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This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…

Quantum Physics · Physics 2020-01-24 Manabu Hagiwara , Ayumu Nakayama

Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…

Quantum Physics · Physics 2023-07-26 Adam Siegel , Armands Strikis , Thomas Flatters , Simon Benjamin

We considered the interaction of semiconductor quantum register with noisy environment leading to various types of qubit errors. We analysed both phase and amplitude decays during the process of electron-phonon interaction. The performance…

Quantum Physics · Physics 2015-04-10 Alexey A. Melnikov , Leonid E. Fedichkin

Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical…

Quantum Physics · Physics 2013-05-29 A. M. Stephens , Z. W. E. Evans

Quantum error correction (QEC) codes are traditionally defined and searched for without specifying the manner in which its syndrome extraction circuits are executed using elementary gates and measurements. We show how morphing circuits…

Quantum Physics · Physics 2026-04-22 Mackenzie H. Shaw , Barbara M. Terhal

We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…

Quantum Physics · Physics 2009-11-13 Rochus Klesse

Encoding quantum information in a quantum error correction (QEC) code offers protection against decoherence and enhances the fidelity of qubits and gate operations. One of the fundamental challenges of QEC is to construct codes with…

Quantum Physics · Physics 2026-05-01 Jasper Johannes Postema , Servaas J. J. M. F. Kokkelmans

We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…

Quantum Physics · Physics 2009-11-13 David Poulin

Quantum Error Correction (QEC) is the process of detecting and correcting errors in quantum systems, which are prone to decoherence and quantum noise. QEC is crucial for developing stable and highly accurate quantum computing systems,…

Quantum Physics · Physics 2024-12-31 Zihao Wang , Hao Tang

Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…

Quantum Physics · Physics 2026-05-22 Christopher Gerhard , Todd A. Brun

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

Quantum error correction (QEC) is essential for enabling quantum advantages, with decoding as a central algorithmic primitive. Owing to its importance and intrinsic difficulty, substantial effort has been made to QEC decoder design, among…

Quantum Physics · Physics 2026-05-13 Ge Yan , Shanchuan Li , Yuxuan Du

We propose and analyze a hierarchical quantum error correction (QEC) scheme that concatenates hypergraph product (HGP) codes with rotated surface codes, which is compatible with quantum computers with only nearest-neighbor interactions. The…

Quantum Physics · Physics 2025-06-26 Junichi Haruna , Keisuke Fujii

Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error…

Quantum Physics · Physics 2022-01-12 Davide Vodola , Manuel Rispler , Seyong Kim , Markus Müller

Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…

Quantum Physics · Physics 2025-02-12 César Benito , Esperanza López , Borja Peropadre , Alejandro Bermudez

For a simple model of mutually interacting qubits it is shown how the errors induced by mutual interactions can be eliminated using concatenated coding. The model is solved exactly for arbitrary interaction strength, for two well-known…

Quantum Physics · Physics 2009-11-06 Julio Gea-Banacloche

Near-term quantum computers have been built as intermediate-scale quantum devices and are fragile against quantum noise effects, namely, NISQ devices. Traditional quantum-error-correcting codes are not implemented on such devices and to…

Quantum Physics · Physics 2024-03-18 Yusuke Hama , Hirofumi Nishi

Fabrication errors pose a significant challenge in scaling up solid-state quantum devices to the sizes required for fault-tolerant (FT) quantum applications. To mitigate the resource overhead caused by fabrication errors, we combine two…

The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are…

Quantum Physics · Physics 2008-02-03 A. R. Calderbank , E. M Rains , P. W. Shor , N. J. A. Sloane

In this paper, based on the relationship between logic functions and quantum error correcting codes(QECCs), we unify the construction of QECCs via graphs, projectors and logic functions. A construction of QECCs over a prime field GF(p) is…

Quantum Physics · Physics 2008-01-06 Yajie Xu , Zhi Ma , Chunyuan Zhang , Xin Lü