The decoding error probability of a code C measures the quality of performance when C is used for error correction in data transmission. In this note we compare different types of codes with regard to the decoding error probability.

I give an overview of the basic concepts behind quantum error correction and quantum fault tolerance. This includes the quantum error correction conditions, stabilizer codes, CSS codes, transversal gates, fault-tolerant error correction, and the threshold theorem. 1 Quantum Error Correction Building a quantum computer or a quantum communications device in the real world means having to deal wit...

we present an approach to design of fault tolerant computing systems. in this paper, a technique is employed that enable the combination of several codes, in order to obtain flexibility in the design of error correcting codes. code combining techniques are very effective, which one of these codes are turbo codes. the algorithm-based fault tolerance techniques that to detect errors rely on the c...

To write an ethnography about poor urban people is to risk courting controversy. While all ethnographers face questions about how well they knew their site or how much their stories can be trusted, the tone and content of those questions typically remain within the bounds of collegial discourse. Ethnographers of poor minorities have incited distinct passion and at times acrimony, inspiring accu...

Let Bt(n) be the number of set partitions of a set of size t into at most n parts and let B′ t(n) be the number of set partitions of {1, . . . , t} into at most n parts such that no part contains both 1 and t or both i and i+ 1 for any i ∈ {1, . . . , t− 1}. We give two new combinatorial interpretations of the numbers Bt(n) and B ′ t(n) using sequences of random-to-top shuffles, and sequences o...

Inherent gate errors can arise in quantum computation when the actual system Hamiltonian or Hilbert space deviates from the desired one. Two important examples we address are spin-coupled quantum dots in the presence of spin-orbit perturbations to the Heisenberg exchange interaction, and off-resonant transitions of a qubit embedded in a multilevel Hilbert space. We propose a "dressed qubit" tra...