Related papers: The Algebra for Stabilizer Codes
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Simulation of stabilizer circuits is a well-studied problem in quantum information processing, with a number of highly optimized algorithms available. Yet, we argue that further improvements can arise from the theoretical structure of…
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…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated…
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…
The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the…
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 introduce new algorithms and provide example constructions of stabilizer models for the gapped boundaries, domain walls, and $0D$ defects of Abelian composite-dimensional twisted quantum doubles. Using the physically intuitive concept of…
We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…
In this paper, we give a constructive proof to show that if there exist a classical linear code C is a subset of F_q^n of dimension k and a classical linear code D is a subset of F_q^k^m of dimension s, where q is a power of a prime number…
Traditional stabilizer codes operate over prime power local-dimensions. In this work we extend the stabilizer formalism using the local-dimension-invariant setting to import stabilizer codes from these standard local-dimensions to other…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
In this work, we explore a new approach to designing both algorithms and error detection codes for preparing approximate ground states of molecules. We propose a classical algorithm to find the optimal stabilizer state by using excitations…
We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace…
We prove that an algebraic stack with affine stabilizers over an arbitrary base is \'etale-locally a quotient stack around any point with a linearly reductive stabilizer. This generalizes earlier work by the authors of this article (stacks…
We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph…
Classical designs and their (projective) q-analogs can both be viewed as designs in matroids, using the matroid of all subsets of a set and the matroid of linearly independent subsets of a vector space, respectively. Another natural matroid…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…