



@article {3295,
	title = {Qubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison},
	journal = {PRX Quantum},
	volume = {4},
	year = {2023},
	month = {6/14/2023},
	pages = {020342},
	abstract = {<p>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 that there are several bosonic codes and concatenation schemes to choose from, including the recently discovered Gottesman-Kitaev-Preskill (GKP)\&thinsp;\&ndash;\&thinsp;stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)] that allow protection of a logical bosonic mode from fluctuations of the conjugate variables of the mode. 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 or 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.</p>},
	doi = {10.1103/PRXQuantum.4.020342},
	url = {https://arxiv.org/abs/2209.04573},
	author = {Xu, Yijia and Wang, Yixu and Kuo, En-Jui and Victor V. Albert}
}
@article {3146,
	title = {Quantum state tomography via non-convex Riemannian gradient descent},
	year = {2022},
	month = {10/10/2022},
	abstract = {<p>The recovery of an unknown density matrix of large size requires huge computational resources. The recent Factored Gradient Descent (FGD) algorithm and its variants achieved state-of-the-art performance since they could mitigate the dimensionality barrier by utilizing some of the underlying structures of the density matrix. Despite their theoretical guarantee of a linear convergence rate, the convergence in practical scenarios is still slow because the contracting factor of the FGD algorithms depends on the condition number κ of the ground truth state. Consequently, the total number of iterations can be as large as O(κ\&minus;\&minus;\&radic;ln(1ε)) to achieve the estimation error ε. In this work, we derive a quantum state tomography scheme that improves the dependence on κ to the logarithmic scale; namely, our algorithm could achieve the approximation error ε in O(ln(1κε)) steps. The improvement comes from the application of the non-convex Riemannian gradient descent (RGD). The contracting factor in our approach is thus a universal constant that is independent of the given state. Our theoretical results of extremely fast convergence and nearly optimal error bounds are corroborated by numerical results.</p>},
	keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)},
	doi = {10.48550/ARXIV.2210.04717},
	url = {https://arxiv.org/abs/2210.04717},
	author = {Hsu, Ming-Chien and Kuo, En-Jui and Yu, Wei-Hsuan and Cai, Jian-Feng and Hsieh, Min-Hsiu}
}
