Compare Papers

Paper 1

Tailoring three-dimensional topological codes for biased noise

Eric Huang, Arthur Pesah, Christopher T. Chubb, Michael Vasmer, Arpit Dua

Year

2022

Journal

arXiv preprint

DOI

arXiv:2211.02116

arXiv

2211.02116

Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for several advantages including a transversal implementation of non-Clifford logical gates, single-shot decoding strategies, parallelized decoding in the case of fracton codes as well as construction of fractal lattice codes. Motivated by this, we tailor 3D topological codes for enhanced storage performance under biased Pauli noise. We present Clifford deformations of various 3D topological codes, such that they exhibit a threshold error rate of $50\%$ under infinitely biased Pauli noise. Our examples include the 3D surface code on the cubic lattice, the 3D surface code on a checkerboard lattice that lends itself to a subsystem code with a single-shot decoder, the 3D color code, as well as fracton models such as the X-cube model, the Sierpinski model and the Haah code. We use the belief propagation with ordered statistics decoder (BP-OSD) to study threshold error rates at finite bias. We also present a rotated layout for the 3D surface code, which uses roughly half the number of physical qubits for the same code distance under appropriate boundary conditions. Imposing coprime periodic dimensions on this rotated layout leads to logical operators of weight $O(n)$ at infinite bias and a corresponding $\exp[-O(n)]$ subthreshold scaling of the logical failure rate, where $n$ is the number of physical qubits in the code. Even though this scaling is unstable due to the existence of logical representations with $O(1)$ low-rate Pauli errors, the number of such representations scales only polynomially for the Clifford-deformed code, leading to an enhanced effective distance.

Open paper

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.

Open paper