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arXiv · 1912.00829

Memory-assisted decoder for approximate Gottesman-Kitaev-Preskill codes

Kwok Ho Wan·Alex Neville·W. S. Kolthammer
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Abstract

We propose a quantum error correction protocol for continuous-variable finite-energy, approximate Gottesman-Kitaev-Preskill (GKP) states undergoing small Gaussian random displacement errors, based on the scheme of Glancy and Knill [Phys. Rev. A {\bf 73}, 012325 (2006)]. We show that combining multiple rounds of error-syndrome extraction with Bayesian estimation offers enhanced protection of GKP-encoded qubits over comparible single-round approaches. Furthermore, we show that the expected total displacement error incurred in multiple rounds of error followed by syndrome extraction is bounded by $2\sqrt{\pi}$. By recompiling the syndrome-extraction circuits, we show that all squeezing operations can be subsumed into auxiliary state preparation, reducing them to beamsplitter transformations and quadrature measurements.

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Kwok Ho Wan, Alex Neville, W. S. Kolthammer. 2019-12-02. Memory-assisted decoder for approximate Gottesman-Kitaev-Preskill codes. https://doi.org/10.1103/physrevresearch.2.043280

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