The toric code 7 was the first topological quantum error correction. In order to motivate the development of topological quantum computing we begin by discussing typical quantum computing its problems. Mathematics of topological quantum computing article pdf available in bulletin of the american mathematical society 552 may 2017 with 403 reads how we measure reads. We continued our efforts in combining material science, theory, and novel device design to obtain more control of the underlying constituents of.
Quantum computational approaches improve upon classical methods for a number of special ized tasks. Topological quantum computationfrom basic concepts to. Topological quantum computation purdue engineering. So its the highest temperature 2d topological insulator so far, says postdoc sanfeng wu, who also was a first author of the earlier paper. Gil kalais argument against quantum computers quanta. In topological quantum computing, information is encoded in knotted quantum states of topological phases of matter, thus being locked into topology to prevent decay. The josephson junction is the basic building block of a superconducting qubit, and thus a quantum computer. Mathematics of topological quantum computing microsoft research. Among these, topological states have become a major research direction in the past decade, from quantum spin liquids, to topological insulators and superconductors, to examples in photonics and mechanical systems. In mathematical terms, these are unitary topological modular functors. The future of quantum computing could depend on this tricky. Topological quantum computing with majorana fermions.
The braiding and fusion of anyonic excitations in quantum hall electron liquids and 2dmagnets are modeled by modular functors, opening a new. First twodimensional material that performs as both. Quantum computing and topological qubits explained clearly. The computational answer is accessed by bringing anyons together and observing the result. Topological properties are unchanged by small perturbations, leading to a builtin resistance to errors such as those caused by stray interactions with the surrounding environment. They underlie the jones polynomial and arise in wittenchernsimons theory.
Topological quantum materials for realizing majorana. Pdf photonic topological quantum computer george rajna. 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. Physics copyright 2020 manybody topological invariants. Nearly two years ago, ibm made a quantum computer available to the world.
The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but a re particles known as nonabelian anyons, meaning that they obey nonabelian braiding statistics. Depth optimization for topological quantum circuits. Topological quantum computing the focus of the topological quantum computing roadmap is to develop, build and demonstrate the first topologically protected quantum bit based on majoranabound states. In this book, the author presents a variety of different topics developed together for the first time.
One salient feature of tqc is the extensive use of graphical calculus. Topological quantum computing has the promise of reaching up to six or seven nines, which means we wouldnt need to have this. 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. Our algorithm shows that you dont need a big quantum computer to kick some serious topological butt, he says. The focus of the topological quantum computing roadmap is to develop, build and demonstrate the first topologically protected quantum bit based on majoranabound states. 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. Aug 16, 2017 that ceiling may soon crumble howevervaulting topological qubits into a fascinating new chapter in the quest for scalable quantum hardware. A s condensedmatter analogs of majoranafermions particles that are their own antiparticles 1majorana bound states mbss are anticipated to exhibit nonabelian exchange statistics, providing a basis for naturally faulttolerant topological quantum computing 27. Groups of particles similarly have quantum numbers topological quantum numbers. A circuit implemented under tqc is optimized by reducing its depth due to special construction requirements in such technology. A pivotal goal of this research has been to realize materials hosting majorana quasiparticles, thereby making topological quantum computing a technological reality. An approach based on topological techniques reduces the sensitivity to errors and boosts the prospects for building practical quantum computers. We take a foundational approach, showing how knots are related not just to braiding and quantum operators, but to quantum set theoretical foundations and.
We will then introduce the concept of anyons as a generalization of bosons and fermions. Jan 25, 2016 solving the same problem with the new system, using a quantum computer, would require just 300 quantum bits and a device this size may be achieved in the next few years, according to lloyd. The characterization and identification of topological phases in an experimental setting represents, however, a substantial challenge. In topological quantum computing, information is encoded in. It advertised a series of lectures by michel devoret, a wellknown expert on experimental efforts in quantum computing. Longtime microsoft executive todd holmdahl who has a history of successfully bringing seemingly magical research projects to life as. Pdf combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused. Majorana bound state in a coupled quantumdot hybrid. This dear colleague letter dcl is intended to challenge the fundamental research community to achieve the transformative experimental realization of topological quantum computing. Quantum topological states of matter with applications in solid state physics, quantum computing, and quantum information theory a white paper on applications of m. The units of information, or logical qubits, are encoded as collective states in an array. Topological quantum computation is an approach to storing and. Combining the results together, we obtain an equivalence of the topolog. Qubits 1 introduction throughout the seminar, we encountered tqfts with anyonic excitations in various.
