Deterministic Fast Scrambling with Neutral Atom Arrays

Abstract

Fast scramblers are dynamical quantum systems that produce many-body entanglement on a timescale that grows logarithmically with the system size N . We propose and investigate a family of deterministic, fast scrambling quantum circuits realizable in near-term experiments with arrays of neutral atoms. We show that three experimental tools -nearest-neighbor Rydberg interactions, global single-qubit rotations, and shuffling operations facilitated by an auxiliary tweezer array -are sufficient to generate nonlocal interaction graphs capable of scrambling quantum information using only O(log N ) parallel applications of nearest-neighbor gates. These tools enable direct experimental access to fast scrambling dynamics in a highly controlled and programmable way and can be harnessed to produce highly entangled states with varied applications.

Measurement-induced phase transitions in sparse nonlocal scramblers

“…We now consider what happens in the 'complete' PWR2 k circuit with k = log 2 N , where the longest-range interactions d max = N/2 are extensive, and show that the behavior radically changes relative to the cases previously studied. In particular, the complete PWR2 k circuit without measurements is known to be a fast scrambler capable of generating system-wide volume-law entanglement after only t * ∝ log N interaction layers [48]. In this section we demonstrate that the fast scrambling dynamics in this circuit leads to markedly improved code properties, including a nearly extensive contiguous code distance d code .…”

“…1a. Sparse nonlocal interactions of this type have been shown to generate fast scrambling dynamics [45], and are inspired by the nonlocal coupling patterns that can be engineered in single-mode cavities [49] or in Rydberg arrays with the aid of tweezer-assisted shuffling operations [48]. We expect the fast scrambling dynamics in these nonlocal circuits to rapidly generate many-body entanglement that is increasingly robust to the destructive effects of local measurements relative to circuits featuring only local interactions.…”

“…consist only of short-range couplings which restrict the spread of quantum information [50,51] and therefore generate only slow information scrambling. By contrast, circuits with k ∼ log 2 N consist of highly nonlocal interactions that span the entire system and are known to rapidly scramble quantum information [45,48,52]. The nonlocality parameter k therefore provides a convenient means by which to interpolate between the local and nonlocal limits of the PWR2 k family.…”

“…Fast scrambling was first discussed in the context of information spreading in black holes, and refers to systems that can scramble quantum information on timescales t * ∼ log N that grow only logarithmically with the system size N [37][38][39][40][41]. Random allto-all circuits [42], and other disordered all-to-all coupled models such as the SYK model [43,44] are good examples of fast scramblers, but recently, a number of deterministic and experimentally feasible systems exhibiting fast scrambling have also been explored [45][46][47][48]. These show similar dynamics, but often on sparse nonlocal coupling graphs.…”

“…shuffling operations [48]. The strength of scrambling in these circuits is governed by a nonlocality parameter k. In experimental implementations with Rydberg atoms this parameter is controlled by the number of shuffle operations applied, thereby providing a natural tunable parameter controlling the strength of scrambling in these circuits.…”