scholarly journals Flag Fault-Tolerant Error Correction for any Stabilizer Code

PRX Quantum ◽  
2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Rui Chao ◽  
Ben W. Reichardt
Keyword(s):  
Error Correction ◽  
Fault Tolerant ◽  
Stabilizer Code

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 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 SOFTWARE IMPLEMENTED HARDWARE-TRANSIENT FAULTS DETECTION

2014 ◽  
pp. 26-30
Author(s):  
Goutam Kumar Saha
Keyword(s):  
Error Correction ◽  
Fault Tolerant ◽  
Low Cost ◽  
Transient Faults ◽  
Fault Tolerant System ◽  
Cost Approach ◽  
Run Time ◽  
Commodity Systems ◽  
Fail Safe ◽  
Register Error

This paper examines a software implemented self-checking technique that is capable of detecting processorregisters' hardware-transient faults. The proposed approach is intended to detect run-time transient bit-errors in memory and processor status register. Error correction is not considered here. However, this low-cost approach is intended to be adopted in commodity systems that use ordinary off-the-shelf microprocessors, for the purpose of operational faults detection towards gaining fail-safe kind of fault tolerant system.

Locality bounds on Hamiltonians for stabilizer codes

2009 ◽  
Vol 9 (5&6) ◽  
pp. 487-499
Author(s):  
S.S. Bullock ◽  
D.P. O'Leary
Keyword(s):  
Quantum Computing ◽  
Error Correction ◽  
Energy Gap ◽  
Stabilizer Codes ◽  
Adiabatic Quantum Computing ◽  
Group A ◽  
Stabilizer Code ◽  
Stabilizer Group ◽  
The Cost ◽  
Insight Into

In this paper, we study the complexity of Hamiltonians whose groundstate is a stabilizer code. We introduce various notions of $k$-locality of a stabilizer code, inherited from the associated stabilizer group. A choice of generators leads to a Hamiltonian with the code in its groundspace. We establish bounds on the locality of any other Hamiltonian whose groundspace contains such a code, whether or not its Pauli tensor summands commute. Our results provide insight into the cost of creating an energy gap for passive error correction and for adiabatic quantum computing. The results simplify in the cases of XZ-split codes such as Calderbank-Shor-Steane stabilizer codes and topologically-ordered stabilizer codes arising from surface cellulations.

A General Framework of Algorithm-Based Fault Tolerance Technique for Computing Systems

2014 ◽  
pp. 1-21 ◽  
Author(s):  
Hodjatollah Hamidi
Keyword(s):  
Fault Tolerance ◽  
Error Correction ◽  
General Framework ◽  
Fault Tolerant ◽  
Convolutional Code ◽  
Numerical Algorithms ◽  
Convolutional Codes ◽  
Computing Systems ◽  
Specific Level ◽  
Computing Paradigm

The Algorithm-Based Fault Tolerance (ABFT) approach transforms a system that does not tolerate a specific type of faults, called the fault-intolerant system, to a system that provides a specific level of fault tolerance, namely recovery. The ABFT philosophy leads directly to a model from which error correction can be developed. By employing an ABFT scheme with effective convolutional code, the design allows high throughput as well as high fault coverage. The ABFT techniques that detect errors rely on the comparison of parity values computed in two ways. The parallel processing of input parity values produce output parity values comparable with parity values regenerated from the original processed outputs and can apply convolutional codes for the redundancy. This method is a new approach to concurrent error correction in fault-tolerant computing systems. This chapter proposes a novel computing paradigm to provide fault tolerance for numerical algorithms. The authors also present, implement, and evaluate early detection in ABFT.

“Soft Error” Correction Method Based on Low Complexity Coding and Encoding Algorithm

2014 ◽  
Vol 556-562 ◽  
pp. 6344-6349
Author(s):  
Yan Kang Wei ◽  
Da Ming Wang ◽  
Wei Jia Cui
Keyword(s):  
Fault Tolerance ◽  
Error Correction ◽  
Fault Tolerant ◽  
Low Complexity ◽  
Correction Method ◽  
Block Codes ◽  
Decoding Algorithms ◽  
Linear Block Codes ◽  
Data Errors ◽  
Linear Block

SEU is one of the major challenges affecting the reliability of computers on-board. In this paper, we design a kind of encoding and decoding algorithms with a low complexity based on the data correction method to resolve the data stream errors SEU may bring. Firstly, we use the theory of linear block codes to analyze various methods of data fault tolerance, and then from the encoding and decoding principle of linear block codes we design a kind of encoding and decoding algorithms with a low complexity of linear block code, The fault-tolerant coding method can effectively correct single-bit data errors caused by SEU, with low fault-tolerant overhead. Fault injection experiments show that: this method can effectively correct data errors caused by single event upset. Compared with other common error detection or correction methods, error correction performance of this method is superior, while its fault tolerance cost is less.

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