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Paper 1

Mitigating Temporal Fragility in the XY Surface Code

Pei-Kai Tsai, Yue Wu, Shruti Puri

Year

2023

Journal

arXiv preprint

DOI

arXiv:2310.17697

arXiv

2310.17697

An important outstanding challenge that must be overcome in order to fully utilize the XY surface code for correcting biased Pauli noise is the phenomena of fragile temporal boundaries that arise during the standard logical state preparation and measurement protocols. To address this challenge we propose a new logical state preparation protocol based on locally entangling qubits into small Greenberger-Horne-Zeilinger-like states prior to making the stabilizer measurements that place them in the XY-code state. We prove that in this new procedure $O(\sqrt{n})$ high-rate errors along a single lattice boundary can cause a logical failure, leading to an almost quadratic reduction in the number of fault-configurations compared to the standard state-preparation approach. Moreover, the code becomes equivalent to a repetition code for high-rate errors, guaranteeing a 50% code-capacity threshold during state preparation for infinitely biased noise. With a simple matching decoder we confirm that our preparation protocol outperforms the standard one in terms of both threshold and logical error rate in the fault-tolerant regime where measurements are unreliable and at experimentally realistic biases. We also discuss how our state-preparation protocol can be inverted for similar fragile-boundary-mitigated logical-state measurement.

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Paper 2

Qubit-oscillator concatenated codes: decoding formalism & code comparison

Yijia Xu, Yixu Wang, En-Jui Kuo, Victor V. Albert

Year

2022

Journal

arXiv preprint

DOI

arXiv:2209.04573

arXiv

2209.04573

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and concatenation schemes to choose from, including the recently discovered GKP-stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)}] that allow protection of a logical bosonic mode from fluctuations of the mode's conjugate variables. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog/Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing, and formulate qudit versions of GKP-stabilizer codes.

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