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We introduce a methodology for generating random multi-qubit stabilizer codes based on solving a constraint satisfaction problem (CSP) on random bipartite graphs. This framework allows us to enforce stabilizer commutation, $X/Z$ balancing,…

Quantum Physics · Physics 2023-04-26 Maxime Tremblay , Guillaume Duclos-Cianci , Stefanos Kourtis

We show how to explicitly construct an $O(nd)$ size and constant quantum depth circuit which encodes any given $n$-qubit stabilizer code with $d$ generators. Our construction is derived using the graphic description for stabilizer codes and…

Quantum Physics · Physics 2008-08-18 Wei Huang , Zhaohui Wei

Divisible codes are defined by the property that codeword weights share a common divisor greater than one. They are used to design signals for communications and sensing, and this paper explores how they can be used to protect quantum…

Quantum Physics · Physics 2022-04-29 Jingzhen Hu , Qingzhong Liang , Robert Calderbank

A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…

Quantum Physics · Physics 2012-07-04 Radu Ionicioiu , Tim P. Spiller

Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…

Quantum Physics · Physics 2007-05-23 Daniel Gottesman

We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces…

Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of…

Quantum Physics · Physics 2026-05-18 Tom Peham , Matthew Steinberg , Robert Wille , Sascha Heußen

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

According to the Gottesman-Knill theorem, a class of quantum circuits, namely the so-called stabilizer circuits, can be simulated efficiently on a classical computer. We introduce a new algorithm for this task, which is based on the…

Quantum Physics · Physics 2007-05-23 Simon Anders , Hans J. Briegel

This is a short review on an interdisciplinary field of quantum information science and statistical mechanics. We first give a pedagogical introduction to the stabilizer formalism, which is an efficient way to describe an important class of…

Quantum Physics · Physics 2013-11-12 Keisuke Fujii

Topological quantum error correcting codes have emerged as leading candidates towards the goal of achieving large-scale fault-tolerant quantum computers. However, quantifying entanglement in these systems of large size in the presence of…

Quantum Physics · Physics 2020-08-18 David Amaro , Markus Müller , Amit Kumar Pal

We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a…

Quantum Physics · Physics 2021-08-09 Andrey Boris Khesin , Kevin Ren

In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…

Quantum Physics · Physics 2009-11-13 Dan Hu , Weidong Tang , Meisheng Zhao , Qing Chen , Sixia Yu , C. H. Oh

Graph states are the main computational building blocks of measurement-based computation and a useful tool for error correction in the gate model architecture. The graph states form a class of quantum states which are eigenvectors for the…

Quantum Physics · Physics 2022-12-26 Sebastiano Corli , Enrico Prati

Two new qubit stabilizer codes with parameters $[77, 0, 19]_2$ and $[90, 0, 22]_2$ are constructed for the first time by employing additive symplectic self-dual $\F_4$ codes from multidimensional circulant (MDC) graphs. We completely…

Information Theory · Computer Science 2023-09-06 Padmapani Seneviratne , Hannah Cuff , Alexandra Koletsos , Kerry Seekamp , Adrian Thnanopavarn

Construction of quantum codes and entanglement-assisted quantum codes with good parameters via classical codes is an important task for quantum computing and quantum information. In this paper, by a family of one-generator quasi-cyclic…

Information Theory · Computer Science 2020-09-08 Jingjie Lv , Ruihu Li , Yu Yao

Quantum error-correcting codes can be used to protect qubits involved in quantum computation. This requires that logical operators acting on protected qubits be translated to physical operators (circuits) acting on physical quantum states.…

Information Theory · Computer Science 2021-08-20 Narayanan Rengaswamy , Robert Calderbank , Swanand Kadhe , Henry D. Pfister

In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…

Quantum Physics · Physics 2008-07-01 Pradeep Kiran Sarvepalli , Andreas Klappenecker

We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…

Quantum Physics · Physics 2018-09-26 Kristina R. Colladay , Erich J. Mueller

Scaling quantum computing to practical applications necessitates reliable quantum error correction. Although numerous correction codes have been proposed, the overall correction efficiency critically limited by the decode algorithms. We…

Quantum Physics · Physics 2025-06-04 Gengyuan Hu , Wanli Ouyang , Chao-Yang Lu , Chen Lin , Han-Sen Zhong