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Quantum Number
Published in Shashi Bhushan, Manoj Kumar, Pramod Kumar, Renjith V. Ravi, Anuj Kumar Singh, Holistic Approach to Quantum Cryptography in Cyber Security, 2023
A code that implements both bit flip code and phase flip code is described here (7-bit Steane code. The Steane code could be a perfect tool in quantum error correction. It was introduced by Andrew in 1996. It employs the classical binary self-dual programming code (x errors) and the turn of the programming code, along with phase flip errors. The Steane code has the ability to correct discretionally single-qubit error. Within the stabilizer formalin, the Steane code has six generators and therefore the check matrix in a standardized form. This representation gives us a compact illustration for a code. The generator represented here involved I's and X's as well as the I's and Z's. The pattern obtained from these operators follows the parity check matrix H of a classical linear code.
Fault tolerance and ultimate physical limits of nanocomputation
Published in David Crawley, Konstantin Nikolić, Michael Forshaw, 3D Nanoelectronic Computer Architecture and Implementation, 2020
A S Sadek, K Nikolić, M Forshaw
We have already discussed the potentially serious effects of noise in quantum computation. Until the work of Shor demonstrating the possibility of quantum error correction [92], practical implementation of quantum computing seemed impossible. Quantum error-correcting codes are, in fact, very closely related to their classical counterparts. For example, the seven-qubit Steane code is the quantum implementation of a Hamming code [93]. The Hamming code uses seven bits of information to encode four bits. The initially independent four bits are correlated with one another through the addition of redundant bits. In the case of the Hamming code, this is done by using seven-bit codewords that annihilate in modular two arithmetic when operated on by a parity check matrix. If an unknown bit-flip occurs anywhere in the Hamming code due to noise, it is possible to measure what error occurred and correct it without ever knowing what the encoded data are. This is the key to why the Hamming code can be extended to quantum information, since if decoding was ever necessary to correct errors, in the quantum case this would lead to state collapse of the encoded qubit. In the Steane code, a single qubit is encoded and expanded to a seven-qubit block. The quantum state of the original qubit is stored in the code block through entanglement between the seven qubits. As no information about the original state is stored in any one qubit, decoherence of one of the qubits does not destroy the original information. By using ancillary bits, the exact location and type of error that occurred can be determined, this being known as the syndrome. Measurement of the syndrome is made by the ancilla and a ‘decision’ is made as to what type of quantum operation should be made to the code block to correct the error. The entire encoding, correction and decoding procedure is unitary (reversible) and, in principle, requires no energy, with the exception of the ‘decision’ which is a classical entropy-producing majority vote.
Improving the Designs of Nearest Neighbour Quantum Circuits for 1D and 2D Architectures
Published in IETE Journal of Research, 2023
Chandan Bandyopadhyay, Anirban Bhattacharjee, Robert Wille, Rolf Drechsler, Hafizur Rahaman
Although several developments have taken place, many challenges have also originated and one such problem is de-coherence [8], where the coherent superposition of basis states is lost. To address this problem, the concept of Neutral atoms [9] has been introduced which allows for longer coherence time. In another approach, to control de-coherence caused due to the thermal vibrations, the use of diamond qubits [10] structure has been developed. To make the quantum circuits more efficient, fault-tolerant implementation [11] using quantum error correction codes such as Surface code and Steane code also has been investigated.