Probing many-body quantum states in large-scale experimentsWith an upgraded randomized measurements toolbox

Benoît Vermersch

Mikhail D. Lukin

Simone Notarnicola, Andreas Elben, Thierry Lahaye +3 more

Abstract We present a toolbox to probe quantum many-body states implemented on Rydberg-atoms quantum hardware via randomized measurements. We illustrate the efficacy of this measurement toolbox in the context of probing entanglement, via the estimation of the purity, and of verifying a ground-state preparation using measurements of the Hamiltonian variance. To achieve this goal, we develop and discuss in detail a protocol to realize independent, local unitary rotations. We benchmark the protocol by investigating the ground state of the one-dimensional Su–Schrieffer–Heeger model, recently realized on a chain of Rydberg atom, and the state resulting after a sudden quench in a staggeredXYchain. We probe the robustness of our toolbox by taking into account experimental imperfections, such as pulse fluctuations and measurement errors.

Andreas Elben

Andreas Elben, Benoît Vermersch, Christian F. Roos +1 more

We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models. In particular, we discuss the theoretical details underlying the recent measurement of the second R\'enyi entropy of highly mixed quantum states consisting of up to ten qubits in a trapped-ion quantum simulator [Brydges et al., Science 364, 260 (2019)]. We generalize the protocol to access the overlap of quantum states, prepared sequentially in one experiment. Furthermore, we discuss proposals for quantum state tomography based on randomized measurements within our framework and the respective scaling of statistical errors with system size.

Hannes Bernien, Sylvain Schwartz, Alexander Keesling +9 more