The future of quantum computing could depend on this. The roadmap topological quantum computing aims at such topological protection. Associated quantum states have limited longevities leading to loss of quantum coherence. Pdf photonic topological quantum computer george rajna.
In the case of topological quantum computing, a qubit is encoded in non local properties of a system and hence is not subject to change under any local perturbations on the system. Building qubits phase across junction energy maximum 0 energy energy minimum energy diagram of a junction electrons weak link superconductor what are the basic principles. The topological ground states of the system are therefore sep. Keeping highlevel and technical language to a minimum, the author adopts a pedagogical style, making the book accessible to nonspecialists and researchers from a variety of subdisciplines. Scientists have developed a topological photonic chip to process quantum information, promising a more robust option for scalable quantum computers. Pdf introduction to topological quantum computation. The topological degree of freedom can be thought of as the configuration class of the emergent chernsimons gauge field. Magnetism, when combined with an unconventional electronic band structure, can give rise to forefront electronic properties such as the quantum anomalous hall effect, axion electrodynamics, and majorana fermions. A twodimensional medium that supports abelian anyons has a topological. Topological quantum computer the central idea of tqc is to encode qubits into states of topological phases of matter see collection on topological phases.
Sets of topological superconductors containing six elements hexons, all hosting majorana zero modes mzms on the same side of the set, are interfaced with conventional superconductors and semiconductors to perform quantum computation. Topological quantum computing topological phases of matter are quantum computers, and form the foundation for building a scalable universal quantum computer. A crucial problem in the construction of a large, many qubit quantum computer is quantum decoherence. Topological quantum computers promise a fault tolerant means to perform quantum computation. As building blocks we use pairs of majoranas that emerge in semiconductor nanowires in contact with a.
Ising anyons 17 4 quantum computation with anyons 19 4. This seeming curiosity is actually the tip of an iceberg which links quantum computation both to low dimensional topology and the theory of. Introduction majorana fermions in superconducting heterostructures provide one of the most challenging but also interesting candidates for quantum computation 14. The topological invariance of the aharonovbohm phenomenon is the.
Here we report the characterization of highquality crystals of eusn2p2, a new quantum material specifically designed to engender unconventional electronic states plus magnetism. In this book, a variety of different topics are presented together for the first time, forming a thorough introduction to topological quantum computation. We introduce anyons at the systemindependent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions for encoding and processing quantum information. In contrast, qubits based on topological states offer a potentially robust vehicle to quantum computing. Braiding not only provides definitive evidence of majoranas, but perhaps more importantly, it also proves the feasibility of topological quantum computing in which the fundamental assumption of. Tanimura playing games in quantum mechanical settings. The firm has been developing topological quantum computing for more than a decade and today has researchers writing software for future machines, and working with academic laboratories to. Topological quantum computing heidelberg university. To make its first topological quantum computer, microsoft is bringing on board multiple quantum computing experts from top universities in denmark. The fiveyear objective of the topological roadmap is the realization of a topological qubit encoding a quantum state that is protected for at least a second. One of the main challenges in condensed matter physics is the exploration of topological phases of matter that could be used to build a scalable quantum computer. Introduction to topological quantum computation with nonabelian.
Dissipative quantum computing with majorana fermions. Pdf knot logic and topological quantum computing with. We will then introduce the concept of anyons as a generalization of bosons and fermions. Quantum computing and topological qubits explained clearly.
Microsoft aims to create worlds first topological quantum. In this book, the author presents a variety of different topics developed. It is here that the proposals for topological quantum computing seem promising4,10,11. Topological quantum computers use particles with exotic exchange statistics called nonabelian anyons, and the simplest anyon model which allows for universal quantum computation by particle exchange or braiding alone is the fibonacci anyon model. Adiabatic quantum computing is a framework for quantum computing that is superficially very different to the standard. Abstract for topological quantum computing for beginners, by john preskill i will describe the principles of faulttolerant quantum computing, and explain why topological approaches to fault tolerance seem especially promising. Decoherence leads to state dissipation and increases errors in computation.
