English
Related papers

Related papers: Faster Optimal Decoder for Graph Codes with a Sing…

200 papers

The Gottesman-Kitaev-Preskill (GKP) error correcting code encodes a finite dimensional logical space in one or more bosonic modes, and has recently been demonstrated in trapped ions and superconducting microwave cavities. In this work we…

Quantum Physics · Physics 2024-03-05 Mackenzie H. Shaw , Andrew C. Doherty , Arne L. Grimsmo

We consider the possibility of using stabilizer states to perform deterministic dense coding among multiple senders and a single receiver. In the model we studied, the utilized stabilizer state is partitioned into several subsystems and…

Quantum Physics · Physics 2011-08-26 Guoming Wang , Mingsheng Ying

In this letter, we propose a novel image denoising method based on correlation preserving sparse coding. Because the instable and unreliable correlations among basis set can limit the performance of the dictionary-driven denoising methods,…

Computer Vision and Pattern Recognition · Computer Science 2016-12-26 Rui Chen , Huizhu Jia , Xiaodong Xie , Wen Gao

We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a…

Information Theory · Computer Science 2012-11-20 Daniel Cullina , Ankur A. Kulkarni , Negar Kiyavash

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

Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these…

Quantum Physics · Physics 2021-01-12 Ryan Sweke , Markus S. Kesselring , Evert P. L. van Nieuwenburg , Jens Eisert

In this work we study the single-shot performance of higher dimensional hypergraph product codes decoded using belief-propagation and ordered-statistics decoding [Panteleev and Kalachev, 2021]. We find that decoding data qubit and syndrome…

Quantum Physics · Physics 2023-06-28 Oscar Higgott , Nikolas P. Breuckmann

A fault-tolerant quantum computer will be supported by a classical decoding system interfacing with quantum hardware to perform quantum error correction. It is important that the decoder can keep pace with the quantum clock speed, within…

Quantum Physics · Physics 2023-03-17 Samuel C. Smith , Benjamin J. Brown , Stephen D. Bartlett

The GKP encoding is a top contender among bosonic codes for fault-tolerant quantum computation. Analysis of the GKP code is complicated by the fact that finite-energy code states leak out of the ideal GKP code space and are not orthogonal.…

Quantum Physics · Physics 2026-01-01 Mahnaz Jafarzadeh , Jonathan Conrad , Rafael N. Alexander , Ben Q. Baragiola

Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…

Quantum Physics · Physics 2024-02-02 Yugo Takada , Yusaku Takeuchi , Keisuke Fujii

The syndrome decoding problem is known to be NP-complete. The goal of the decoder is to find an error of low weight that corresponds to a given syndrome obtained from a parity-check matrix. We use the quantum approximate optimization…

Quantum Physics · Physics 2024-11-21 Ching-Yi Lai , Kao-Yueh Kuo , Bo-Jyun Liao

Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes are leading candidates for…

Quantum Physics · Physics 2022-10-12 Pedro Parrado-Rodríguez , Manuel Rispler , Markus Müller

We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or…

Quantum Physics · Physics 2021-06-03 Christopher T. Chubb , Steven T. Flammia

We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and Haah 3D code. The…

Quantum Physics · Physics 2015-06-12 Justyna Łodyga , Paweł Mazurek , Andrzej Grudka , Michał Horodecki

Flag-style fault-tolerance has become a linchpin in the realization of small fault-tolerant quantum-error correction experiments. The flag protocol's utility hinges on low qubit overhead, which is typically much smaller than in other…

Quantum Physics · Physics 2023-12-05 Dhruv Bhatnagar , Matthew Steinberg , David Elkouss , Carmen G. Almudever , Sebastian Feld

Photonic graph states are important for measurement- and fusion-based quantum computing, quantum networks, and sensing. They can in principle be generated deterministically by using emitters to create the requisite entanglement. Finding…

Quantum Physics · Physics 2024-07-23 Evangelia Takou , Edwin Barnes , Sophia E. Economou

Transversal logical gates offer the opportunity for fast and low-noise logic, particularly when interspersed by a single round of parity check measurements of the underlying code. Using such circuits for the surface code requires decoding…

Quantum Physics · Physics 2026-02-23 Marc Serra-Peralta , Mackenzie H. Shaw , Barbara M. Terhal

Practically good error-correcting codes should have good parameters and efficient decoding algorithms. Some algebraically defined good codes such as cyclic codes, Reed-Solomon codes, and Reed-Muller codes have nice decoding algorithms.…

Information Theory · Computer Science 2019-11-19 Lucky Galvez , Jon-Lark Kim

Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabilizer codes, surface code computations consist of a syndrome decoding step where measured stabilizer…

Quantum Physics · Physics 2023-07-14 Spiro Gicev , Lloyd C. L. Hollenberg , Muhammad Usman

Device error rates on current quantum computers have improved enough to where demonstrations of error correction below break-even are now possible. Still, the circuits required for quantum error correction introduce significant overhead and…

Quantum Physics · Physics 2025-10-01 Noah Berthusen , Shi Jie Samuel Tan , Eric Huang , Daniel Gottesman