Resource-Efficient Emulation of Majorana Zero Mode Braiding on a Superconducting Trijunction

TL;DR

This paper presents a resource-efficient quantum emulation method for Majorana Zero Mode braiding on superconducting trijunctions, reducing circuit complexity and enabling scalable topological quantum computation simulation.

Contribution

The authors introduce direct braiding operators for efficient emulation of MZM braiding, extending to larger architectures based on Kitaev chains.

Findings

Reduced quantum gate overhead in emulation

Successful simulation of braiding operations in extended architectures

Enhanced understanding of topological quantum system control

Abstract

Topological superconductivity could host quasiparticles that are key candidates for fault-tolerant quantum computation due to their immunity to noise as they obey non-Abelian exchange statistics. For example, in the case of Majorana Zero Modes (MZM), braiding enables two topologically protected quantum gates. While their direct manipulation in solid-state systems remains experimentally challenging, digital emulation of MZM behavior has provided insight as well as a deeper understanding of controlling these topological quantum systems. This emulation is typically accomplished by mapping the topological and trivial phases of a Majorana system to ferromagnetic and paramagnetic Hamiltonians of a spin-glass model. This approach usually relies on adiabatic evolution of superconducting Hamiltonians, which require circuits with very large depths. In this work, we present a resource-efficient method to emulate MZM braiding in a trijunction geometry using a quantum processor. We introduce direct braiding operators which simulate the evolution more efficiently, reducing the quantum gate overhead. We then further generalize this method to emulate braiding operations in extended trijunction architectures based on Kitaev chains.