A short introduction to topological quantum computation. Elusive majorana particle takes major step towards quantum. With an emphasis on introduction to basic notions and current research, the book is almost entirely about the mathematics of topological quantum computation. Qubits 1 introduction throughout the seminar, we encountered tqfts with anyonic excitations in various. In order to motivate the development of topological quantum computing we begin by discussing typical quantum computing its problems. One can show that a topological, anyonbased quantum computer can be well emulated by a qubit quantum computer.
Physical applications of topological quantum field theory topological quantum computing lukas hahn 1 introduction1 2 qubits and universality1 3 simulating quantum physics6 4 abstract anyonsense. Nonabelian anyons and topological quantum computation. Readrezayi fractional quantum hall states are among the prime candidates for realizing nonabelian anyons which in principle can be used for topological. Introduction to topological quantum computation with non. Conceptual approaches to topological computing include braiding anyon world. This gives rises to the topological quantum information braiding particles with nonabelian statistics entangled and i shall talk more about it in the end of this work.
Topological quantum computing avoids these problems by making the state immune to most types of noise. We take a foundational approach, showing how knots are related not just to braiding and quantum operators, but to quantum set theoretical foundations and. Pdf combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the. Energy is independent of this topological degree of freedom. Topological quantum computation zhenghan wang ucsb math. A physical system will remain in a coherent superposition. Topological quantum computation institute of laser physics.
Topological quantum computing with majorana zero modes and. Nakahara braid group and topological quantum computing t. In this book, the author presents a variety of different topics developed together for the. Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. Topological quantum states can still be destroyed by the environment, but there are ways to mitigate the problem that other sorts of quantum states dont have access to. Kitaevs topological quantum computing scheme caused great excitement because a particle that was strongly suspected to be a nonabelian anyon already existed. In a one dimensional topological superconductor, a single.
Topological quantum computing with majorana fermions. Combining physics,mathematicsandcomputerscience,topological quantumcomputation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. Information encoded in the degenerate state space of pairs of nonabelian anyons or defects is robust to local perturbations, reducing its susceptiblity to environmental errors and potentially providing a scalable approach to quantum computing. Purdue university doctoral student yang xu, lead author of a new research paper on topological insulators, an emerging class of materials that could make possible spintronic devices and practical quantum computers far more powerful than todays technologies, is shown here inspecting devices made from topological insulators under a microscope before electrical measurements. Markham holonomic quantum computing and its optimization s. Introduction to topological quantum computation university of leeds. The josephson junction is the basic building block of a superconducting qubit, and thus a quantum computer.
A roadmap for a scalable topological quantum computer. Typically, the only thing that can destroy a topologically entangled pair of majoranas, is the interaction with another pair in a state that can collide with it. Topological properties are those that remain invariant when we smoothly deform a system, and a faulttolerant quantum gate is one whose action on protected information remains invariant or nearly so when we deform the implementation of the gate by adding noise. In this article, i am going to cover some of the basics of quantum computing and also set up an environment on our local machine with visual studio 2017 to get started with quantum programming. Dissipative quantum computing, phonon interaction, majorana fermions, universal quantum computation 1. We outline the general steps of topological quantum computation, as well as discuss various challenges faced by it. Topological quantum computing seeks to store and manipulate information in a protected manner using topological phases of matter. Then we use a simulation of a topological quantum computer to explicitly demonstrate a quantum computation using fibonacci anyons. Topological quantum computing suppression of effective noise in hamiltonian simulations, phys. A gentle introduction eleanor rieffel and wolfgang polak. Topological surface states are a new class of electronic states with no vel properties. In topological quantum computing, information is encoded in knotted quantum states of topological phases of matter, thus being locked into topology to prevent decay. A new magnetic topological quantum material candidate by. This paper is an introduction to relationships between quantum topology and quantum computing.
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