barcodefontsoft.com

y C2 in .NET Writer Data Matrix ECC200 in .NET y C2

y C2 generate, create data matrix barcodes none for .net projects About 2D Code (24.55) . x1 + x2 x1 + x3 x2 + x3 x1 + x2 + x3 x1 . x2 . x3 . . x1 ,x2 ,x3 24.4 Hadamard Steane code As shown in Eq. (24.54), the other Steane codeword 1 is generate d by the bitwise addition of z = 1111111 to each of the elements in C2 /0 + C2 , which yields the alternate de nition: 1 . 1 = . x + y + z 8 y C2 1 (. x1 + x2 + 1 x1 + x3 + 1 x2 + x3 + 1 data matrix barcodes for .NET 8 x1 ,x2 ,x3 =0,1 . x1 + x2 + x3 + 1 x1 + 1 x2 + 1 x3 + 1 ).. (24.56). Letting the b .net vs 2010 datamatrix 2d barcode it variable a = 0, 1 we nally obtain a common de nition for the Steane codewords: 1 . a 8 (. x1 + x2 + a x1 + x3 + a x2 + x3 + a x1 ,x2 ,x3 =0,1. x1 + x2 + x3 + a x1 + a x2 + a x3 + a ).. (24.57). We may simpli fy the above de nition even further by setting the bit variables y1 = x1 + a, y2 = x2 + a and y3 = x3 + a, which gives 1 . a 8 (. y1 + y2 + a y1 + y3 + a y2 + y3 + a y1 ,y2 ,y3 =0,1. y1 + y2 + y3 y1 . y2 . y3 ).. (24.58). (where the mo datamatrix 2d barcode for .NET dulo-2 addition property u + u = 0 is applied for any bit u = xi , y, a = 0, 1). As we shall see next, the general de nition of .

a in Eq. (24. 57) represents the magic formula needed to build a complete Steane encoder circuit! Indeed, consider the rst qubit in .

a , namely y1 + y2 + a . The most elementary subcircuit that can be implemented to generate y1 + y2 + a w VS .NET data matrix barcodes ith y1 , y2 = 0, 1 is shown in Figure 24.7.

It is seen from the gure that the two Hadamard gates produce two . yi = + states that can act as control qubits on the target qubit a through CNOT gates (recalling that y CNOT x = . y x x + y ). We observe that a , which rep ECC200 for .NET resents the originator s message qubit to be encoded, is not limited to the basis states . 0 or 1 ; most generally, it can be of the form a = . 0 + . 1 , where, as usual, , are complex amplitudes satisfying 2 + . 2 = 1. Based on the above, it is not at all dif cult to conceive the full Steane-code encoding circuit shown in Fig. 24.

8, which represents only one possible implementation out of many other variants, let alone the exibility associated with the many other choices for generator matrix G in the (7, 4) code. Note that the same circuit, as traversed from right to left, can be used for decoding, i.e.

, retrieving the message qubit . a = . 0 + . 1 from the 7-qubit a , as obtain ed from the recipient after implementing error correction. This concludes this chapter on quantum error correction. An eerie feeling may rise from realising that the above-described CSS codes only represent another conceptual subspace within a grander space of the so-called stabilizer codes.

Such codes, which are, by and large, not limited to error correction but rather are at the root of advanced. Quantum error correction y1 + a y1 + y2 + a 0 +1 2. y1 y2 = yi y1 y2 Figure 24.7 Elementary circuit to generate the quantum state y1 + y2 + a g .net vs 2010 DataMatrix iven bit values , y1 , y2 = 0, 1, as based on H (Hadamard) and CNOT gates. The states obtained at intermediate stages are shown and pointed to by dotted arrows.

. a 0 0 0 0 0 0.
Copyright © barcodefontsoft.com . All rights reserved.