Quantum Teleportation Error Suppression Algorithm Based on Convolutional Neural Networks and Quantum Topological Semion Codes

Abstract

Quantum error correction (QEC) is a key technique for building scalable quantum computers that can be used to mitigate the effects of errors on physical quantum bits. Since quantum states are more or less affected by noise, errors are inevitable. Traditional QEC codes face huge challenges. Therefore, designing an error suppression algorithm based on neural networks (NN) and quantum topological error correction (QTEC) codes is particularly important for quantum teleportation. In this paper, QTEC codes: semion codes—a greater than 2 dimensional (2D) error correction code based on the double semion model—are used to suppress errors during quantum teleportation, using a NN to build a decoder based on semion codes and to simulate the quantum information error suppression process and the suppression effect. The proposed convolutional neural network (CNN) decoder is suitable for small distance topological semion codes. The aim is to optimize the NN for better decoder performance while deriving the relationship between decoder performance and slope and pseudothreshold during training and calculate the thresholds for different noise areas when the code distances are the same, P t h r e s h o l d = 0.082 for A r e a < 0.007 d B and P t h r e s h o l d = 0.096 for A r e a < 0.01 d B . This paper demonstrates the ability of CNNs to suppress errors in quantum transmission information and the great potential of NNs in the field of quantum computing.

Rough Entanglement: Not Enough Fourier

“…Therefore, rough entanglement does not seek to replace the original versions of entanglement (maximally and nonmaximally), but to complement them to better understand this fascinating phenomenon of current Physics, and in this way take advantage of its virtues so that it can be exploited with the greatest success in applications, such as quantum cryptography, [8] in particular, QSDC, [23][24][25][26][27][28][29][30][31][32][33][34] and QKD; [9][10][11][12] and quantum communications, [7] in particular, quantum teleportation, [21,[41][42][43][44] with a marked commitment to the future quantum Internet. [13][14][15][16][17][18] Finally, the act of finishing characterizing this very peculiar phenomenon of Physics called entanglement, understanding first that it has intermediate instances, and second the springs that connect those instances with quantum communications protocols already established in the literature, is not a minor issue, for which the deepening of this study is provided in future works.…”

“…A simple visual inspection of Figure 3a-d tells us that rough entanglement is a very different case from previously known entanglements. [1] However, as will be seen in Section 2.5, the rough form of entanglement will allow successful teleportations of qubits useful in QKD [9][10][11][12] and the future quantum Internet. [13][14][15][16][17][18]…”

“…being the elements of its main diagonal (associated with their respective computational basis states), i.e., those recovered by Bob In all cases, a teleportation based on the distribution of roughly-entangled particles requires post-processing, although as we will see in the following implementations, the resulting fidelities are similar to those obtained in a traditional teleportation. [3][4][5][6] We must bear in mind that the central idea around this new type of entanglement is not to displace the maximally or nonmaximally entangled states or to compete with them, but rather to complement them, in order to thicken the knowledge we have of this fascinating Physics phenomenon called entanglement, so as to master it to obtain better protocols of quantum communications, [7,[38][39][40] and quantum cryptography, [8][9][10][11][12][23][24][25][26][27][28][29][30][31][32][33][34] with a strong commitment to the future quantum Internet. [13][14][15][16][17][18] Now, if…”

“…The spectral manifestation of entanglement has been exploited to the limit in previous works in implementations ranging from quantum teleportation, [3][4][5][6] through quantum secret sharing (QSS), [3][4][5][6] to quantum repeaters. [3][4][5][6] These applications have a marked projection on the quantum key distribution (QKD) [9][10][11][12] protocols, although their greatest contribution is expected to happen in the field of the future quantum Internet. [13][14][15][16][17][18] Specifically, in the quantum cryptography [8] context, fiber optic cabling for terrestrial implementations of QKD protocols [9][10][11][12] requires quantum repeaters every certain number DOI: 10.1002/qute.202200176 of kilometers, [19,20] which in turn requires a large amount of quantum memory.…”

“…[3][4][5][6] These applications have a marked projection on the quantum key distribution (QKD) [9][10][11][12] protocols, although their greatest contribution is expected to happen in the field of the future quantum Internet. [13][14][15][16][17][18] Specifically, in the quantum cryptography [8] context, fiber optic cabling for terrestrial implementations of QKD protocols [9][10][11][12] requires quantum repeaters every certain number DOI: 10.1002/qute.202200176 of kilometers, [19,20] which in turn requires a large amount of quantum memory. The problem is that the key is exposed in its passage through them.…”