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We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic…

Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…

Quantum Physics · Physics 2026-01-29 Hoshitaro Ohnishi , Hideo Mukai

Typical topological systems undergo a topological phase transition in the presence of a strong enough perturbation. In this paper, we propose an adjustable frustrated Toric code with a "topological line" at which no phase transition happens…

Strongly Correlated Electrons · Physics 2021-09-29 M. H. Zarei , J. Abouie

We consider the problem of preparing topologically ordered states using unitary and non-unitary circuits, as well as local time-dependent Hamiltonian and Liouvillian evolutions. We prove that for any topological code in $D$ dimensions, the…

Quantum Physics · Physics 2014-07-09 Robert Koenig , Fernando Pastawski

Quantum error correction (QEC) is crucial for realizing scalable quantum technologies, and topological quantum error correction (TQEC) has emerged as the most experimentally advanced paradigm of QEC. Existing homological and topological…

Quantum Physics · Physics 2026-01-21 Xiang Zou , Hoi-Kwong Lo

The recently introduced tile codes are a promising alternative to surface codes, combining two-dimensional locality with higher encoding efficiency. While surface codes are well understood in terms of their logical operators and boundary…

Surface codes$\unicode{x2014}$leading candidates for quantum error correction (QEC)$\unicode{x2014}$and entanglement phases$\unicode{x2014}$a key notion for many-body quantum dynamics$\unicode{x2014}$have heretofore been unrelated. Here, we…

Quantum Physics · Physics 2024-02-06 Jan Behrends , Florian Venn , Benjamin Béri

This paper attempts to establish the connection among classifications of gapped boundaries in topological phases of matter, bosonic symmetry-protected topological (SPT) phases and fault-tolerantly implementable logical gates in quantum…

Strongly Correlated Electrons · Physics 2017-08-25 Beni Yoshida

Quantum LDPC codes have attracted intense interest due to their advantageous properties for realizing efficient fault-tolerant quantum computing. In particular, sheaf codes represent a novel framework that encompasses all well-known good…

Quantum Physics · Physics 2026-01-01 Yiming Li , Zimu Li , Zi-Wen Liu , Quynh T. Nguyen

We develop a topological theory for fault-tolerant quantum computation in quantum low-density parity-check (qLDPC) codes. We show that there exist hidden simplicial or CW complex structures encoding the topological data for all qLDPC and…

Quantum Physics · Physics 2025-09-24 Guanyu Zhu

Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits. Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable. This…

We present a 1D repetition code based on the so-called cat qubits as a viable approach toward hardware-efficient universal and fault-tolerant quantum computation. The cat qubits that are stabilized by a two-photon driven-dissipative…

Quantum Physics · Physics 2019-12-18 Jérémie Guillaud , Mazyar Mirrahimi

We construct a family of constant-rate highly-symmetric self-dual qLDPC codes on high dimensional expanders. This is the first self-dual code constructed on high dimensional expanders and also the first such code with a rich (e.g.…

Quantum Physics · Physics 2026-03-13 Kyle Gulshen , Tali Kaufman

A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…

Quantum Physics · Physics 2012-05-15 Ruben S. Andrist , H. Bombin , Helmut G. Katzgraber , M. A. Martin-Delgado

We give a fault tolerant construction for error correction and computation using two punctured quantum Reed-Muller (PQRM) codes. In particular, we consider the $[[127,1,15]]$ self-dual doubly-even code that has transversal Clifford gates…

Quantum Physics · Physics 2024-11-01 Anqi Gong , Joseph M. Renes

The surface code scheme for quantum computation features a 2d array of nearest-neighbor coupled qubits yet claims a threshold error rate approaching 1% (NJoP 9:199, 2007). This result was obtained for the toric code, from which the surface…

Quantum Physics · Physics 2014-11-18 D. S. Wang , A. G. Fowler , A. M. Stephens , L. C. L. Hollenberg

While quantum low-density parity check (qLDPC) codes are a low-overhead means of quantum information storage, it is valuable for quantum codes to possess fault-tolerant features beyond this resource efficiency. In this work, we introduce…

Quantum Physics · Physics 2026-01-30 Abraham Jacob , Campbell McLauchlan , Dan E. Browne

Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…

Quantum Physics · Physics 2013-10-14 Markus Grassl , Martin Roetteler

We propose a new model of quantum computation comprised of low-weight measurement sequences that simultaneously encode logical information, enable error correction, and apply logical gates. These measurement sequences constitute a new class…

Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be…

Quantum Physics · Physics 2016-09-08 Naomi H. Nickerson