Floquet circuits inspired by holographic matrix models

Abstract

We argue that near-term experiments with neutral atoms in movable optical tweezers can simulate circuits that mimic the Trotterized time-evolution of simple matrix models in quantum mechanics. As a cartoon of this proposal, we study Floquet Clifford circuits which exhibit a number of signatures of fast scrambling. One such illustration is a simplified Hayden-Preskill recovery protocol, in which stabilizer quantum error correction replaces postselection.

Figures (15)

• Figure 1: Illustration of: (a) the rule defined in (\ref{['eq:diagonal_rule']}); (b) the rule defined in (\ref{['eq:off-diagonal_rule']}).
• Figure 2: The dynamics of a row/column infection process driven by permutations and cyclic connectivity is demonstrated. At $t=0$, the first qubit is infected, and by $t=3$ all eight qubits are infected, indicating full scrambling of the system.
• Figure 3: Growth of the number of infected qubits $n(t)$ as a function of time $t$ in random unitary circuits. The onset of full scrambling occurs no earlier than $\log_4 N^2$.
• Figure 4: Growth of the operator size $n(t)$ as a function of time $t$ in fixed Clifford dynamics. The onset of full scrambling occurs no earlier than $\log_4 N^2$; the time at which this bound is reached is depicted as a solid circle in each plot.
• Figure 5: Growth of the scrambling time $t_s$ as a function of $\ln(N^2/2)$. For Rule 2, we use $2|N$, since it is defined generically for any even $N$.