Observation of many-body Fock space dynamics in two dimensions

Abstract

Quantum many-body simulation provides a straightforward way to understand fundamental physics and connect with quantum information applications. However, suffering from exponentially growing Hilbert space size, characterization in terms of few-body probes in real space is often insufficient to tackle challenging problems such as quantum critical behavior and many-body localization (MBL) in higher dimensions. Here, we experimentally employ a new paradigm on a superconducting quantum processor, exploring such elusive questions from a Fock space view: mapping the many-body system onto an unconventional Anderson model on a complex Fock space network of many-body states. By observing the wave packet propagating in Fock space and the emergence of a statistical ergodic ensemble, we reveal a fresh picture for characterizing representative many-body dynamics: thermalization, localization, and scarring. In addition, we observe a quantum critical regime of anomalously enhanced wave packet width and deduce a critical point from the maximum wave packet fluctuations, which lend support for the two-dimensional MBL transition in finite-sized systems. Our work unveils a new perspective of exploring many-body physics in Fock space, demonstrating its practical applications on contentious MBL aspects such as criticality and dimensionality. Moreover, the entire protocol is universal and scalable, paving the way to finally solve a broader range of controversial many-body problems on future larger quantum devices.

Observation of critical phase transition in a generalized Aubry-André-Harper model with superconducting circuits

“…Just like the critical line (V = 2 for small μ) exhibiting intermediate behavior, the critical phase (μ > maxð1; V=2Þ) also exhibits properties that are in the other two phases. Therefore, the critical phase shares some similarities with the extended phase, such as its delocalized nature; and it also resembles the localized phase in some respects, for example, only a small fraction of the Fock space which is actively involved 54,55 , leading to oscillations of the participation entropy similar to that in the localized phase, and stronger than that in the extended phase for the same system size and the same number of different choices of δ. A more detailed discussion from the perspective of Fock space can be found in Supplementary Note 6.…”

“…In the Supplementary Note 3, we also display the results of first-order participation entropy. The dynamical participation entropy is a characterization quantifying how fast ψðtÞ j i spreads over the Hilbert space 19,54 . Initial product states, with probability one as a Fock state, diffuse in Fock space as the system evolves, and the wave functions have more and more non-zero probabilities in the computational (Fock) basis, which results in the increase of the participating entropy with time.…”

Creating and controlling global Greenberger-Horne-Zeilinger entanglement on quantum processors

“…We emphasize that our protocol is universal as it can be adapted to any particular qubit layout topology in 2D. In a parallel effort, we entangle all 6 × 6 qubits on Processor II [51] with F = 0.723 ± 0.010 for N = 36. Numerical simulations suggest that the reported F values are consistent with our calibrated gate fidelities (see Methods and Supplementary Information).…”

Disorder-tunable entanglement at infinite temperature

“…The latter entanglement structures have recently been identified (13,14) in a class of systems known as quantum many-body scars (QMBS) (15)(16)(17). When QMBS systems are prepared in special initial states, their dynamics become trapped in a subspace that does not mix with the thermalizing bulk of the spectrum, leading to the coherent time evolution of local observables (18)(19)(20)(21)(22)(23). The observation of QMBS has triggered a flurry of theoretical efforts to understand and classify the general mechanisms of weak ergodicity breaking in isolated quantum systems (24)(25)(26)(27)(28)(29)(30)(31)(32)(33).…”