In this approach, information is stored in the lowest energy states of manyanyon systems and processed by braiding nonabelian anyons. Topological quantum computation microsoft research. Kitaev, faulttolerant quantum computation by anyons. As an essential step toward topological quantum computing, the braiding of mzms has not yet been experimentally demonstrated. I will not be as precise as mathematicians usually want. Even a small perturbation from the environment can have catastrophic effects on the quantumness of the system, which is precisely what were interested in with quantum computing. The process of building a quantum computer includes creating the raw materials needed to make topological quantum devices, fabricating the cold electronics and refrigeration systems, and developing the overall infrastructure needed to bring the solution to life. A twodimensional medium that supports abelian anyons has a topological. Similarly, not long after the first observations of topological insulators in the late 2000s, the. Can quantum chemistry be performed on a small quantum computer. 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. The discovery of topological insulators and progress towards topological superconductors realizing nonabelian statistics has moved topological phases of matter onto the center stage in the interaction of topology and physics beyond the quantum hall effect.
After decades of heavy slog with no promise of success, quantum computing is suddenly buzzing with almost feverish excitement and activity. A short introduction to topological quantum computation. Topological quantum computation based on chiral majorana. 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. Nov 20, 2016 microsoft is doubling down on its commitment to the tantalizing field of quantum computing, making a strong bet that it is possible to create a scalable quantum computer using what is called a topological qubit. Nonabelian anyons and topological quantum computation. Ascr report on quantum computing for science sponsored by. This quantum spin hall effect persisted up to a temperature of about 100 kelvins 279.
Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. A promising technology is the quantum computers, and this paper gives a general overview about this subject. A gentle introduction eleanor rieffel and wolfgang polak. We continued our efforts in combining material science, theory, and novel device design to obtain more control of the underlying constituents of the topological qubit. The microsoft approach to quantum computing microsoft.
Although quantum computing is still in its infancy, experiments have been carried out in which quantum computational operations were executed on a very small number of qubits quantum binary. Time crystals and topological superconductors merge. Thus, the world lines of two anyons cannot intersect or merge, which allows their paths to form stable braids in. In the past decade, basic physics, chemistry, and materials science research on topological quantum materialsand their potential use to implement reliable quantum computershas rapidly expanded to become a major endeavor. Quantum computing is plagued by noise and small errors. Topological quantum computation topological quantum computationtqc is a computational model built upon systems oftopological phases. Quantum computing qubits quantum decoherence noise extremely fragile need to be shielded from environmental perturbations topological quantum computing topological qubits based on nonabelian anyons these twodimensional quasiparticles form braids which are much more stable. The braiding and fusion of anyonic excitations in quantum hall electron. A topological quantum computer is a theoretical quantum computer that employs. Here we show that the propagation of chiral majorana fermions leads to the same unitary transformation as that in the braiding of majorana zero modes and propose a platform to perform quantum computation with chiral majorana fermions. He defines quantum gates, considers the speed of quantum algorithms, and describes the building of quantum computers. Pdf knot logic and topological quantum computing with. Time crystals and topological superconductors merge 12 february 2020, by anna demming.
Nov 12, 2014 topological quantum computing tqc model is one of the most promising models for quantum computation. Spacetime trajectories of anyons will be represented by braids, and more general quantum processes, such as creation. 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. On the another hand, when it comes to the realization of quantum computers in the applications of topological. For readers interested in the physics of topological quantum. December, 20 one of the main problems with experimental realizations of quantum computation is performing the required operationsresiliently. The abcs of topological quantum computing we introduce three basic notions in topological quantum computing tqc.
In this work, we propose a hybrid approach that combines a leftedge greedy heuristic with genetic algorithm ga to minimize circuit depth through combined line and. Im typing as we go so please forgive all typos and unclear parts etc. Topological quantum computers use particles with exotic exchange statis. Topological quantum computing with a very noisy network and. Topological precision has been confirmed in quantum hall liquids by experiments to an accuracy of 1010, and harnessed to stabilize quantum memory. The topological quantum computation model is eciently equivalent to other models of quantum computation such as the quan tum circuit model in the sense that all models solve the same class of problems in polynomial time fklw. The theory of quantum computation can be constructed from the abstract study of anyonic systems. Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. Oct 21, 2016 inside microsofts quest for a topological quantum computer. This topological property is always present in the material at cold temperatures. Lattice surgery translation for quantum computation.
