This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or phase-flip or both.

In this paper we construct some algebraic geometric error-correcting codes on surfaces whose Neron-Severi group has low rank. If the rank of the Neron-Severi group is 1, the intersection of this surface with an irreducible surface of lower degree will be an irreducible curve, and this makes possible the construction of codes with good parameters. Rank 1 surfaces are not easy to find, but we are...

For any integral convex polytope in R there is an explicit construction of an error-correcting code of length (q 1) over the nite eld Fq , obtained by evaluation of rational functions on a toric surface associated to the polytope. The dimension of the code is equal to the number of integral points in the given polytope and the minimumdistance is estimated using the cohomology and intersection t...

The theory of quantum error-correcting codes (QECCs, for short) has been exhaustively studied in the literature; see [1–8]. The most widely studied class of quantum codes are binary quantum stabilizer codes. A thorough discussion on the principles of quantum coding theory was given in [3] and [4] for binary quantum stabilizer codes. An appealing aspect of binary quantum codes is that there exis...

Analysis of quantum error correcting codes is typically done using a stochastic, Pauli channel error model for describing the noise on physical qubits. However, it was recently found that coherent errors (systematic rotations) on physical data qubits result in both physical and logical error rates that differ significantly from those predicted by a Paulimodel. Herewe examine the accuracy of the...

Can robustness against experimental imperfections and noise be embedded into a quantum simulation? In this paper, we report on a special case in which this is possible. A spin chain can be engineered such that, in the absence of imperfections and noise, an unknown quantum state is transported from one end of the chain to the other, due only to the intrinsic dynamics of the system. We show that ...

The higher rank numerical range is useful for constructing quantum error correction code for a noisy quantum channel. It is known that if a normal matrix A ∈ Mn has eigenvalues a1, . . . , an, then its rank-k numerical range Λk(A) is the intersection of convex polygons with vertices aj1 , . . . , ajn−k+1 , where 1 ≤ j1 < · · · < jn−k+1 ≤ n. In this paper, it is shown that the higher rank numeri...

Error correction codes are used for long years to protect memories from the soft errors. For a single bit error correction, the SEC single bit error correction code that correct one bit error per word are used. Double bit error detection code are used to detect the double bit errors. In the increasing of the technology the single bit error correction codes are used in the various places such as...

This report contains the comprehensive explanation of some most important quantum error correction codes. After the brief corroboration of the quantum mechanical principles that govern any quantum mechanical process, we introduce stabilizer formalism and stabilizer codes for quantum error correction (QEC). As an interesting derivative from classical counterpart we also present Quantum Reed Mull...

This article addresses the impact of exchange rate volatility on U.S. exports of four forest commodities. Exchange rate volatility is measured by the standard deviation of the growth rate of real effective exchange rate of the U.S. dollar. The nonstationarity of individual time series is explicitly taken into account by employing multivariate cointegration analysis and error correction models. ...