Peter Shor

A desire to understand quantum entanglement is fueled by the development of quantum computation, which started in the 1980s with the pioneering work of Benioff [26], Bennett [27], Deutsch [28], Feynman [29] and Landauer [30] but gathered momentum and research interest only after Peter Shor s revolutionary... 

Peter Shor from The AT T Bell Laboratories showed in 1994 that in principle a quantum computer could factor products of prime numbers in practical times. 

This realization is at the heart of quantum computation and led, in 1993, to Peter Shor s astounding result of a polynomial-time algorithm for factoring on a quantum computer [Shor 1994], In contrast, the best known classical algorithms for factoring are virtually exponential in run time. 

Other simple codes exist such as the phase flip code, which protects information against phase flip (see below for the definition of the phase flip) and can be simply derived from the bit flip code. Merging these two codes, Peter Shor proposed a code which protects one qubit of information against the action of arbitrary single qubit errors (bit and phase flips) this code involves nine physical qubits and shows the same schematic structure as the previous example. Its publication renewed the interest of physicists for the domain and gave hope that quantum errors are correctable. 

Shoe s algorithnn An algorithm in quantum computing that enables large numbers to be factorized into prime numbers in a way which is much quicker than using tradition computers. This algorithm, which was proposed by the American computer scientist Peter Shor (1959- ) in 1994, has major implications for the security of Internet information transfer. 

However, it was in 1994 that a main breakthrough happened, calling the attention of the scientific community for the potential practical importance of quantum computation and its possible consequences for modem society. Peter Shor discovered a quantum algorithm capable of factorizing large numbers in polynomial time [8]. Classical factorization is a kind of problem considered by computation scientists to be of exponential complexity. 

Sect. 6.8 deals with an issue that is of crucial importance to the possible realization of a QC the correction of errors which take place during storage and manipulation of quantum information. The main problem is the coupling of the QC to its environment which tends to destroy quantum mechanical coherence properties. In Sect. 6.8.5 I will discuss an error correction scheme which was proposed by Peter Shor and Andrew Steane independently (Shor 1995, Steane 1996). This scheme is designed to correct for storage errors of qubits. 

In this section I will outline the idea of memory error correction as put forward by Peter Shor and Andrew Steane (Shor 1995, Steane 1996). In classical bits the only kind of error which can happen is a hit flip which changes the logical value from 0 to 1 and vice versa. In qubits a second type of error can happen which we shall call phase errors. A bit flip error in a qubit will give rise to the following... 

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