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This talk will present several computation aspects of spin glasses. The first part focuses on quantum simulation of spin glasses. I will first describe how a non-local spin glass maps onto a local Ising model on a cubic lattice by a quantum wiring scheme, which then makes a local quantum annealing architecture [1]. This scheme has recently been experimentally implemented by Rydberg atoms in solving partition problems of non-plannar graphs. The second part focuses on how a ground state of Ising spin glasse encodes a computation history. For a classical model, we show a dynamical chaos transition maps to a ground state phase transition in an anisotrpic Ising glass model, leading to an exotic phase transition characterized by bulk-to-surface response, which is dubbed “peratic phase transition” [2]. We further generalize this phase transition to a quantum system by constructing a two-dimensional qudit model, for which we show rigorously how a time-like dimension emerges in the static quantum ground state. This ground state is a quantum superposition of geometrical lines on a two-dimensional array. Our theory implies that the study of unconventional phases in non-equilibrium systems would rather inspire discovery of more exotic equilibrium phases and transitions than reaching beyond.
[1] Xingze Qiu, Peter Zoller, Xiaopeng Li, PRX Quantum 1, 020311 (2020)
[2] Xingze Qiu, Hai Wang, Wei Xia, Xiaopeng Li, arXiv: 2109.13254
Xiaopeng Li is professor of physics in the Physics Department of Fudan University, China, jointly employed by Shanghai Qi Zhi Institute. He is active in quantum information science and condensed-matter theories, with his primary research interests in exploiting the quantum computation power of various quantum simulation platforms. He received his Ph.D. in physics from the University of Pittsburgh in 2013 and joined Fudan University as a faculty member in 2016 after three years at the University of Maryland, supported by a Joint Quantum Institute theoretical postdoctoral fellowship. He has been a full professor since 2019.