The microsoft approach to quantum computing microsoft. Topological quantum computation based on chiral majorana. Fortunately, they do exist tqc could be carried out by braiding these. Topological quantum computers use particles with exotic exchange statistics called nonabelian anyons, and the simplest anyon model which. A quantum computer, quantum logic circuit, material for forming qubits, and method of operating a quantum computer is described.
One salient feature of tqc is the extensive use of graphical calculus. Topological quantum computation is an approach to storing and manipulating. 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. Topological precision has been confirmed in quantum. We address both the mathematical underpinnings of topological quantum computation and the physics of the subject using the. Topological quantum computation zhenghan wang ucsb math.
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. The discovery of the quantum hall effects has inspired developments in similar topological phenomena in a range of platforms, including ultracold neutral atoms 1, 2, photonics 3, 4, and mechanical structures 57. As an essential step toward topological quantum computing, the braiding of mzms has not yet been experimentally demonstrated. The topological qubit is a key ingredient in our scalable quantum system. This paper is an introduction to relationships between quantum topology and quantum computing. Such phases allow for quantum information to be stored and manipulated. Tqc is an approach to realizing quantum computing with nonabelian anyonsquasiparticles. From the cooling system to qubits to algorithms, scalability is a fundamental part of the microsoft vision for quantum computing.
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. 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 understanding these topological properties, it is equally important to study the mechanisms behind why topological insulators are ideal for applications of quantum computing. Mathematics of topological quantum computing microsoft. 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. Hastings, matthias troyer as quantum computing technology improves and quantum. Quantum science and technology paper introduction to topological quantum computation with nonabelian anyons to cite this article. In topological quantum computing, information is encoded in knotted quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological quantum materials for realizing majorana. Nonabelian anyons and topological quantum computation.
Scientists have developed a topological photonic chip to process quantum information, promising a more robust option for scalable quantum computers. In particular, scientists have observed what is known as an emergent particle at the interface between two topological. In this paper, we propose a platform to implement topologically protected quantum. Quantum computing qubits quantum decoherence noise extremely fragile need to be shielded from environmental perturbations topological quantum computing topological qubits based on non. A twodimensional medium that supports abelian anyons has a topological. Topological quantum computation purdue engineering.
The abcs of topological quantum computing we introduce three basic notions in topological quantum computing tqc. Physics is a foundational science that enables advances in chemistry, biology, medicine, earth and space science, anthropology, etc. Ising anyons 17 4 quantum computation with anyons 19 4. 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. A short introduction to topological quantum computation. Topological quantum computationfrom basic concepts to. Follow along on our journey to scalable quantum computing by signing up for the microsoft quantum. Topological quantum computation microsoft research.
The material is formed from a quasicrystal or quasicrystalline approximant. Topological quantum systems hold exceptional promise in quantum computing and tiny quantum. What is a quantum computer the memory consists of n qubits. A gentle introduction eleanor rieffel and wolfgang polak.
Introduction to topological quantum computation with nonabelian. If a physical system were to have quantum topological. Pdf introduction to topological quantum computation. 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. Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. Topological quantum computing is desirable because of intrinsic decoherence resistance to do tqc, need nonabelian anyons. Can quantum chemistry be performed on a small quantum computer. Both the encoding and the processing are inherently resilient against. This decoherence would be suppressed if the quantum state would somehow be stored in a topological variable. Pdf photonic topological quantum computer george rajna. 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 three. Topological insulators and applications to 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. We take a foundational approach, showing how knots are related not just to braiding and quantum operators, but to quantum. The roadmap topological quantum computing aims at such topological. 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. Topological quantum computation aims to achieve this goal by using nonabelian quantum phases of matter. Groups of particles similarly have quantum numbers topological quantum numbers. Quantum computing is built on quantum bits, known as qubits, and these particles not only represent 1s and 0s but due to the quantum mechanical. Pdf combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused. Im typing as we go so please forgive all typos and unclear parts etc. Spacetime trajectories of anyons will be represented by braids, and more general quantum.
Related content braiding operators are universal quantum. The topological invariance of the aharonovbohm phenomenon is the. Why quantum computers cannot work gil kalai hebrew university of jerusalem and yale university. Us20190080256a1 topological quantum computing, apparatus. Quantum states are fragile and tend to decohere quickly. Topological quantum computers use particles with exotic exchange statis. Introduction to topological quantum computation with non. Pdf knot logic and topological quantum computing with. Universality is an important property that needs to be satis. Introduction to topological quantum computation theoretical. For readers interested in the physics of topological quantum. With an emphasis on introduction to basic notions and current research, the book is almost entirely about the mathematics of topological quantum computation. 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. Physical applications of topological quantum field theory topological quantum computing lukas hahn 1 introduction1 2 qubits and universality1 3 simulating quantum physics6 4 abstract.
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