Jan 04, 2001 the theory of quantum computation can be constructed from the abstract study of anyonic systems. Quantum computing is the use of quantum mechanical phenomena such as superposition and entanglement to perform computation. Apr 23, 20 topological codes are an elegant and practical method for representing information in a quantum computer. Follow along on our journey to scalable quantum computing by signing up for the microsoft quantum. Topological quantum computation wayne state university.
Scientists have developed a topological photonic chip to process quantum information, promising a more robust option for scalable quantum computers. Topological quantum computation based on chiral majorana fermions. The application of topology to physics has become an integral part of a second quantum revolution in the sciences. Topological quantum computing kyle evitts introduction quantum computers have generated a lot of interest in the academic world, security circles, and tech companies because of their computational advantages over classical com. In this paper, we propose a platform to implement topologically protected quantum gates at mesoscopic scales, which uses propagation of chiral majorana fermions with purely electrical manipulations instead of mzms. 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. Introduction to topological quantum computation with nonabelian. With an emphasis on introduction to basic notions and current research, the book is almost entirely about the mathematics of topological quantum computation. The fundamental constants h and e combine to form a quan tum of resistance he2. By the end of the book, readers understand that quantum computing and classical computing are not two distinct disciplines, and that quantum computing is the fundamental form of computing. They found that a conventional quantum computer device, given an errorfree operation of its logic circuits, will give a solution with an absolute level of accuracy, whereas a topological quantum computing device with flawless operation will give the solution with only a finite level of accuracy. The extent of quantum computing s applicability is still being determined. The future of quantum computing could depend on this tricky qubit.
A roadmap for a scalable topological quantum computer. Inside microsofts quest for a topological quantum computer. Mathematics of topological quantum computing american. Sep 22, 2011 topological quantum computing evades this barrier by exploiting topological materials that by their nature limit errors. Quantum computing is based on the ability to generate, manipulate, read, entangle and write quantum states of physical qubits.
Computers that perform quantum computation are known as a quantum computers i5 quantum computers are believed to be able to solve certain computational problems, such as the integer factorization that underlies rsa encryption, significantly faster than. Despite a plethora of promising visions towards application and implementation, a number of serious challenges remain. This paper is an introduction to relationships between quantum topology and quantum computing. This insight put the study of anyons at the center of topological quantum computation. However, the computing process of a topological quantum computer heavily relies on the properties of the specific particle used, thus it is a vital part of the explanation. The synthesis of the two ideas ushered in topological quantum computation. The topological qubit achieves this extra protection in two different ways. Topological quantum computing avoids these problems by making the state immune to most types of noise. A complete quantum system from hardware to software.
A topological quantum computer is a theoretical quantum computer that employs twodimensional quasiparticles called anyons, whose world lines pass around one another to form braids in a threedimensional spacetime i. Introduction to topological quantum computation theoretical. Pdf introduction to topological quantum computation. Topological quantum computation zhenghan wang ucsb math. Mathematics of topological quantum computing microsoft. A topological approach to quantum mechanics and the philosophy of nature. At microsoft, the development of the topological qubit continues, bringing us closer to scalable quantum computing and finding solutions to some of the worlds most challenging problems. That is, any of these models can efficiently simulate any of the others. Microsoft doubles down on quantum computing bet the ai blog. Topological quantum computation aims to achieve this goal by using nonabelian quantum phases of matter. Topological quantum computation tqc is a paradigm that information is en coded in topological degrees of freedom of certain quantum systems, thereby pro tected from local decoherence.
As quantum computing progresses from minimalist quantum supremacy demonstrations to attacking realworld problems, hardware demands will naturally steepen. Topological quantum computation using majorana fermions. Topological quantum computing tqc model is one of the most promising model for quantum computation. Pdf classical and quantum computation download full. When applied to quantum computing, topological properties create a level of protection that helps a qubit retain information despite whats happening in the environment. In this survey, we discuss the conceptual development of. Nonetheless, certain algorithms may be a more natural fit to the topological quantum computer model. Quantum states tend to be confined to small scales and low temperatures, because interaction with large and warm systems will destroy them. Topological quantum computing topological phases of matter are quantum computers, and form the foundation for building a scalable universal quantum computer. In quantum computing, the application of topology is most interesting because the simplest nontrivial example of the temperleylieb recoupling theory gives the socalled fibonacci model. An alternative design is the socalled topological quantum computer, which would use a radically different physical system to implement quantum computation. Schematic of one of the scalable architectures for topological quantum computation proposed by karzig and colleagues.
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