Universal quantum operation of spin-3/2 Blume-Capel chains

TL;DR

This paper introduces a universal quantum operation framework using a spin-3/2 Blume-Capel chain, enabling topologically protected qubit manipulation via Majorana bound states, with potential implications for quantum computing.

Contribution

It presents a novel logical qubit encoding in the spin-3/2 Blume-Capel model and demonstrates universal gate operations through Majorana bound states.

Findings

Supports localized Majorana bound states at chain ends

Demonstrates universal gate operations on encoded qubits

Preserves rotational invariance with on-site anisotropy

Abstract

We propose a logical qubit based on the Blume-Capel model: a higher spin generalization of the Ising chain and which allows for an on-site anisotropy preserving rotational invariance around the Ising axis. We show that such a spin-3/2 Blume-Capel model can also support localized Majorana bound states at the ends of the chain. Inspired by known braiding protocols of these Majorana bound states, upon appropriate manipulation of the system parameters, we demonstrate a set of universal gate operations which act on qubits encoded in the doubly degenerate ground states of the chain.