The work provides a good reference for quantum computation and quantum information courses, allowing for students to become familiar with major points on the quantum information theoretical aspects of topological quantum computation and the advantages of topological quantum computation for quantum noise resistance. Two top scientists are now facing off over whether it will exist by 2030. Topological faulttolerance in cluster state quantum computation r raussendorf, j harrington and k goyalrecent citations a survey on quantum computing technology laszlo gyongyosi and sandor imrequbit mapping of oneway quantum computation patterns onto 2d nearestneighbor architectures sajjad sanaei and naser mohammadzadeh. Classical control of largescale quantum computers springerlink. Overview of topological clusterstate quantum computation on 2d. This constitutes a simplification over the standard gatebased model of quantum computing, as it replaces complex coherent unitary dynamics with simple projective measurements. The teams cluster state comprises eight entangled photons, each acting as a physical qubit that can have a value of 0 and 1 depending upon its polarization state. Physics copyright 2020 manybody topological invariants. Briegel and raussendorf show that any quantum logic circuit can be implemented on a cluster state, which demonstrates universality of the proposed scheme 1.
Blind quantum computation is a novel secure quantum computing protocol that enables alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to. 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 cluster state quantum computing arxiv vanity. Can quantum chemistry be performed on a small quantum computer. We combine the recent developments in topological cluster state computation with the photonic module, a simple chipbased device that can be. However, there has been a lack of sufficiently powerful highlevel languages to describe computing. Topological faulttolerance in cluster state quantum computation r. Architectural design for a topological cluster state quantum computer. 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. The surface code cannot be used when qubits vanish during computation. Dedicated research into the design and construction of a largescale quantum.
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. Nielsen 6 extended this result to no longer require coherent dynamics, instead relying on a method to teleport quantum gates, and he. Practical topological cluster state quantum computing requires. Topological qubits are similar in the sense that they are not easily perturbed by noise and heat, and must take a big hit before they are destroyed. In this approach, information is stored in the lowest energy states of manyanyon systems and processed by braiding nonabelian anyons. Upper bound for loss in practical topologicalcluster. Such a method of computing is a leading candidate for largescale quantum computing. 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. As quantum computing progresses from minimalist quantum supremacy demonstrations to attacking realworld problems, hardware demands will naturally steepen. This decoherence would be suppressed if the quantum state would somehow be stored in a topological variable. Topological cluster state quantum computing caltechauthors.
Fowler1 and kovid goyal2 1centre for quantum computer technology, university of. Quantum computing deterministic generation of a two. We say two knots are topologically equivalent if they can be deformed. Introduction this paper is a quick introduction to key relationships between the. Upper bound for loss in practical topologicalclusterstate quantum. The doping, however, introduces inhomogeneity, reducing the temperature at which the effect occurs. Pdf architectural design for a topological cluster state. Quantum computation with topological codes from qubit to. A gentle introduction eleanor rieffel and wolfgang polak. Topological quantum computing is a way of allowing precise quantum computations to run on noisy and imperfect hardware. Chapter 2 kau man knot invariant and relation to physics 2. Analog approaches are further divided into quantum. Quantum picturalism for topological clusterstate computing. An implementation of the topological cluster state quantum computer is suggested, in which the basic elements are linear optics, measurements, and a twodimensional array of quantum dots.
Quantum anomalous hall effect in intrinsic magnetic. A photonic implementation for the topological cluster. Experimental demonstration of topological error correction nature. The story of the topological insulator began with the discovery of the quantum spin hall effect qsh in 1980. A topological approach to quantum mechanics and the philosophy of nature. For practical quantum computation with tec, a larger cluster state of more qubits would be needed. Pdf topological cluster state quantum computing semantic.
To perform a quantum algorithm with a cluster state, individual qubits are measured. Such a method of computing is a leading candidate for largescale qc. An approach based on topological techniques reduces the sensitivity to errors and boosts the prospects for building practical quantum computers. General interest and excitement in quantum computing was initially triggered by peter shor 1994 who showed how a quantum algorithm could exponentially. One implementation uses surface codes created by forming defects in a highlyentangled cluster state. Hastings, matthias troyer as quantum computing technology improves and quantum computers with a small but nontrivial number of n 100 qubits appear feasible in the near future the question of possible. A roadmap for a scalable topological quantum computer. Fowler1 and kovid goyal 2 1centre for quantum computer technology, university of. Centre for quantum computer technology, university of melbourne, victoria, australia.
Qubits can be in a 1 or 0 quantum state, or they can be in a superposition of the 1 and 0 states. May 16, 2019 what is topological quantum computing, where is the field heading into, what is the current state of the art researchin this blog, which was part of uc berkeleys quantum computing course. Quantum states are fragile and tend to decohere quickly. In contrast to symmetrybreaking phases of landaus theory with local order parameters 9, topological phases are characterized by global. A gentle introduction eleanor rieffel and wolfgang polak the mit press cambridge, massachusetts london, england. In algebraic topology in general, and in persistent homology in particular, this analysis is performed by investigating the properties of linear maps on the space of simplices. For readers interested in the physics of topological quantum. Jan 14, 2017 topological quantum computing is topological because it utilizes topological degrees of freedom as well as operations that are topological in nature. Two physicists bet over a quantum computing moon shot wired. Topological quantum computing has long been a beautiful dream. Quantumpicturalismfor topologicalclusterstate computing. In traditional 2d cluster state computing, one dimension of the cluster represents al. The characterization and identification of topological phases in an experimental setting represents, however, a substantial challenge.
