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Paper 1
Scalable Postselection of Quantum Resources
J. Wilson Staples, Winston Fu, Jeff D. Thompson
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.08697
- arXiv
- 2603.08697
The large overhead imposed by quantum error correction is a critical challenge to the realization of quantum computers, and motivates searching for alternative error correcting codes and fault-tolerant circuit constructions. Postselection is a powerful tool that builds large programs out of probabilistically generated sub-circuits, and has been shown to increase the threshold of quantum error correction based on fusing fixed-size resource states or concatenated codes. In this work, we present an approach to lower the overhead of quantum computing using scalable postselection, based on directly postselecting sub-circuits with a size extensive in the code distance using decoder soft information. We introduce a metric, the partial gap, that estimates what the logical gap of a resource state will be after it is consumed, and show that postselection based on the partial gap leads to scalable improvements in the logical error rate. In the specific context of implementing logical gates via teleportation through a cluster state, we demonstrate that scalable postselection provides a $4\times$ reduction in the overhead per logical gate, at the same logical error probability.
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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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