Abstract:

With recent experimental progress in quantum technology, unprecedented programmability has been achieved in various atomic quantum systems from cold atoms to Rydberg tweezer arrays, and trapped ions. This gives new opportunities for Hamiltonian quantum simulations. In this talk I will describe our recently developed algorithmic protocols for programmable quantum simulations of long-range coupled Hamiltonians including all-to-all coupled spin glasses [1], “perfect” 2D topological flatbands, and Poincaré crystals [2]. Programmable quantum simulations of spin glasses provide a systematic way to solve such difficult computation problems as binary optimization, Max-Cut and prime factorization. In an anisotropic spin-glass like model, which has a natural realization with Rydberg p-wave atoms, we discover a “peratic” phase transition in the ground state. This unconventional phase transition is described by a bulk-to-surface response, and has a rigorous duality to the dynamical order-to-chaos transition [3]. We establish the peratic phase transition and its quantum generalization by constructing a frustration-free Ising lattice and a qudit model.

References:

[1] Xingze Qiu, Peter Zoller, Xiaopeng Li, Programmable Quantum Annealing Architecture with Ising Quantum Wires, PRX Quantum 1, 020311 (2020) with Editorial Suggestion

[2] Pei Wang, Zhijuan Huang, Xingze Qiu, Xiaopeng Li, Programmable Hamiltonian Engineering with Quadratic Quantum Fourier Transform, arXiv: 2204.04378 (2022)

[3] Xingze Qiu, Hai Wang, Wei Xia, Xiaopeng Li, Peratic Phase Transition by Bulk-to-Surface Response, arXiv: 2109.13254 (2021)