Related papers: Fault-tolerant Compass Codes
Information obtained from noise characterization of a quantum device can be used in classical decoding algorithms to improve the performance of quantum error-correcting codes. Focusing on the surface code under local (i.e. single-qubit)…
We numerically study coherent errors in surface codes on planar graphs, focusing on noise of the form of $Z$- or $X$-rotations of individual qubits. We find that, similarly to the case of incoherent bit- and phase-flips, a trade-off between…
We present a [[7, 1, 3]] quantum error-correcting code that is able to achieve fault-tolerant syndrome measurement using one ancillary qubit per stabilizer for an error model of independent single-qubit Pauli errors. All single-qubit Pauli…
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information…
Different choices of quantum error-correcting codes can reduce the demands on the physical hardware needed to build a quantum computer. To achieve the full potential of a code, we must develop practical decoding algorithms that can correct…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
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…
Implementing algorithms on a fault-tolerant quantum computer will require fast decoding throughput and latency times to prevent an exponential increase in buffer times between the applications of gates. In this work we begin by quantifying…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…
We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a…
In order to build a scalable quantum computer error correction will be required to reduce the impact of errors. Implementing error correction in the framework of measurement based computation manifests itself as the construction of fault…
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,…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
There are several models of quantum computation which exhibit shared fundamental fault-tolerance properties. This article makes commonalities explicit by presenting these different models in a unifying framework based on the ZX calculus. We…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is…
In this work, we develop an efficient decoding method for graph codes, a class of stabilizer quantum error-correcting codes constructed from graph states. While optimal decoding is generally NP-hard, we propose a faster decoder exploiting…
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…
With quantum devices rapidly approaching qualities and scales needed for fault tolerance, the validity of simplified error models underpinning the study of quantum error correction needs to be experimentally evaluated. In this work, we have…
Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these…