Sachdev-Ye-Kitaev Circuits for Braiding and Charging Majorana Zero Modes

Area of Science:

• Condensed Matter Physics
• Quantum Information Science
• High Energy Physics

Background:

• The Sachdev-Ye-Kitaev (SYK) model is a pivotal theoretical framework for understanding many-body quantum chaos and holographic duality.
• Existing analog simulations of the SYK model face challenges in reconciling all-to-all interactions with topological protection.

Purpose of the Study:

• To construct a novel analog-digital quantum simulation of the SYK model.
• To address limitations in current proposals for analog SYK simulations by incorporating topological protection.

Main Methods:

• Construction of fermionic all-to-all Floquet quantum circuits utilizing random four-body gates.
• Implementation using local Majorana device ingredients: charging-mediated interactions and braiding of Majorana zero modes.
• Development of methods for measuring dynamical and out-of-time-ordered correlation functions.

Main Results:

• A viable analog-digital route for SYK quantum simulations is established.
• The proposed method successfully integrates all-to-all interactions with the topological protection of Majorana zero modes.
• Feasibility of measuring complex correlation functions in analog-digital Majorana devices is demonstrated.

Conclusions:

• This work presents a significant advancement in analog quantum simulation, offering a path towards experimentally probing SYK model dynamics.
• The developed approach provides a unique pathway to explore quantum chaos and holographic principles using protected Majorana zero modes.