English
Related papers

Related papers: Kitaev's Z_d-Codes Threshold Estimates

200 papers

We introduce a family of 2D topological subsystem quantum error-correcting codes. The gauge group is generated by 2-local Pauli operators, so that 2-local measurements are enough to recover the error syndrome. We study the computational…

Quantum Physics · Physics 2010-03-04 H. Bombin

The general features of renormalization and the renormalization group in QED and in general quantum field theories in curved spacetime with additional Lorentz- and CPT-violating background fields are reviewed.

High Energy Physics - Phenomenology · Physics 2017-08-23 Ilya L. Shapiro

Discovering low-overhead quantum error-correcting codes is of significant interest for fault-tolerant quantum computation. For hardware capable of long-range connectivity, the bivariate bicycle codes offer significant overhead reduction…

Quantum Physics · Physics 2026-01-15 Jinkang Guo , Yifan Hong , Adam Kaufman , Andrew Lucas

In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling…

Quantum Physics · Physics 2013-05-29 Su-Peng Kou

To implement fault-tolerant quantum computation with continuous variables, the Gottesman-Kitaev-Preskill (GKP) qubit has been recognized as an important technological element. However,it is still challenging to experimentally generate the…

Quantum Physics · Physics 2018-05-29 Kosuke Fukui , Akihisa Tomita , Atsushi Okamoto , Keisuke Fujii

Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be…

Quantum Physics · Physics 2016-06-30 Christopher Chamberland , Tomas Jochym-O'Connor , Raymond Laflamme

Biased-noise qubits, in which one type of error (e.g. $X$- and $Y$-type errors) is significantly suppressed relative to the other (e.g. $Z$-type errors), can significantly reduce the overhead of quantum error correction. Codes such as the…

Quantum Physics · Physics 2026-01-19 Peter Shanahan , Diego Ruiz

To date, a great deal of attention has focused on characterizing the performance of quantum error correcting codes via their thresholds, the maximum correctable physical error rate for a given noise model and decoding strategy. Practical…

Quantum Physics · Physics 2014-09-29 Fern H. E. Watson , Sean D. Barrett

We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our…

Quantum Physics · Physics 2007-05-23 Panos Aliferis , Daniel Gottesman , John Preskill

The code-capacity threshold of a scalable quantum error correcting stabilizer code can be expressed as a thermodynamic phase transition of a corresponding random-bond Ising model. Here we study the XY and XZZX surface codes under…

Quantum Physics · Physics 2024-09-11 Yinzi Xiao , Basudha Srivastava , Mats Granath

In this work we study the single-shot performance of higher dimensional hypergraph product codes decoded using belief-propagation and ordered-statistics decoding [Panteleev and Kalachev, 2021]. We find that decoding data qubit and syndrome…

Quantum Physics · Physics 2023-06-28 Oscar Higgott , Nikolas P. Breuckmann

Kitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum error-correcting code. We offer an explicit proof that this…

Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…

Quantum Physics · Physics 2018-10-23 Ben Criger , Imran Ashraf

Encoding quantum information in a quantum error correction (QEC) code enhances protection against errors. Imperfection of quantum devices due to decoherence effects will limit the fidelity of quantum gate operations. In particular, neutral…

Quantum Physics · Physics 2026-03-03 J. J. Postema , S. J. J. M. F. Kokkelmans

The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate…

Quantum Physics · Physics 2014-02-18 Ashley M. Stephens

Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes are leading candidates for…

Quantum Physics · Physics 2022-10-12 Pedro Parrado-Rodríguez , Manuel Rispler , Markus Müller

We include the full second-order corrections to the static QCD potential in the analysis of the ttbar threshold cross section. There is an unexpectedly large difference between the QCD potential improved by the renormalization-group…

High Energy Physics - Phenomenology · Physics 2009-10-31 M. Jezabek , J. H. Kuhn , M. Peter , Y. Sumino , T. Teubner

We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We develop a customised decoder to process the information about the likely…

Quantum Physics · Physics 2019-12-11 Xiaosi Xu , Qi Zhao , Xiao Yuan , Simon C. Benjamin

This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…

Quantum Physics · Physics 2015-04-08 Keisuke Fujii

This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or…

Quantum Physics · Physics 2007-05-23 Subhash Kak