scholarly journals Fault-tolerant quantum computing in the Pauli or Clifford frame with slow error diagnostics

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 43 ◽  
Author(s):  
Christopher Chamberland ◽  
Pavithran Iyer ◽  
David Poulin
Keyword(s):  
Quantum Computing ◽  
Error Correction ◽  
Quantum Computation ◽  
Fault Tolerant ◽  
Independent Interest ◽  
Optimal Correction ◽  
Decoding Algorithms ◽  
Gate Time

We consider the problem of fault-tolerant quantum computation in the presence of slow error diagnostics, either caused by measurement latencies or slow decoding algorithms. Our scheme offers a few improvements over previously existing solutions, for instance it does not require active error correction and results in a reduced error-correction overhead when error diagnostics is much slower than the gate time. In addition, we adapt our protocol to cases where the underlying error correction strategy chooses the optimal correction amongst all Clifford gates instead of the usual Pauli gates. The resulting Clifford frame protocol is of independent interest as it can increase error thresholds and could find applications in other areas of quantum computation.

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 Improved Resource State for Verifiable Blind Quantum Computation

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 996
Author(s):  
Qingshan Xu ◽  
Xiaoqing Tan ◽  
Rui Huang
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Fault Tolerant ◽  
Maximal Degree ◽  
Recent Advances ◽  
Quantum Computations ◽  
Blind Quantum Computation ◽  
Computation Graph ◽  
Resource State

Recent advances in theoretical and experimental quantum computing raise the problem of verifying the outcome of these quantum computations. The recent verification protocols using blind quantum computing are fruitful for addressing this problem. Unfortunately, all known schemes have relatively high overhead. Here we present a novel construction for the resource state of verifiable blind quantum computation. This approach achieves a better verifiability of 0.866 in the case of classical output. In addition, the number of required qubits is 2N+4cN, where N and c are the number of vertices and the maximal degree in the original computation graph, respectively. In other words, our overhead is less linear in the size of the computational scale. Finally, we utilize the method of repetition and fault-tolerant code to optimise the verifiability.

“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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