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Article Dans Une Revue Physical Review A Année : 2024

Factory-based fault-tolerant preparation of quantum polar codes encoding one logical qubit

Résumé

A fault-tolerant way to prepare logical code-states of $Q_1$ codes, i:e:, quantum polar codes encoding one qubit, has been recently proposed. The fault tolerance therein is guaranteed with the help of an error detection gadget, where if an error is detected during the preparation, one declares a preparation failure and discards entirely the preparation. Due to error detection, the preparation is probabilistic, whose success rate, referred to as the preparation rate, decreases rapidly with the codelength, hence preventing the preparation of code-states of large codelengths. In this paper, to improve the preparation rate, we consider a factory preparation of $Q_1$ code-states, where one attempts to prepare several copies of $Q_1$ code-states in parallel. With the help of an extra scheduling step, we can avoid discarding the preparation entirely, every time an error is detected, hence, achieving an increased preparation rate in turn. We further provide a theoretical method to estimate preparation and logical error rates of the $Q_1$ codes, prepared using factory preparation, which is shown to tightly fit the Monte-Carlo simulation based numerical results. Therefore, our theoretical method is useful for providing estimates for large code-lengths, where Monte-Carlo simulations are practically not feasible. Our numerical results, for a circuit-level depolarizing noise model, indicate that the preparation rate increases significantly, especially for large $N$. For example, for $N$ = 256, it increases from 0.02% to 27% for a practically interesting physical error rate of $p$ = 10$^{-3}$. Remarkably, a $Q_1$ code of length $N$ = 256 achieves logical error rates around 10$^{-11}$ and 10$^{-15}$ for the physical error rates of $p$ = 10$^{-3}$ and $p$ = 3 X 10$^{-4}$, respectively. This corresponds to an improvement of about three orders of magnitude compared to a surface code with similar length and minimum distance, thus showing the promise of the proposed scheme for large-scale fault-tolerant quantum computing.
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Dates et versions

hal-04647822 , version 1 (26-07-2024)

Identifiants

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Ashutosh Goswami, Mehdi Mhalla, Valentin Savin. Factory-based fault-tolerant preparation of quantum polar codes encoding one logical qubit. Physical Review A, 2024, 110 (1), pp.012438. ⟨10.1103/PhysRevA.110.012438⟩. ⟨hal-04647822⟩
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