Quantum complexity of time evolution with chaotic Hamiltonians

• DOI: 10.1007/jhep01(2020)134
• Publication Date: 2020-01-29T05:02:59Z
• Authors: Vijay Balasubrama...; Matthew DeCross; Arjun Kar; Onkar Parrikar
• Keywords: Time evolution

A bstract We study the quantum complexity of time evolution in large- N chaotic systems, with SYK model as our main example. This is expected to increase linearly for exponential prior saturating at its maximum value, and related length minimal geodesics on manifold unitary operators that act Hilbert space. Using Euler-Arnold formalism, we demonstrate there always a geodesic between identity operator e −iHt whose grows time. until an obstruction minimality, after which it can fail be minimum either locally or globally. identify criterion — Eigenstate Complexity Hypothesis (ECH) bounds overlap off- diagonal energy eigenstate projectors k -local theory, use argue linear will least local show numerically (which chaotic) satisfies ECH thus has no obstructions growth time, from holographic duality. In contrast, also case = 2 fermions integrable) find short-time followed by oscillations. Our analysis relates familiar properties physical theories like their spectra structure eigenstates implications hypothesized computational class separations PSPACE "Image missing" BQP/poly BQSUBEXP/subexp, “fast-forwarding” Hamiltonians.