Good quantum error-correcting codes exist
A. R. Calderbank,Peter W. Shor +1 more
Reads0
Chats0
TLDR
The techniques investigated in this paper can be extended so as to reduce the accuracy required for factorization of numbers large enough to be difficult on conventional computers appears to be closer to one part in billions.Abstract:
With the realization that computers that use the interference and superposition principles of quantum mechanics might be able to solve certain problems, including prime factorization, exponentially faster than classical computers @1#, interest has been growing in the feasibility of these quantum computers, and several methods for building quantum gates and quantum computers have been proposed @2,3#. One of the most cogent arguments against the feasibility of quantum computation appears to be the difficulty of eliminating error caused by inaccuracy and decoherence @4#. Whereas the best experimental implementations of quantum gates accomplished so far have less than 90% accuracy @5#, the accuracy required for factorization of numbers large enough to be difficult on conventional computers appears to be closer to one part in billions. We hope that the techniques investigated in this paper can eventually be extended so as to reduce this quantity by several orders of magnitude. In the storage and transmission of digital data, errors can be corrected by using error-correcting codes @6#. In digital computation, errors can be corrected by using redundancy; in fact, it has been shown that fairly unreliable gates could be assembled to form a reliable computer @7#. It has widely been assumed that the quantum no-cloning theorem @8# makes error correction impossible in quantum communication and computation because redundancy cannot be obtained by duplicating quantum bits. This argument was shown to be in error for quantum communication in Ref. @9#, where a code was given that mapped one qubit ~two-state quantum system! into nine qubits so that the original qubit could be recovered perfectly even after arbitrary decoherence of any one of these nine qubits. This gives a quantum code on nine qubits with a rate 1read more
Citations
More filters
Quantum Computation and Quantum Information
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
Journal ArticleDOI
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms on a quantum computer and gave an efficient randomized algorithm for these two problems, which takes a number of steps polynomial in the input size of the integer to be factored.
Journal ArticleDOI
Quantum entanglement
TL;DR: In this article, the basic aspects of entanglement including its characterization, detection, distillation, and quantification are discussed, and a basic role of entonglement in quantum communication within distant labs paradigm is discussed.
Journal ArticleDOI
Fault tolerant quantum computation by anyons
TL;DR: A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer Unitary transformations can be performed by moving the excitations around each other Unitary transformation can be done by joining excitations in pairs and observing the result of fusion.
Journal ArticleDOI
Mixed State Entanglement and Quantum Error Correction
Charles H. Bennett,Charles H. Bennett,Charles H. Bennett,David P. DiVincenzo,David P. DiVincenzo,David P. DiVincenzo,John A. Smolin,John A. Smolin,John A. Smolin,William K. Wootters,William K. Wootters,William K. Wootters +11 more
TL;DR: It is proved that an EPP involving one-way classical communication and acting on mixed state M (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa, and it is proved Q is not increased by adding one- way classical communication.
References
More filters
Proceedings ArticleDOI
Algorithms for quantum computation: discrete logarithms and factoring
TL;DR: Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given.
Journal ArticleDOI
A single quantum cannot be cloned
TL;DR: In this article, the linearity of quantum mechanics has been shown to prevent the replication of a photon of definite polarization in the presence of an excited atom, and the authors show that this conclusion holds for all quantum systems.
Journal ArticleDOI
Quantum theory, the Church-Turing principle and the universal quantum computer
TL;DR: In this paper, it is argued that underlying the Church-Turing hypothesis there is an implicit physical assertion: every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means.
Journal ArticleDOI
Scheme for reducing decoherence in quantum computer memory
TL;DR: In the mid-1990s, theorists devised methods to preserve the integrity of quantum bits\char22{}techniques that may become the key to practical quantum computing on a large scale.
Journal ArticleDOI
Quantum Computations with Cold Trapped Ions.
J. I. Cirac,Peter Zoller +1 more
TL;DR: A quantum computer can be implemented with cold ions confined in a linear trap and interacting with laser beams, where decoherence is negligible, and the measurement can be carried out with a high efficiency.