Sachdev-Ye-Kitaev circuits for braiding and charging Majorana zero modes

TL;DR

This paper proposes a novel approach to simulate the Sachdev-Ye-Kitaev model using Majorana-based quantum circuits that combine all-to-all interactions with topological protection, enabling new avenues for studying quantum chaos and holography.

Contribution

It introduces fermionic Floquet circuits with local ingredients to emulate SYK dynamics, bridging all-to-all interactions and Majorana zero modes for quantum simulation.

Findings

Design of Majorana-based Floquet circuits capturing SYK features

Method to measure out-of-time-ordered correlators in Majorana devices

Reconciliation of all-to-all interactions with topological protection

Abstract

The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. Here we construct fermionic all-to-all Floquet quantum circuits of random four-body gates designed to capture key features of SYK dynamics. Our circuits can be built using local ingredients in Majorana devices, namely charging-mediated interactions and braiding Majorana zero modes. This offers an analog-digital route to SYK quantum simulations that reconciles all-to-all interactions with the topological protection of Majorana zero modes, a key feature missing in existing proposals for analog SYK simulation. We also describe how dynamical, including out-of-time-ordered, correlation functions can be measured in such analog-digital implementations by employing foreseen capabilities in Majorana devices.