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Theoretical and Natural Science

Analysis of Majorana-based quantum computation

Yutong Bi

Published Nov 16, 2023• 0 citations
Publisher

Abstract

In recent years, the realization of quantum computation is a compelling research direction. To realize an error-tolerate quantum computer, topological quantum computation is considered as the most promising direction. Plenty of scholars have proved that non-abelian particles may play an important role on it. As a matter of fact, among particles obey non-abelian statistics, Majorana fermions is a typical example. On this basis, this study aims at introducing the development of Majorana-based quantum computation. To be specific, it will contain the conceptual framework of topological computation and introduce some recent research about Majorana-based quantum computation including the principles, configurations as well as the state-of-art analysis results. In addition, the current limitations for these studies will be demonstrated accordingly. Moreover, based on the summary the development of this field in recent years, this research will provide reference direction for future researchers. Overall, these results shed light on guiding further exploration of quantum computers.

DOI
10.54254/2753-8818/12/20230439

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In recent years, the realization of quantum computation is a compelling research direction. To realize an error-tolerate quantum computer, topological quantum computation is considered as the most promising direction. Plenty of scholars have proved that non-abelian particles may play an important role on it. As a matter of fact, among particles obey non-abelian statistics, Majorana fermions is a typical example. On this basis, this study aims at introducing the development of Majorana-based quantum computation. To be specific, it will contain the conceptual framework of topological computation and introduce some recent research about Majorana-based quantum computation including the principles, configurations as well as the state-of-art analysis results. In addition, the current limitations for these studies will be demonstrated accordingly. Moreover, based on the summary the development of this field in recent years, this research will provide reference direction for future researchers. Overall, these results shed light on guiding further exploration of quantum computers.
D eep in the heart of the topological world lives the Majorana fermion. There are several reasons the Majorana quasiparticle occu- pies a focal point within topological quantum matter. Of course, conceptually, it is a classical example of boundary mode that reveals the topological properties of the bulk, in this case a topological superconductor; an example that captures extremely well the very character of topological matter: simple yet subtle, hiding in plain view. But what enables the Majorana to play an important symbolic role is its conspicuous position at the crossroad that defines the new paradigm underlying the study of topological quantum matter. A child of particle physics, the Majorana was reborn in condensed matter physics and grew under the guidance of quantum computation. Lost before it was even found, it is fervently searched for in solid state and cold atom systems because it carries the promise to revolutionize the manner in which we process information and understand the foundations of the quantum world. Whether or not the Majorana will ever fulfill this promise is a minor detail; its main role is that of a legend, to give hope and move things forward. Practically, the search for zero-energy Majorana modes will play an important role in achieving the key condition for getting experimental access to topological quantum matter and quantum computation: an unprecedented level of control over quantum systems. At the time of this writing (spring 2016), the technological impact of these developments cannot be clearly foreseen.
The majorana fermion represents a kind of particle which is its own antiparticle. This paper aims to analyze the majorana fermions from theoretical aspect and application aspect, including the derivation of Dirac equation and the practicality of topological quantum computer. This paper explores the idea of Majorana fermions from Dirac equation and the anyons which is an important quasi-particle to build a topological quantum computer. After that, the potentials of quantum computer are emphasized as well. Several current major difficulties faced by building a quantum computer have also been discussed, including the decoherence of qubit and the errors during the operation of qubit. The advantages of topological computer are mentioned as well, especially the high resistance to local perturbation. The important property of two-dimensional non-abelian anyons has been discussed as well. Finally, the important relation of majorana fermions with anyons are introduced and the reason why majorana fermions is important has also been revealed.
I will discuss the revolutionary new concept of topological quantum computation, which is fault-tolerant at the hardware level with no need, in principle, of any quantum error correction protocols. Errors simply do not occur since the physical qubits and the computation steps are protected against decoherence by non-local topological correlations in the underlying physical system. The key idea is non-Abelian statistics of the quasiparticles (called 'anyons' as opposed to fermions or bosons), where the space-time braiding of the anyons around each other, i.e. quantum 'knots', form topologically protected quantum gate operations. I will describe in detail the theoretical principles guiding the experimental search for the appropriate topological phases of matter where such non-Abelian anyons, which are low-dimensional solid state versions of the elusive and exotic Majorana fermions hypothesized seventy-five years ago, may exist. I will critically discuss the recent experimental claims of observing the Majorana modes in semiconductor nanowire structures following earlier theoretical proposals, outlining the future developments which would be necessary to eventually build a topological quantum computer.
Quantum computation requires controlled engineering of quantum states to perform tasks that go beyond those possible with classical computers. Topological quantum computation aims to achieve this goal by using non-Abelian quantum phases of matter. Such phases allow for quantum information to be stored and manipulated in a nonlocal manner, which protects it from imperfections in the implemented protocols and from interactions with the environment. Recently, substantial progress in this field has been made on both theoretical and experimental fronts. We review the basic concepts of non-Abelian phases and their topologically protected use in quantum information processing tasks. We discuss different possible realizations of these concepts in experimentally available solid-state systems, including systems hosting Majorana fermions, their recently proposed fractional counterparts, and non-Abelian quantum Hall states.
Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This 'focus on' collection brings together several of the latest developments in the field and facilitates the synergy between different approaches.
The development of practical quantum computers hinges critically on the ability to reliably store and retrieve quantum information – a challenge known as quantum memory. Current quantum computing approaches face significant decoherence issues, limiting the duration and fidelity of quantum computations. This work investigates the potential of utilizing topological quantum states, specifically Majorana fermions, as a foundation for robust quantum memory architectures. We explore theoretical designs leveraging the unique topological protection inherent in these states, aiming to mitigate decoherence and enable long-term quantum storage. This research presents a novel approach to quantum memory that directly addresses the fundamental limitations of conventional qubit technologies. The core concept revolves around encoding quantum information within the non-local properties of Majorana fermions, offering a pathway towards fault-tolerant quantum storage. The presented architectures focus on creating and manipulating these states to perform quantum memory operations, and the underlying mathematical framework is detailed throughout this document. The investigation considers various approaches to controlling and reading out the state of Majorana fermions, and outlines the key challenges and potential solutions for realizing such a system.