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We introduce and analyze a new type of decoding algorithm called General Color Clustering (GCC), based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under code capacity…

Quantum Physics · Physics 2017-11-20 Jacob Marks , Tomas Jochym-O'Connor , Vlad Gheorghiu

We introduce a fault-tolerant protocol for code concatenation of a generalized Shor code using a butterfly network architecture with high noise thresholds and low ancilla overhead to allow implementation on current devices. We develop a…

Quantum Physics · Physics 2025-11-03 Grace M. Sommers , Michael Foss-Feig , David Hayes , David A. Huse , Michael J. Gullans

We introduce a construction for protocols for fault-tolerant quantum computing based on code concatenation and transversal gates. These protocols can be interpreted as families of quantum circuits of low-weight stabilizer measurements…

Quantum Physics · Physics 2025-06-17 Daniel Litinski

Quantum Error Correction (QEC) is essential for future quantum computers due to its ability to exponentially suppress physical errors. The surface code is a leading error-correcting code candidate because of its local topological structure,…

Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an…

Quantum Physics · Physics 2024-12-23 Felix Thomsen , Markus S. Kesselring , Stephen D. Bartlett , Benjamin J. Brown

Vast numbers of qubits will be needed for large-scale quantum computing due to the overheads associated with error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density parity-check…

Quantum Physics · Physics 2022-05-24 Lawrence Z. Cohen , Isaac H. Kim , Stephen D. Bartlett , Benjamin J. Brown

We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic…

High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…

Quantum Physics · Physics 2026-01-15 Chao Zhang , Zipeng Wu , Jiahui Wu , Shilin Huang

Concatenated bosonic-stabilizer codes have recently gained prominence as promising candidates for achieving low-overhead fault-tolerant quantum computing in the long term. In such systems, analog information obtained from the syndrome…

Quantum Physics · Physics 2025-05-13 Shantom K. Borah , Asit K. Pradhan , Nithin Raveendran , Michele Pacenti , Bane Vasic

Quantum low-density parity-check (qLDPC) codes are a promising construction for drastically reducing the overhead of fault-tolerant quantum computing (FTQC) architectures. However, all of the known hardware implementations of these codes…

Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…

Quantum Physics · Physics 2024-09-06 Hayato Goto

Fault tolerant quantum error correction (QEC) networks are studied by a combination of numerical and approximate analytical treatments. The probability of failure of the recovery operation is calculated for a variety of CSS codes, including…

Quantum Physics · Physics 2009-11-07 Andrew M. Steane

Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that…

Information Theory · Computer Science 2010-01-15 Mayank Bakshi , Sidharth Jaggi , Michelle Effros

We study the use of triorthogonal codes for universal fault-tolerant quantum computation and propose two methods to circumvent the Eastin-Knill theorem, which prohibits any single quantum error-correcting code from supporting both…

Quantum Physics · Physics 2025-11-06 Dawei Jiao , Mahdi Bayanifar , Alexei Ashikhmin , Olav Tirkkonen

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

A major challenge in fault-tolerant quantum computation (FTQC) is to reduce both space overhead -- the large number of physical qubits per logical qubit -- and time overhead -- the long physical gate sequences per logical gate. We prove…

Quantum Physics · Physics 2024-12-06 Shiro Tamiya , Masato Koashi , Hayata Yamasaki

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

We analyze the resource overhead of recently proposed methods for universal fault-tolerant quantum computation using concatenated codes. Namely, we examine the concatenation of the 7-qubit Steane code with the 15-qubit Reed-Muller code,…

Quantum Physics · Physics 2017-06-20 Christopher Chamberland , Tomas Jochym-O'Connor , Raymond Laflamme

We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…

Quantum Physics · Physics 2010-06-01 Markus Grassl , Peter W. Shor , Bei Zeng

The promise of quantum computers hinges on the ability to scale to large system sizes, e.g., to run quantum computations consisting of more than 100 million operations fault-tolerantly. This in turn requires suppressing errors to levels…