C optimized pulse sequence implementing a single error correction cycle. If a stabilizer set is defined over this system containing k multiplicativity independent generators, then the dimension of the subspace is 2 n. In this chapter, we discuss the basic theory of quantum error correcting codes, faulttolerant quantum computation, and the threshold theorem. Chapter 7 quantum error correction caltech particle theory. Quantum computer architecture scalable and reliable quantum computers greg byrd ece csc 801 feb, 2018. Pdf quantum error correction and fault tolerant quantum. Experimental quantum error correction kristen pudenz and daniel lidar introduction while it is clear that some form of error correction will be. Apr 29, 2015 the physical realization of a quantum computer requires builtin error correcting codes that compensate the disruption of quantum information arising from noise.
Then you can start reading kindle books on your smartphone, tablet, or computer. Largescale quantum information processors must be able to transport and maintain quantum information and repeatedly perform logical operations. Errorfree into the quantum computer age iconnect007. Quantum error correction is a set of methods to protect quantum. May 27, 2011 a schematic view of three subsequent error correction cycles. The couplings between the system operators and the reservoir operators are usually assumedto be weak and linear. New class of quantum errorcorrecting codes for a bosonic mode marios h. Kim2,3 trapped atomic ions are standards for quantum information processing, serving as quantum memories, hosts of quantum gates in quantum computers and simulators, and nodes of quantum communication networks. Analogoustoclassicalbit errors,wewillconsidersinglequbiterrors,whicharejustanx,y,orzoperator onasinglequbit. Here, we show a combination of all of the fundamental elements required to perform scalable quantum computing through the use of qubits stored in the internal states of trapped atomic ions. We will see that the recovery procedure can work e. Daniel lidar is the viterbi professor of engineering at usc, and a professor of electrical engineering, chemistry, and physics.
We estimate the parameters required to couple atoms using light via cavity qed in order to achieve quantum gates. We want to make clearer what we mean by quantum error correction qec and errors. Pdf quantum error correction qec and faulttolerant quantum computation. Enter your mobile number or email address below and well send you a link to download the free kindle app. By markus grassl, national university of singapore, martin rotteler, nec laboratories america, inc.
To overcome this, a different method, such as the socalled threequbit bit flip code, has to be used. Therefore, recent efforts have been concentrated on using quantum communication to link a number of small iontrap quantum systems. Quantum error correction via convex optimization springerlink. B quantum circuit for the implemented phaseflip error correction code. Fulfillment by amazon fba is a service we offer sellers that lets them store their products in amazons fulfillment centers, and we directly pack, ship, and provide customer service for these products. This barcode number lets you verify that youre getting exactly the right version or edition of a book. The repetition code works in a classical channel, because classical bits are easy to measure and to repeat. Another way this is stated is that measurement disturbs the state of a quantum system. In our study of quantum algorithms, we have found persuasive evidence that.
A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Quantum error correction cambridge studies in linguistics. The introduction of quantum error correction in 1995 showed that active techniques could be. Pdf quantum error correction for beginners researchgate. Quantum computing with trapped ions, atoms and light. Introduction quantum error correction qec comes from the marriage of quantum mechanics with the classical. Complete methods set for scalable ion trap quantum. Mar 14, 2001 we consider experimental issues relevant to quantum computing, and discuss the best way to achieve the essential requirements of reliable quantum memory and gate operations. Whaley, robustness of decoherencefree subspaces for quantum. By demonstrating that quantum information can exist in. Demonstration of a quantum error detection code using a.
First, they have to be made bigger, which means they need to consist of a considerably higher number of quantum bits. Girvin departments of physics and applied physics, yale university, new haven, connecticut 06520, usa received 29 january 2016. Nuclear spins in trapped ions or atoms are a very promising candidate for the qubits. Quantum computing in the presence of spontaneous emission by a combined dynamical decoupling and quantumerrorcorrection strategy, phys. Quantum error correction pdf 1 a quantum error correcting code. And we will learn how to process encoded information, so that a quantum computation. Lidar is a professor of electrical engineering, chemistry and physics at the university of southern california, and directs the usc center for quantum information. Overview 1 principlesoferrorcorrection classicalerrorcorrection basicsofqec 2 experimentalrealisation qecwithions 3qubitrepetitioncode highfidelityentanglementmolmersorensengates. In quantum optics, decoherence is described by coupling the system to an in nitely large reservoir which models the environment. Error free into the quantum computer age swansea, uk posted on december 15th, 2017. Errorfree into the quantum computer age nanotechnology now. Lidar, 9780521897877, available at book depository with free delivery worldwide.
Motional quantum error correction connecting repositories. Language english format pdf isbn 9781107439054 editor todd a. This stops being the case for a quantum channel in which, due to the nocloning theorem, it is no longer possible to repeat a single qubit three times. Cse 599d quantum computing introduction to quantum. Robust quantum error correction via convex optimization. These codes make it possible to store quantum information so that one can reverse the effects of the most likely errors. Then in chapter 8, we will extend the theory in two important ways.
In general, for an n qubit system, the total dimensionality of the hilbert space is 2 n. In order to reach their full potential, todays quantum computer prototypes have to meet specific criteria. Us8510618b1 error correction in quantum computing system. Experimental repetitive quantum error correction science. Pdf an introduction to formalism of quantum computation and to the theory of quantum error correcting codes is presented. Quantum error correction damage if the noise is not too severe. Lidar publisher cambridge university press published 20 downloadable 6 times currency eur id 2777982 copy protection adobe drm. Cse 599d quantum computing introduction to quantum error. To achieve large scale quantum computers and communication networks it is essential not only to overcome noise in stored quantum information, but also in general faulty. Quantum computation and information is one of the most exciting developments in science and technology of the last twenty years.