Fault-tolerant wormhole routing in two-dimensional mesh networks with convex faults

This paper mainly focuses on routing in two-dimensional mesh networks. We propose a novel faulty block model, which is cracky rectangular block, for fault-tolerant adaptive routing. All the faulty nodes and faulty links are surrounded in this type of block, which is a convex structure, in order to avoid routing livelock. Additionally, the model constructs the interior spanning forest for each block in order to keep in touch with the nodes inside of each block. The procedure for block construction is dynamically and totally distributed. The construction algorithm is simple and ease of implementation. And this is a fully adaptive block which will dynamically adjust its scale in accordance with the situation of networks, either the fault emergence or the fault recovery, without shutdown of the system. Based on this model, we also develop a distributed fault-tolerant routing algorithm. Then we give the formal proof for this algorithm to guarantee that messages will always reach their destinations if and only if the destination nodes keep connecting with these mesh networks. So the new model and routing algorithm maximize the availability of the nodes in networks. This is a noticeable overall improvement of fault tolerability of the system.

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Fault-tolerant routing in two-dimensional mesh networks with less-restricted fault patterns

Proceedings 2001 Pacific Rim International Symposium on Dependable Computing ◽

10.1109/prdc.2001.992687 ◽

2002 ◽

Cited By ~ 1

Author(s):

Sheng-De Wang ◽

Po-Hwa Sui

Keyword(s):

Mesh Networks ◽

Fault Tolerant ◽

Two Dimensional

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Exponential suppression of bit or phase errors with cyclic error correction

Nature ◽

10.1038/s41586-021-03588-y ◽

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.

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