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Building reliable quantum computers requires protecting fragile quantum states from inevitable environmental noise and operational errors. While quantum error correction codes like the Steane $[\![7,1,3]\!]$ code provide elegant theoretical…

Quantum Physics · Physics 2026-01-14 Soham Bhadra , Diyansha Singh , Angana Chowdhury

We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…

Quantum Physics · Physics 2009-11-07 Eric Dennis , Alexei Kitaev , Andrew Landahl , John Preskill

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

Qudits can be described by a state vector in a $q$-dimensional Hilbert space, enabling a more extensive encoding and manipulation of information compared to qubits. This implies that conducting fault-tolerant quantum computations using…

Quantum Physics · Physics 2025-09-08 James Keppens , Quinten Eggerickx , Vukan Levajac , George Simion , Bart Sorée

A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing…

Quantum Physics · Physics 2024-07-29 Chris N. Self , Marcello Benedetti , David Amaro

A scheme for linear optical implementation of fault-tolerant quantum computation is proposed, which is based on an error-detecting code. Each computational step is mediated by transfer of quantum information into an ancilla system embedding…

Quantum Physics · Physics 2007-10-07 Jaeyoon Cho

Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and…

Information Theory · Computer Science 2024-11-11 Jifan Liang , Qianfan Wang , Lvzhou Li , Xiao Ma

I discuss how to perform fault-tolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when next-to-nearest-neighbor…

Quantum Physics · Physics 2015-06-26 Daniel Gottesman

Bosonic quantum error correction is a viable option for realizing error-corrected quantum information processing in continuous-variable bosonic systems. Various single-mode bosonic quantum error-correcting codes such as cat, binomial, and…

Quantum Physics · Physics 2020-01-14 Kyungjoo Noh , Christopher Chamberland

Fault-tolerant quantum computation traditionally incurs substantial resource overhead, with both qubit and time overheads scaling polylogarithmically with the size of the computation. While prior work by Gottesman showed that constant qubit…

Quantum Physics · Physics 2025-12-03 Matthias Christandl , Omar Fawzi , Ashutosh Goswami

Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…

Quantum Physics · Physics 2009-10-30 Emanuel Knill , Raymond Laflamme , Wojciech H. Zurek

The topological color code and the toric code are two leading candidates for realizing fault-tolerant quantum computation. Here we show that the color code on a $d$-dimensional closed manifold is equivalent to multiple decoupled copies of…

Quantum Physics · Physics 2015-09-02 Aleksander Kubica , Beni Yoshida , Fernando Pastawski

Instead of a quantum computer where the fundamental units are 2-dimensional qubits, we can consider a quantum computer made up of d-dimensional systems. There is a straightforward generalization of the class of stabilizer codes to…

Quantum Physics · Physics 2010-05-27 Daniel Gottesman

We consider the problem of fault-tolerant quantum computation in the presence of slow error diagnostics, either caused by measurement latencies or slow decoding algorithms. Our scheme offers a few improvements over previously existing…

Quantum Physics · Physics 2018-01-08 Christopher Chamberland , Pavithran Iyer , David Poulin

A major obstacle towards realizing a practical quantum computer is the noise that arises due to system-environment interactions. While it is very well known that quantum error correction (QEC) provides a way to protect against errors that…

Quantum Physics · Physics 2023-02-24 Akshaya Jayashankar

Decoherence of quantum states is a major hurdle towards scalable and reliable quantum computing. Lower decoherence (i.e., higher fidelity) can alleviate the error correction overhead and obviate the need for energy-intensive noise reduction…

Emerging Technologies · Computer Science 2019-04-10 Abdullah Ash Saki , Mahabubul Alam , Swaroop Ghosh

Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by…

Quantum error correction (QEC) entails the encoding of quantum information into a QEC code space, measuring error syndromes to properly locate and identify errors, and, if necessary, applying a proper recovery operation. Here we compare…

Quantum Physics · Physics 2015-05-28 Yaakov S. Weinstein

We report on the fault-tolerant operation of logical qubits on a neutral atom quantum computer, with logical performance surpassing physical performance for multiple circuits including Bell states (12x error reduction), random circuits…

The aim of this paper is to propose an alternative method to solve a Fault Tolerant Control problem. The model is a linear system affected by a disturbance term: this represents a large class of technological faulty processes. The goal is…

Optimization and Control · Mathematics 2010-11-15 Sophie M. Fosson