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We construct a new family of permutationally invariant codes that correct $t$ Pauli errors for any $t\ge 1$. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction…

Quantum Physics · Physics 2024-05-01 Arda Aydin , Max A. Alekseyev , Alexander Barg

Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum…

Quantum Physics · Physics 2022-03-17 Patricio Fuentes

Stabilizer states are extensively studied in quantum information theory for their structures based on the Pauli group. Calderbank-Shor-Steane (CSS) stabilizer states are of particular importance in their application to fault-tolerant…

Quantum Physics · Physics 2017-04-05 Ching-Yi Lai , Yi-Cong Zheng , Todd A. Brun

We apply the recent graphical framework of "Quantum Lego" to XP stabilizer codes where the stabilizer group is generally non-Abelian. We show that the idea of operator matching continues to hold for such codes and is sufficient for…

Quantum Physics · Physics 2025-10-08 Ruohan Shen , Yixu Wang , ChunJun Cao

In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat…

Information Theory · Computer Science 2018-04-04 Jihao Fan , Min-Hsiu Hsieh , Hanwu Chen , He Chen , Yonghui Li

We examine the efficiency of pure, nondegenerate quantum-error correction-codes for Pauli channels. Specifically, we investigate if correction of multiple errors in a block is more efficient than using a code that only corrects one error…

Quantum Physics · Physics 2009-05-19 Gunnar Bjork , Jonas Almlof , Isabel Sainz

Characterizing how quantum error correction circuits behave under realistic hardware noise is essential for testing the premises that enable scalable fault tolerance. Logical error rates conditioned on syndrome outcomes are needed to enable…

Quantum Physics · Physics 2025-08-12 Matthew Girling , Ben Criger , Cristina Cirstoiu

Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…

Information Theory · Computer Science 2016-02-05 Alexei Ashikhmin , Ching-Yi Lai , Todd Brun

We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…

Quantum Physics · Physics 2007-09-13 Sixia Yu , Qing Chen , C. H. Oh

We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string…

Quantum Physics · Physics 2019-05-31 Guillaume Dauphinais , Laura Ortiz , Santiago Varona , Miguel Angel Martin-Delgado

Quantum error correction requires the use of error syndromes derived from measurements that may be unreliable. Recently, quantum data-syndrome (QDS) codes have been proposed as a possible approach to protect against both data and syndrome…

Quantum Physics · Physics 2023-02-06 Andrew Nemec

Surface codes are the most promising candidates for fault-tolerant quantum computation. Single qudit errors are typically modelled as Pauli operators, to which general errors are converted via randomizing methods. In this Letter, we…

Quantum Physics · Physics 2023-11-28 Yue Ma , Michael Hanks , M. S. Kim

Stabilizer circuits play an important role in quantum error correction protocols, and will be vital for ensuring fault tolerance in future quantum hardware. While stabilizer circuits are defined on the Clifford generating set, {H, S, CX},…

Quantum Physics · Physics 2024-05-01 Brendan Reid

Transformations which convert between Fermionic modes and qubit operations have become a ubiquitous tool in quantum algorithms for simulating systems. Similarly, collections of Pauli operators might be obtained from solutions of non-local…

Quantum Physics · Physics 2023-06-28 Lane G. Gunderman

We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism and classical error correction, and…

Quantum Physics · Physics 2010-02-20 Isaac Kremsky , Min-Hsiu Hsieh , Todd A. Brun

Characterization of quantum devices generates insights into their sources of disturbances. State-of-the-art characterization protocols often focus on incoherent noise and eliminate coherent errors when using Pauli or Clifford twirling…

Quantum Physics · Physics 2025-03-18 Noah Kaufmann , Ivan Rojkov , Florentin Reiter

A key task in quantum computation is the application of a sequence of gates implementing a specific unitary operation. However, the decomposition of an arbitrary unitary operation into simpler quantum gates is a nontrivial problem. Here we…

Quantum Physics · Physics 2016-03-23 Swathi S. Hegde , K. R. Koteswara Rao , T. S. Mahesh

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…

Quantum Physics · Physics 2017-10-04 Muyuan Li , Mauricio Gutiérrez , Stanley E. David , Alonzo Hernandez , Kenneth R. Brown

The calculating of the coherent information is a fundamental step in obtaining the quantum capacity of a quantum channel. We introduce orthogonal and complete code basis to evaluate the coherent information per channel use when the input is…

Quantum Physics · Physics 2010-07-28 Xiao-yu Chen , Li-zhen Jiang

Quantum error-correcting codes, such as subspace, subsystem, and Floquet codes, are typically constructed within the stabilizer formalism, which does not fully capture the idea of fault-tolerance needed for practical quantum computing…

Quantum Physics · Physics 2025-11-12 Peter-Jan H. S. Derks , Alex Townsend-Teague , Ansgar G. Burchards , Jens Eisert