English
Related papers

Related papers: Fiber Bundle Fault Tolerance of GKP Codes

200 papers

We propose a scheme for the fault-tolerant implementation of arbitrary Clifford circuits. To achieve this, we extend previous work on flag gadgets for syndrome extraction to a general framework that flags any Clifford circuit. This…

Quantum Physics · Physics 2025-10-10 Benjamin Anker , Milad Marvian

We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…

Information Theory · Computer Science 2011-08-16 Qiwen Wang , Sidharth Jaggi , Shuo-Yen Robert Li

Bosonic quantum error correction enables hardware-efficient protection of quantum information by encoding logical qubits in harmonic oscillators. Bosonic grid states, such as Gottesman-Kitaev-Preskill (GKP) states, are particularly…

We propose a scheme for detecting and correcting faults in any Clifford circuit. The scheme is based on the observation that the set of all possible outcome bit-strings of a Clifford circuit is a linear code, which we call the outcome code.…

Quantum Physics · Physics 2023-05-29 Nicolas Delfosse , Adam Paetznick

Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…

Quantum Physics · Physics 2018-05-30 Tomas Jochym-O'Connor , Aleksander Kubica , Theodore J. Yoder

We estimate the success probability of quantum protocols composed of Clifford operations in the presence of Pauli errors. Our method is derived from the fault-point formalism previously used to determine the success rate of low-distance…

Quantum Physics · Physics 2017-01-26 Smitha Janardan , Yu Tomita , Mauricio Gutierrez , Kenneth R. Brown

We investigate state designs for continuous-variable quantum systems using the aid of lattice-like quantum states. These are code states of Gottesman-Kitaev-Preskill (GKP) codes. We show that for an n-mode system, the set of all GKP states…

Quantum Physics · Physics 2026-01-14 Jonathan Conrad , Joseph T. Iosue , Ansgar G. Burchards , Victor V. Albert

We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional…

Quantum Physics · Physics 2007-05-23 Eric M. Rains

By using totally isotropic subspaces in an orthogonal space Omega^{+}(2i,2), several infinite families of packings of 2^k-dimensional subspaces of real 2^i-dimensional space are constructed, some of which are shown to be optimal packings. A…

Combinatorics · Mathematics 2007-05-23 A. R. Calderbank , R. H. Hardin , E. M. Rains , P. W. Shor , N. J. A. Sloane

We introduce a general framework for weak transversal gates -- probabilistic implementation of logical unitaries realized by local physical unitaries -- and propose a novel partially fault-tolerant quantum computing architecture that…

Quantum Physics · Physics 2025-10-10 Nobuyuki Yoshioka , Alireza Seif , Andrew Cross , Ali Javadi-Abhari

Fault-tolerant quantum computation using two-dimensional topological quantum error correcting codes can benefit from multi-qubit long-range operations. By using simple commutation rules, a quantum circuit can be transpiled into a sequence…

We propose a family of surface codes with general lattice structures, where the error-tolerances against bit and phase errors can be controlled asymmetrically by changing the underlying lattice geometries. The surface codes on various…

Quantum Physics · Physics 2015-06-04 Keisuke Fujii , Yuuki Tokunaga

We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a…

We present an entirely 2D transversal realization of phase gates at any level of the Clifford hierarchy, and beyond, using non-Abelian surface codes. Our construction encodes a logical qubit in the quantum double $D(G)$ of a non-Abelian…

Quantum Physics · Physics 2026-01-19 Alison Warman , Sakura Schafer-Nameki

The generation of a logical qubit called the Gottesman-Kitaev-Preskill qubit in an optical traveling wave is a major challenge for realizing large-scale universal fault-tolerant optical quantum computers. Recently, probabilistic generation…

The development of quantum codes with good error correction parameters and useful sets of transversal gates is a problem of major interest in quantum error-correction. Abundant prior works have studied transversal gates which are restricted…

Quantum Physics · Physics 2025-07-10 Zhiyang He , Vinod Vaikuntanathan , Adam Wills , Rachel Yun Zhang

A promising route towards fault-tolerant quantum error correction is the concatenation of a Gottesman-Kitaev-Preskill (GKP) code with a qubit code. Development of such concatenated codes requires simulation tools which realistically model…

We compute the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates, when both qubit and measurement errors are present. By mapping the problem onto a…

Quantum Physics · Physics 2011-08-10 Ruben S. Andrist , Helmut G. Katzgraber , H. Bombin , M. A. Martin-Delgado

Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…

Quantum Physics · Physics 2008-12-18 Daniel Gottesman , Alexei Kitaev , John Preskill

We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the…

Quantum Physics · Physics 2025-02-27 Yijia Xu , Yixu Wang , Victor V. Albert