Related papers: Geometric Graph-Theoretic Aspects of Quantum Stabi…
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,…
We start by studying the subgroup structures underlying stabilizer circuits and we use our results to propose a new normal form for stabilizer circuits. This normal form is computed by induction using simple conjugation rules in the…
The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
Gottesman-Knill theorem states that computations on stabilizer circuits can be simulated on a classical computer, conventional simulation algorithms extensively use linear algebra over bit strings. For instance, given a non-adaptive…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
We show how, given any set of generators of the stabilizer of a quantum code, an efficient gate array that computes the codewords can be constructed. For an n-qubit code whose stabilizer has d generators, the resulting gate array consists…
We introduce a stabilizer formalism for the general quantum error correction framework called operator algebra quantum error correction (OAQEC), which generalizes Gottesman's formulation for traditional quantum error correcting codes (QEC)…
The present paper is concerned with the concept of the one-way quantum computer, beyond binary-systems, and its relation to the concept of stabilizer quantum codes. This relation is exploited to analyze a particular class of quantum…
In this paper, we examine algebraic geometric (AG) codes associated with curves generated by separated polynomials, and we create AG codes and quantum stabilizer codes from these curves by varying their parameters. Our research involves a…
The standard stabilizer formalism provides a setting to show that quantum computation restricted to operations within the Clifford group are classically efficiently simulable: this is the content of the well-known Gottesman-Knill theorem.…
We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new…
The stabilizer formalism is a scheme, generalizing well-known techniques developed by Gottesman [quant-ph/9705052] in the case of qubits, to efficiently simulate a class of transformations ("stabilizer circuits", which include the quantum…
This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to…
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 computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Quantum error-correcting codes are used to protect qubits involved in quantum computation. This process requires logical operators, acting on protected qubits, to be translated into physical operators (circuits) acting on physical quantum…
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…