Mathematics of topological quantum computing microsoft. Quantum topological states of matter with applications in solid state physics, quantum computing, and quantum information theory a white paper on applications of m. Topological cluster state quantum computing quantum. Topological faulttolerance in cluster state quantum. Follow along on our journey to scalable quantum computing by signing up for the microsoft quantum. A quantum computer, quantum logic circuit, material for forming qubits, and method of operating a quantum computer is described. Topological quantum compiling with reinforcement learning yuanhang zhang,1,2 peilin zheng,3,4 yi zhang,3,4, and dongling deng1, y 1center for quantum information, iiis, tsinghua university, beijing 84, peoples republic of china 2department of physics, university of california, san diego, ca 92093, usa 3international center for quantum materials, peking university, beijing 100871, china. Schematic of one of the scalable architectures for topological quantum computation proposed by karzig and colleagues. Topological phases and quantum information stephen bartlett centre for engineered quantum systems, school of physics z z z z z zz z z x x a x x x x x x b figure 3. Topological quantum computing topological qubits based on nonabelian anyons. Topological quantum computing qc is a way of allowing precise quantum computations to run on noisy and imperfect hardware.
Mathematics of topological quantum computing microsoft research. Topological insulators and applications to quantum. Pdf a photonic implementation for the topological cluster. Fowler,2 1centre for quantum computation and communication technology, school of physics, university of melbourne, victoria, 3010, australia. Topological quantum computation microsoft research. Upper bound for loss in practical topologicalclusterstate. Combining physics, mathematics and computer science, quantum computing and its sister discipline of quantum information have developed in the past few decades from visionary ideas to two of the most fascinating areas of quantum theory. Computation on 2d clusterstate based on highthreshold universal quantum computation on the surface code. We describe a faulttolerant version of the oneway quantum computer using a cluster state in three spatial dimensions. The quantum computing scheme described by raussendorf et. Percolationbased architecture for cluster state creation using. Aug 16, 2017 that ceiling may soon crumble howevervaulting topological qubits into a fascinating new chapter in the quest for scalable quantum hardware. With an emphasis on introduction to basic notions and current research, the book is almost entirely about the mathematics of topological quantum computation. An implementation of the topological clusterstate quantum computer is suggested, in which the basic elements are linear optics, measurements, and a twodimensional array of quantum dots.
Topological cluster state quantum computing fowler, austin g. Having constructed a quantum state that represents the simplicial complex s. In traditional 2d cluster state computing, one dimension of the cluster. Topological cluster state computation is closely related to kitaevs toric code, as the 3d topological cluster state can be constructed and measured over time by a repeated sequence of gates on a 2d array. The material is formed from a quasicrystal or quasicrystalline approximant. Quantum algorithms for topological and geometric analysis. A short introduction to topological quantum computation. Us20190080256a1 topological quantum computing, apparatus. Blind topological measurementbased quantum computation.
Nonabelian anyons and topological quantum computation. Architectural design for a topological cluster state. Architectural design for a topological cluster state quantum. 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. The 3d archi tecture can be further mapped onto a local. Cluster states are thus oneway quantum computers, as raussendorf and briegel put it in their initial paper, and the measurements form the program.
Fowler,2 1centre for quantum computation and communication technology, school of physics, university of melbourne, victoria, 3010, australia 2department of physics, university of california, santa barbara, california 93106, usa. Nemoto, k architectural design for a topological cluster state quantum computer. Oneway quantum computation has been demonstrated by running the 2 qubit grovers algorithm on a 2x2 cluster state of photons. In some examples, topological quantum computing is performed based on the quasicrystal or quasicrystalline approximant materials. Quantum computing is plagued by noise and small errors. Topological quantum compiling with reinforcement learning. Topological precision has been confirmed in quantum hall liquids by experiments to an accuracy of 1010, and harnessed to stabilize quantum memory. The development of a large scale quantum computer is a highly sought after goal of fundamental research and consequently a highly nontrivial problem. Topological faulttolerance in cluster state quantum computation. Quantum circuits are based on the quantum bit, or qubit, which is somewhat analogous to the bit in classical computation.
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 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. The basis of topological quantum computing is the anyon. Qsh was the first example of a quantum state with spontaneously broken symmetry, meaning it comprises of a symmetric probability distribution where any pair of outcomes has the same probability of occurring. Theoretical investigations suggest that some exotic fermionic quasiparticles in a variety of solid state matters, such as the fractional. 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. Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. Topological superconductor phase may solve decoherence. The roadmap topological quantum computing aims at such topological protection. Recently, majorana fermions have attracted a great deal of interest in condensed matter physics, mainly because of their nonabelian statistics that can be utilized for faulttolerant quantum computing 2,3.
Pdf the quantum computing scheme described in phys. Cluster state quantum computing umd department of computer. Topological quantum computation purdue engineering. We address both the mathematical underpinnings of topological quantum computation and the physics of the subject using the. A quantum computer, implemented theoretically or physically, is used to perform such computation i5 there are currently two main approaches to physically implementing a quantum computer. In principle, many researchers believe that oneway quantum computing offers a potentially more scalable approach than the quantum circuit model. A twodimensional medium that supports abelian anyons has a topological. Quantum computing stanford encyclopedia of philosophy. Creating majorana fermions in topological insulators. In this survey, we discuss the conceptual development of. Quantum computing is the use of quantum mechanical phenomena such as superposition and entanglement to perform computation.