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Dynamical stabilizer codes may offer a practical route to large-scale quantum computation. Such codes are defined by a schedule of error-detecting measurements, which allows for flexibility in their construction. In this work, we ask how…

High-fidelity decoding of quantum error correction codes relies on an accurate experimental model of the physical errors occurring in the device. Because error probabilities can depend on the context of the applied operations, the error…

Quantum Surface codes are a kind of quantum topological stabilizer codes whose stabilizers and qubits are geometrically related. Due to their special structures, surface codes have great potential to lead people to large-scale quantum…

Quantum Physics · Physics 2022-05-23 Yaping Yuan , Chung-Chin Lu

Recently, quantum error-correcting codes were proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit flip and phase flip errors. An example for a channel which…

Quantum Physics · Physics 2016-11-17 Pradeep Kiran Sarvepalli , Martin Roetteler , Andreas Klappenecker

The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic…

Quantum Physics · Physics 2026-04-03 Fernando Hernando , Gregorio Quintana-Ortí , Markus Grassl

We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated…

We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice…

Quantum Physics · Physics 2009-01-06 Zhuo Li , Li-Juan Xing

We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new…

Quantum Physics · Physics 2009-05-24 Markus Grassl , Andreas Klappenecker , Martin Roetteler

A major difficulty in quantum computation is the ability to implement fault tolerant computations, protecting information against undesired interactions with the environment. Stabiliser codes were introduced as a means to protect…

Quantum Physics · Physics 2025-12-17 Simeon Ball , Raven Zhang

Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…

Quantum Physics · Physics 2024-03-21 Arijit Mondal , Keshab K. Parhi

Quasi-twisted codes are used here as the classical ingredients in the so-called Construction X for quantum error-control codes. The construction utilizes nearly self-orthogonal codes to design quantum stabilizer codes. We expand the choices…

Quantum Physics · Physics 2024-12-30 Martianus Frederic Ezerman , Markus Grassl , San Ling , Ferruh Özbudak , Buket Özkaya

Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…

Quantum Physics · Physics 2026-04-17 Nico Meyer , Christopher Mutschler , Dominik Seuß , Andreas Maier , Daniel D. Scherer

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

A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…

Quantum Physics · Physics 2009-10-28 A. R. Calderbank , Peter W. Shor

Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…

Quantum Physics · Physics 2019-10-14 Joschka Roffe

Topological stabilizer codes with different spatial dimensions have complementary properties. Here I show that the spatial dimension can be switched using gauge fixing. Combining 2D and 3D gauge color codes in a 3D qubit lattice,…

Quantum Physics · Physics 2016-05-13 H. Bombin

Experimental realization of stabilizer-based quantum error correction (QEC) codes that would yield superior logical qubit performance is one of the formidable task for state-of-the-art quantum processors. A major obstacle towards realizing…

Quantum Physics · Physics 2022-03-14 I. A. Simakov , I. S. Besedin , A. V. Ustinov

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and…

Quantum Physics · Physics 2023-06-21 Yijia Xu , Yixu Wang , En-Jui Kuo , Victor V. Albert

The recently introduced detected-jump correcting quantum codes are capable of stabilizing qubit-systems against spontaneous decay processes arising from couplings to statistically independent reservoirs. These embedded quantum codes exploit…

Quantum Physics · Physics 2011-03-31 G. Alber , Th. Beth , Ch. Charnes , A. Delgado , M. Grassl , M. Mussinger

We examine the performance of the single-mode GKP code and its concatenation with the toric code for a noise model of Gaussian shifts, or displacement errors. We show how one can optimize the tracking of errors in repeated noisy error…

Quantum Physics · Physics 2019-04-02 Christophe Vuillot , Hamed Asasi , Yang Wang , Leonid P. Pryadko , Barbara M. Terhal