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Constant Time Decoding of Quantum Expander Codes and Application to Fault-Tolerant Quantum Computation

Abstract : Fault tolerant quantum computation is a technique to perform reliable quantum computation using noisy components. In this context, quantum error correcting codes are used to keep the amount of errors under a sustainable threshold. One of the main problems of this field is to determine the minimum cost, in terms of memory and time, which is needed in order to transform an ideal quantum computation into a fault-tolerant one. In this PhD thesis, we show that the family of quantum expander codes and the small-set-flip decoder can be used in the construction of ref. [46] to produce a fault-tolerant quantum circuit with constant space overhead. The error correcting code family and the decoder that we study has been introduced in ref. [67] where an adversarial error model was examined. Based on the results of this article, we analyze quantum expander codes subjected to a stochastic error model which is relevant for fault-tolerant quantum computation [38], [37]. In addition, we show that the decoding algorithm can be parallelized to run in constant time. This is very relevant to prevent errors from accumulating while the decoding algorithm is running. Beyond the theoretical results described above, we perform a numerical analysis of quantum expander codes to measure their performance in practice [49]. The error model used during these simulations generates X and Z type errors on the qubits with an independent and identically distributed probability distribution. Our results are promising because they reveal that these constant rate codes have a decent threshold and good finite length performance.
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Contributor : Antoine Grospellier <>
Submitted on : Sunday, December 22, 2019 - 4:52:44 PM
Last modification on : Thursday, January 7, 2021 - 3:38:03 PM
Long-term archiving on: : Monday, March 23, 2020 - 3:41:32 PM


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  • HAL Id : tel-02422585, version 1


Antoine Grospellier. Constant Time Decoding of Quantum Expander Codes and Application to Fault-Tolerant Quantum Computation. Quantum Physics [quant-ph]. Sorbonne universités, 2019. English. ⟨tel-02422585v1⟩



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