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PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…

Quantum Physics · Physics 2018-02-06 Nikolas P. Breuckmann

Haah's cubic code is the prototypical type-II fracton topological order. It instantiates the no string-like operator property that underlies the favorable scaling of its code distance and logical energy barrier. Previously, the cubic code…

Quantum Physics · Physics 2024-05-14 Cory T. Aitchison , Daniel Bulmash , Arpit Dua , Andrew C. Doherty , Dominic J. Williamson

We construct a local decoder for the 2D toric code using ideas from the hierarchical classical cellular automata of Tsirelson and G\'acs. Our decoder is a circuit of strictly local quantum operations preserving a logical state for…

Quantum Physics · Physics 2026-05-26 Shankar Balasubramanian , Margarita Davydova , Ethan Lake

In this paper, we demonstrate a direct correspondence between phase-free ZX diagrams, a graphical notation for representing and manipulating a certain class of linear maps on qubits, and Calderbank-Shor-Steane (CSS) codes, a large family of…

Quantum Physics · Physics 2022-05-02 Aleks Kissinger

Is the notion of a quantum computer resilient to thermal noise unphysical? We address this question from a constructive perspective and show that local quantum Hamiltonian models provide self-correcting quantum computers. To this end, we…

Quantum Physics · Physics 2013-05-31 H. Bombin , R. W. Chhajlany , M. Horodecki , M. A. Martin-Delgado

Floquet codes are a recently discovered type of quantum error correction code. They can be thought of as generalising stabilizer codes and subsystem codes, by allowing the logical Pauli operators of the code to vary dynamically over time.…

Quantum Physics · Physics 2023-09-01 Alex Townsend-Teague , Julio Magdalena de la Fuente , Markus Kesselring

We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which…

Quantum Physics · Physics 2024-12-02 Christophe Vuillot , Alessandro Ciani , Barbara M. Terhal

Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…

Quantum Physics · Physics 2025-01-10 Lane G. Gunderman

Microscopic two-level systems (TLS) -- ubiquitous atomic-scale defects in solid-state quantum devices -- are a dominant source of qubit decoherence, yet their role is often considered local and short-memoried. Here, we report the…

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…

We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes, and topological color codes for error correction. Color codes have a set of transversal…

Mesoscale and Nanoscale Physics · Physics 2017-09-25 Daniel Litinski , Markus S. Kesselring , Jens Eisert , Felix von Oppen

Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces…

Quantum Physics · Physics 2018-06-12 Tejas Gandhi , Piyush Kurur , Rajat Mittal

Color codes are promising quantum error correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, thresholds of color codes under circuit-level noise are…

Quantum Physics · Physics 2024-09-18 Yugo Takada , Keisuke Fujii

The robustness of the topological color code, which is a class of error correcting quantum codes, is investigated under the influence of an uniform magnetic field on the honeycomb lattice. Our study relies on two high-order series…

Strongly Correlated Electrons · Physics 2013-04-02 Saeed S. Jahromi , Mehdi Kargarian , S Farhad Masoudi , Kai Phillip Schmidt

Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. We present a no-go theorem that places very strong limitations on the potential of such schemes for…

Quantum Physics · Physics 2020-08-11 Paul Webster , Stephen D. Bartlett

We study finite-length qudit quantum low-density parity-check (LDPC) codes from translation-invariant CSS constructions on two-dimensional tori with twisted boundary conditions. Recent qubit work [PRX Quantum 6, 020357 (2025)] showed that,…

Quantum Physics · Physics 2026-02-05 Mourad Halla

We construct surface codes corresponding to genus greater than one in the context of quantum error correction. The architecture is inspired by the topology of invariant integral surfaces of certain non-integrable classical billiards.…

Quantum Physics · Physics 2023-08-07 Garima Rajpoot , Komal Kumari , Sudhir Ranjan Jain

Topologically-ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models…

Quantum Physics · Physics 2025-02-13 Yaodong Li , Nicholas O'Dea , Vedika Khemani

We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an…

Quantum Physics · Physics 2022-05-03 Christophe Vuillot , Nikolas P. Breuckmann

In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based…

Quantum Physics · Physics 2021-09-21 July X. Li , Joseph M. Renes , Pascal O. Vontobel