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Related papers: Hyperbolic and Semi-Hyperbolic Surface Codes for Q…

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We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the $p$-faces of the $n$-cube (for $n>p$) and stabilizer constraints with faces of dimension $(p\pm1)$. The quantum code obtained by identifying…

Quantum Physics · Physics 2022-03-09 Anthony Leverrier , Vivien Londe , Gilles Zémor

We study how well topological quantum codes can tolerate coherent noise caused by systematic unitary errors such as unwanted $Z$-rotations. Our main result is an efficient algorithm for simulating quantum error correction protocols based on…

Quantum Physics · Physics 2018-11-01 Sergey Bravyi , Matthias Englbrecht , Robert Koenig , Nolan Peard

flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…

Quantum Physics · Physics 2023-08-30 T. R. Scruby , K. Nemoto

An economy of scale is found when storing many qubits in one highly entangled block of a topological quantum code. The code is defined by construction of a topologically convoluted 2-d surface and does not work by compressing redundancy in…

Quantum Physics · Physics 2007-05-23 Eric Dennis

Quantum Error Correction (QEC) is essential for future quantum computers due to its ability to exponentially suppress physical errors. The surface code is a leading error-correcting code candidate because of its local topological structure,…

Logical qubits encoded into a quantum code exhibit improved error rates when the physical error rates are sufficiently low, below the pseudothreshold. Logical error rates and pseudothresholds can be estimated for specific circuits and noise…

Quantum Physics · Physics 2024-02-14 Malcolm S. Carroll , James R. Wootton , Andrew W. Cross

Hyperbolic geometry has been successfully applied in modeling brain cortical and subcortical surfaces with general topological structures. However such approaches, similar to other surface based brain morphology analysis methods, usually…

Image and Video Processing · Electrical Eng. & Systems 2021-02-23 J. Zhang , Q. Dong , J. Shi , Q. Li , C. M. Stonnington , B. A. Gutman , K. Chen , E. M. Reiman , R. J. Caselli , P. M. Thompson , J. Ye , Y. Wang

Scaling fault tolerant quantum computers, especially cryogenic systems based on the surface code, to millions of qubits is challenging due to poorly-scaling data processing and power consumption overheads. One key hurdle is the design of…

Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…

Quantum Physics · Physics 2024-12-23 Samuel C. Smith , Benjamin J. Brown , Stephen D. Bartlett

The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new…

Quantum Physics · Physics 2017-04-26 Theodore J. Yoder , Isaac H. Kim

Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…

With quantum devices rapidly approaching qualities and scales needed for fault tolerance, the validity of simplified error models underpinning the study of quantum error correction needs to be experimentally evaluated. In this work, we have…

Quantum Physics · Physics 2024-12-11 Spiro Gicev , Lloyd C. L. Hollenberg , Muhammad Usman

Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits…

Quantum Physics · Physics 2025-01-29 Hayata Yamasaki , Masato Koashi

Identifying the best families of quantum error correction (QEC) codes for near-term experiments is key to enabling fault-tolerant quantum computing. Ideally, such codes should have low overhead in qubit number, high physical error…

Quantum Physics · Physics 2025-11-17 Laura Pecorari , Guido Pupillo

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the…

Quantum Error Correction (QEC) codes store information reliably in logical qubits by encoding them in a larger number of less reliable qubits. The surface code, known for its high resilience to physical errors, is a leading candidate for…

Quantum Physics · Physics 2025-06-13 Satvik Maurya , Swamit Tannu

We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the…

Information Theory · Computer Science 2013-10-22 Martin Leslie

To produce an operable quantum computer that is made with imperfect hardware, we must design and test scalable quantum error correcting codes that are suited for the devices we can build and, in unison, develop decoding strategies that…

Three-dimensional (3D) topological codes offer the advantage of supporting fault-tolerant implementations of non-Clifford gates, yet their performance against realistic noise remains largely unexplored. In this work, we focus on the…

Quantum Physics · Physics 2025-10-31 Ji-Ze Xu , Yin Zhong , Miguel A. Martin-Delgado , Hao Song , Ke Liu

We estimate optimal thresholds for surface code in the presence of loss via an analytical method developed in statistical physics. The optimal threshold for the surface code is closely related to a special critical point in a…

Quantum Physics · Physics 2015-06-04 Masayuki Ohzeki