Quantum complexity and negative curvature
By Adam R. Brown, L. Susskind, Ying Zhao. 2016
175 citations recorded by the source corpus.
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we show that the same pattern is exhibited by a much simpler system: classical geodesics on a compact two-dimensional geometry of uniform negative curvature. This striking parallel persists whether the system is allowed to evolve naturally or is perturbed from the outside.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/c698cb08358b18775fb2441bdfac037ee556b512
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Citations in the corpus
- Second law of quantum complexity (2017, methodology): “Our intuition for how complexity geometry should work is based on the two-dimensional toy model of [3] and [4].”
- Circuit complexity for free fermions (2018, background): “However, as stressed in [2, 42, 43], this geometry alone is inappropriate to define a notion of circuit complexity for states in quantum field theory since the maximum separation of any two states is only π.”
- Quantum chaos and the complexity of spread of states (2022, unknown): “Recent studies [4–11] investigate such choices of complexity metric for describing physical time evolution, with consequences for separating integrability and chaos.”
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement (2018, background): “) How is the membrane picture for entanglement growth [9, 14, 23] modified by weak breaking of unitarity? Finally, one could also ask how the ‘complexity’ of the evolving state (the minimal number of local operations required to generate it from a product state [81–92]) behaves as the entangling-dis”
- Chaos and complexity by design (2016, background): “While there is nice qualitative evidence for both of these proposals [67, 13, 65], missing is a direct understanding of computational complexity in systems that evolve continuously in time with a time-independent Hamiltonian.”
- Holographic complexity in Vaidya spacetimes. Part II (2018, methodology): “A simple model was proposed in [19, 64] for the evolution of the complexity in terms of an epidemic spreading of infected qubits when the system is evolved in time.”
- Circuit complexity in fermionic field theory (2018, background): “(1)Note also that this definition is usually implemented in discrete qubit systems and often with discrete time evolution [2].”
- Complexity and entanglement for thermofield double states (2018, background): “theories. In fact, the time evolution of the complexity of the TFD in these theories is predicted to initially show linear growth, i.e., @tC˘M, and to saturate only on a time scale of the order eS BH [13,113,114]. This expectation is based on the fact that these CFTs are fast scramblers and the evol”