Fig. 1: Overview.
From: Quantum computing universal thermalization dynamics in a (2 + 1)D Lattice Gauge Theory
a Schematic of the trapped-ion experiment: 15 optically-controlled ions (yellow circles) in a linear trap (electrodes shown as brown rectangular pads) realize a universal digital quantum computer. Single-qubit and all-to-all two-qubit gates are implemented by an array of individually-focused laser beams (blue and purple, vertical) and a global laser beam (blue, horizontal). Two-qubit gates are performed using pairs of individual beams, such as the ones highlighted in purple. b Schematic of the randomized-measurement protocol for entanglement-Hamiltonian tomography. This protocol extracts a classical approximation of a reduced density matrix associated with a subsystem of the quantum state \(\left\vert \right.\psi (t)\left.\right\rangle\), from which the presence or absence of quantum chaos is inferred. The protocol consists of measuring observables in a single-qubit randomized basis, then classically learning the entanglement Hamiltonian HE({βi}), which parameterizes the reduced quantum state with parameters {βi}, so as to optimally reproduce all measurements. The statistical behavior of the eigenvalue spectrum of the entanglement Hamiltonian is then analyzed: e.g., eigenvalue repulsion indicates quantum chaos, as detailed in the main text.
