Monte Carlo studies of modified scalable designs for quantum computation

TL;DR

This study uses Monte Carlo simulations to evaluate a modified mesoscopic island design with Majorana zero modes, demonstrating improved qubit lifetime and effective parity error correction for quantum computing.

Contribution

The paper introduces a novel parity correction scheme for Majorana-based qubits and analyzes its effectiveness through Monte Carlo simulations, enhancing scalability and error resilience.

Findings

Parity correction effectively reduces parity-breaking errors

Qubit lifetime increases with larger island size

Optimal chemical potential and pairing potential improve error correction

Abstract

As the building blocks of topological quantum computation, Majorana zero modes (MZMs) have attracted tremendous attention in recent years. Scalable mesoscopic island designs with MZMs show great potential in quantum information processing. However, these systems are susceptible to quasi-particle poisoning which would induce various parity-breaking errors. To solve this problem, we modify the mesoscopic islands with gate-tunable valves and non-topological backbones. We study the lifetime of the Majorana qubits on these modified islands which are coupled to local bosonic and fermionic thermal baths. We consider both the parity-breaking and parity-preserving errors, and propose a parity correction scheme. By using Jordan-Wigner transformation, we analyze the probability of logical X and Y errors. The open quantum system is described by the Pauli master equation, and standard Monte Carlo simulations are applied to observe the behavior of the system when the parity correction proposal is implemented. The results demonstrate that (1) our parity correction proposal is effective to most of the parity-breaking errors; (2) the lifetime of the qubit benefits from larger island size before it meets the threshold; (3) small chemical potential $ \mu $ on the non-topological backbones and fine tuned paring potential $ \Delta $ of the topological bulk segment are required for high probability of correctness. Our results provide an effective error correction scheme for the parity-breaking errors.