Quantum Error Correction and Its Application

2016 ◽  
pp. 121-162
Author(s):  
Masahito Hayashi
Keyword(s):  
Error Correction ◽  
Quantum Error Correction ◽  
Quantum Error

Quantum Error Correction Code Scheme used for Homomorphic Encryption like Quantum Computation

2019 ◽  
Vol 19 (3) ◽  
pp. 61-70
Author(s):  
Il Kwon Sohn ◽  
◽  
Jonghyun Lee ◽  
Wonhyuk Lee ◽  
Woojin Seok ◽  
...  
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Homomorphic Encryption ◽  
Quantum Error Correction ◽  
Code Scheme ◽  
Error Correction Code ◽  
Quantum Error

scholarly journals 2-designs and redundant syndrome extraction for quantum error correction

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Vickram N. Premakumar ◽  
Hele Sha ◽  
Daniel Crow ◽  
Eric Bach ◽  
Robert Joynt
Keyword(s):  
Error Correction ◽  
Quantum Error Correction ◽  
Quantum Error

scholarly journals Exponential suppression of bit or phase errors with cyclic error correction

Nature ◽  
2021 ◽  
Vol 595 (7867) ◽  
pp. 383-387
Author(s):  
◽  
Zijun Chen ◽  
Kevin J. Satzinger ◽  
Juan Atalaya ◽  
Alexander N. Korotkov ◽  
...  
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Fault Tolerant ◽  
Error Rates ◽  
Quantum Error Correction ◽  
Superconducting Qubits ◽  
Two Dimensional ◽  
Logical Error ◽  
Quantum Error ◽  
Logical Qubit

AbstractRealizing the potential of quantum computing requires sufficiently low logical error rates1. Many applications call for error rates as low as 10−15 (refs. 2–9), but state-of-the-art quantum platforms typically have physical error rates near 10−3 (refs. 10–14). Quantum error correction15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.

scholarly journals Impact of correlations and heavy tails on quantum error correction

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
B. D. Clader ◽  
Colin J. Trout ◽  
Jeff P. Barnes ◽  
Kevin Schultz ◽  
Gregory Quiroz ◽  
...  
Keyword(s):  
Error Correction ◽  
Heavy Tails ◽  
Quantum Error Correction ◽  
Quantum Error

scholarly journals Quantum error correction and entanglement spectrum in tensor networks

2019 ◽  
Vol 99 (2) ◽  
Author(s):  
Yi Ling ◽  
Yuxuan Liu ◽  
Zhuo-Yu Xian ◽  
Yikang Xiao
Keyword(s):  
Error Correction ◽  
Quantum Error Correction ◽  
Entanglement Spectrum ◽  
Tensor Networks ◽  
Quantum Error

Fluxon-controlled quantum computer

2016 ◽  
Vol 14 (07) ◽  
pp. 1650040
Author(s):  
Toshiyuki Fujii ◽  
Shigemasa Matsuo ◽  
Noriyuki Hatakenaka
Keyword(s):  
Error Correction ◽  
Quantum Computer ◽  
Quantum Error Correction ◽  
Capacitively Coupled ◽  
Swap Gate ◽  
Flux Qubits ◽  
Superconducting Flux Qubits ◽  
Quantum Error ◽  
At Home

We propose a fluxon-controlled quantum computer incorporated with three-qubit quantum error correction using special gate operations, i.e. joint-phase and SWAP gate operations, inherent in capacitively coupled superconducting flux qubits. The proposed quantum computer acts exactly like a knitting machine at home.

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