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We show how to perform a fault-tolerant universal quantum computation in 2D architectures using only transversal unitary operators and local syndrome measurements. Our approach is based on a doubled version of the 2D color code. It enables…

Quantum Physics · Physics 2015-09-11 Sergey Bravyi , Andrew Cross

Quantum circuits implementing fault-tolerant quantum error correction (QEC) for the three qubit bit-flip code and five-qubit code are studied. To describe the effect of noise, we apply a model based on a generalized effective Hamiltonian…

Quantum Physics · Physics 2016-09-08 Y. C. Cheng , R. J. Silbey

We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest…

Quantum Physics · Physics 2013-05-29 A. J. F. Hayes , H. L. Haselgrove , Alexei Gilchrist , T. C. Ralph

We prove by construction that the Bravyi-Poulin-Terhal bound on the spatial density of stabilizer codes does not generalize to stabilizer circuits. To do so, we construct a fault tolerant quantum computer with a coding rate above 5% and…

Quantum Physics · Physics 2025-02-25 Craig Gidney , Thiago Bergamaschi

We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…

Quantum Physics · Physics 2011-03-31 Runyao Duan , Markus Grassl , Zhengfeng Ji , Bei Zeng

Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…

Quantum Physics · Physics 2023-12-01 Jon Nelson , Gregory Bentsen , Steven T. Flammia , Michael J. Gullans

The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…

Quantum Physics · Physics 2016-05-10 Marco Tomamichel , Mario Berta , Joseph M. Renes

Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…

Quantum Physics · Physics 2025-01-10 Lane G. Gunderman

Quantum error correction (QEC) is often implemented on hardware that experiences biased noise, where dephasing errors occur more frequently than other errors. This has motivated many recent efforts to develop bias-tailored QEC codes, such…

Quantum Physics · Physics 2026-05-28 Arianna Meinking , Julie Campos , Kenneth R. Brown

We introduce rainbow codes, a novel class of quantum error correcting codes generalising colour codes and pin codes. Rainbow codes can be defined on any $D$-dimensional simplicial complex that admits a valid $(D + 1)$-colouring of its…

Quantum Physics · Physics 2025-12-16 Thomas R. Scruby , Arthur Pesah , Mark Webster

To tackle combinatorial optimization problems using an Ising machine, the objective function and constraints must be mapped onto a quadratic unconstrained binary optimization (QUBO) model. While QUBO involves binary variables, combinatorial…

Statistical Mechanics · Physics 2025-01-22 Shuta Kikuchi , Kotaro Takahashi , Shu Tanaka

Noise poses a challenge for any real-world implementation in quantum information science. The theory of quantum error correction deals with this problem via methods to encode and recover quantum information in a way that is resilient…

Quantum Physics · Physics 2009-09-10 Kurt M. Schreiter , Aron Pasieka , Rainer Kaltenbaek , Kevin J. Resch , David W. Kribs

Fault-tolerant capacities quantify the ability of a quantum channel to reliably transmit information when every component of the encoding and decoding procedure is noisy. Earlier work analyzed achievable communication rates under such noise…

Quantum Physics · Physics 2026-02-11 Paula Belzig , Hayata Yamasaki

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

It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…

Quantum Physics · Physics 2009-10-30 Adriano Barenco , Todd A. Brun , Ruediger Schack , Tim Spiller

Noise-biased qubits are a promising route toward significantly reducing the hardware overhead associated with quantum error correction. The squeezed cat code, a non-local encoding in phase space based on squeezed coherent states, is an…

Quantum Physics · Physics 2023-04-11 Timo Hillmann , Fernando Quijandría

Laboratory hardware is rapidly progressing towards a state where quantum error-correcting codes can be realised. As such, we must learn how to deal with the complex nature of the noise that may occur in real physical systems. Single qubit…

Quantum Physics · Physics 2019-04-10 Naomi H. Nickerson , Benjamin J. Brown

The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at…

Quantum Physics · Physics 2015-06-26 Lev Ioffe , Marc Mezard

We study error correction type protocols in which a quantum channel encodes logical information into an enlarged Hilbert space. Specifically, we consider channels realized by one dimensional random noisy quantum circuits with spatially…

Quantum Physics · Physics 2026-03-24 Arman Sauliere , Guglielmo Lami , Pedro Ribeiro , Andrea De Luca , Jacopo De Nardis

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…

Quantum Physics · Physics 2011-08-10 Ruben S. Andrist , Helmut G. Katzgraber , H. Bombin , M. A. Martin-Delgado