entanglement spectrum statistics and entanglement complexity Majorana fermions with random braidings and local interactions Numerical results Summary and outlook Pontryagin’s minimum principle applied to VQA Numerical studies Braiding statistics of Kekul´ e vortices Engineered phases of matter with full tunability

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