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Paper 1

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

Kwok Ho Wan, Alex Neville, W. S. Kolthammer

Year

2019

Journal

arXiv preprint

DOI

arXiv:1912.00829

arXiv

1912.00829

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 $2\sqrtπ$. 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.

Paper 2

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