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Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes,…
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…
Toric surface codes are a class of error-correcting codes coming from a lattice polytope defining a two-dimensional toric variety. Previous authors have mostly completed classifications of these toric surface codes with dimension up to $k =…
We analyze the properties of a 2D topological code derived by concatenating the [[4, 2, 2]] code with the toric/surface code, or alternatively by removing check operators from the 2D square-octagon or 4.8.8 color code. We show that the…
We construct toric codes on various high-dimensional manifolds. Assuming a conjecture in geometry we find families of quantum CSS stabilizer codes on $N$ qubits with logarithmic weight stabilizers and distance $N^{1-\epsilon}$ for any…
One of the leading quantum computing architectures is based on the two-dimensional (2D) surface code. This code has many advantageous properties such as a high error threshold and a planar layout of physical qubits where each physical qubit…
We build on recent work by B. Brown (Sci. Adv. 6, eaay4929 (2020)) to develop and simulate an explicit recipe for a just-in-time decoding scheme in three 3D surface codes, which can be used to implement a transversal (non-Clifford)…
Surface codes are a promising method of quantum error correction and the basis of many proposed quantum computation implementations. However, their efficient decoding is still not fully explored. Recently, approaches based on machine…
The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The…
Topological stabilizer codes, such as the toric and surface codes, are leading candidates for fault-tolerant quantum computation. While their decodability under stochastic noise has been extensively studied, the effects of coherent errors,…
Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation due to their robustness against errors and their local interactions between qubits. However, decoding these codes efficiently…
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
We still do not have perfect decoders for topological codes that can satisfy all needs of different experimental setups. Recently, a few neural network based decoders have been studied, with the motivation that they can adapt to a wide…
We study the robustness of 3D intrinsic topogical order under external perturbations by investigating the paradigmatic microscopic model, the 3D toric code in an external magnetic field. Exact dualities as well as variational calculations…
We compute the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates, when both qubit and measurement errors are present. By mapping the problem onto a…
We introduce a decoder for the 3D color code with boundaries, which is a variation of the restriction decoder introduced by Kubicka and Delfosse. Specifically, we adapt the lift procedure to efficiently find a correction on qubits adjacent…
We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC), which is a generalization of the stabilizer toric code. The 3D STC can be realized by measuring geometrically-local parity checks of weight at…