scholarly journals Digital System Design for Quantum Error Correction Codes

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Othman O. Khalifa ◽  
Nur Amirah bt Sharif ◽  
Rashid A Saeed ◽  
S. Abdel-Khalek ◽  
Abdulaziz N. Alharbi ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
System Design ◽  
Error Correction ◽  
Quantum Channel ◽  
Quantum Error Correction ◽  
Digital System ◽  
Error Correction Codes ◽  
Error Correction Code ◽  
Digital System Design ◽  
Quantum Error

Quantum computing is a computer development technology that uses quantum mechanics to perform the operations of data and information. It is an advanced technology, yet the quantum channel is used to transmit the quantum information which is sensitive to the environment interaction. Quantum error correction is a hybrid between quantum mechanics and the classical theory of error-correcting codes that are concerned with the fundamental problem of communication, and/or information storage, in the presence of noise. The interruption made by the interaction makes transmission error during the quantum channel qubit. Hence, a quantum error correction code is needed to protect the qubit from errors that can be caused by decoherence and other quantum noise. In this paper, the digital system design of the quantum error correction code is discussed. Three designs used qubit codes, and nine-qubit codes were explained. The systems were designed and configured for encoding and decoding nine-qubit error correction codes. For comparison, a modified circuit is also designed by adding Hadamard gates.

scholarly journals Entropy of a Quantum Error Correction Code

2008 ◽  
Vol 15 (04) ◽  
pp. 329-343 ◽  
Author(s):  
David W. Kribs ◽  
Aron Pasieka ◽  
Karol Życzkowski
Keyword(s):  
Error Correction ◽  
Detailed Analysis ◽  
Quantum Channel ◽  
Error Correcting Codes ◽  
Quantum Error Correction ◽  
Maximal Entropy ◽  
Initial State ◽  
Error Correction Code ◽  
Quantum Error ◽  
Decoherence Free Subspaces

We define and investigate the notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme conditions and the entropy exchange computed with respect to any initial state supported on the code. In general the entropy of a code can be viewed as a measure of how close it is to the minimal entropy case, which is given by unitarily correctable codes (including decoherence-free subspaces), or the maximal entropy case, which from dynamical Choi matrix considerations corresponds to non-degenerate codes. We consider several examples, including a detailed analysis of the case of binary unitary channels, and we discuss an extension of the entropy to operator quantum error correcting subsystem codes.

scholarly journals From Quantum Codes to Gravity: A Journey of Gravitizing Quantum Mechanics

Universe ◽  
2021 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Chun-Jun Cao
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Error Correction ◽  
Quantum Error Correction ◽  
Quantum States ◽  
Quantum Codes ◽  
Error Correction Codes ◽  
Recent Approach ◽  
Tensor Network ◽  
Quantum Error

In this note, I review a recent approach to quantum gravity that “gravitizes” quantum mechanics by emerging geometry and gravity from complex quantum states. Drawing further insights from tensor network toy models in AdS/CFT, I propose that approximate quantum error correction codes, when re-adapted into the aforementioned framework, also have promise in emerging gravity in near-flat geometries.

scholarly journals Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes

2021 ◽  
Author(s):  
Dongsheng Wang ◽  
Yunjiang Wang ◽  
Ningping Cao ◽  
Bei Zeng ◽  
Raymond Lafflamme
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Fault Tolerant ◽  
Valence Bond ◽  
Quantum Error Correction ◽  
Quantum Codes ◽  
Error Correction Codes ◽  
Exact Quantum ◽  
Valence Bond Solid ◽  
Quantum Error

Abstract In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes (``quasi codes''). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi error-correction theory using quantum instrument, the notions of quasi universality, quasi code distances, and quasi thresholds, etc. We find a wide class of quasi codes which are called valence-bond-solid codes, and we use them as concrete examples to demonstrate QEQ computation.

scholarly journals Approximating Decoherence Processes for the Design and Simulation of Quantum Error Correction Codes on Classical Computers

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 172623-172643
Author(s):  
Josu Etxezarreta Martinez ◽  
Patricio Fuentes ◽  
Pedro M. Crespo ◽  
J. Garcia-Frias
Keyword(s):  
Error Correction ◽  
Quantum Error Correction ◽  
Error Correction Codes ◽  
Quantum Error Correction Codes ◽  
Quantum Error

scholarly journals Decoding surface code with a distributed neural network–based decoder

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Savvas Varsamopoulos ◽  
Koen Bertels ◽  
Carmen G. Almudever
Keyword(s):  
Neural Network ◽  
Renormalization Group ◽  
Error Correction ◽  
Quantum Error Correction ◽  
Noise Model ◽  
Error Correction Codes ◽  
Exponential Increase ◽  
Main Challenge ◽  
Surface Code ◽  
Quantum Error

Abstract There has been a rise in decoding quantum error correction codes with neural network–based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger code distances due to an exponential increase of the error syndrome space. Note that successfully decoding the surface code under realistic noise assumptions will limit the size of the code to less than 100 qubits with current neural network–based decoders. Such a problem can be tackled by a distributed way of decoding, similar to the renormalization group (RG) decoders. In this paper, we introduce a decoding algorithm that combines the concept of RG decoding and neural network–based decoders. We tested the decoding performance under depolarizing noise with noiseless error syndrome measurements for the rotated surface code and compared against the blossom algorithm and a neural network–based decoder. We show that a similar level of decoding performance can be achieved between all tested decoders while providing a solution to the scalability issues of neural network–based decoders.

scholarly journals Quantum error-correction codes and absolutely maximally entangled states

2020 ◽  
Vol 101 (4) ◽  
Author(s):  
Paweł Mazurek ◽  
Máté Farkas ◽  
Andrzej Grudka ◽  
Michał Horodecki ◽  
Michał Studziński
Keyword(s):  
Error Correction ◽  
Quantum Error Correction ◽  
Entangled States ◽  
Error Correction Codes ◽  
Maximally Entangled States ◽  
Quantum Error Correction Codes ◽  
Quantum Error
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