Related papers: Non stabilizer Clifford codes with qupits
A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes based on non-Abelian groups are constructed…
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…
Farinholt gives a characterization of Clifford operators for qudits; d both odd and even. In this comment it is shown that the necessary gates for the construction of Clifford operators; N both odd and even, are obtained directly from…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product,…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
We solve the problem of the classification of perfect quantum codes. We prove that the only nontrivial perfect quantum codes are those with the parameters . There exist no other nontrivial perfect quantum codes.
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 consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code.…
We describe the structure of the $n$-qubit Clifford group $C_n$ via Cayley graphs, whose vertices represent group elements and edges represent generators. In order to obtain the action of Clifford gates on a given quantum state, we…
A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable…
In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases…
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…
We study the computational power of unitary Clifford circuits with solely magic state inputs (CM circuits), supplemented by classical efficient computation. We show that CM circuits are hard to classically simulate up to multiplicative…
Cyclic orbit codes are constant dimension subspace codes that arise as the orbit of a cyclic subgroup of the general linear group acting on subspaces in the given ambient space. With the aid of the largest subfield over which the given…
This paper introduces a novel abstraction for programming quantum operations, specifically projective Cliffords, as functions over the qudit Pauli group. Generalizing the idea behind Pauli tableaux, we introduce a type system and lambda…
The Clifford hierarchy is a nested sequence of sets of quantum gates that can be fault-tolerantly performed using gate teleportation within standard quantum error correction schemes. The groups of Pauli and Clifford gates constitute the…
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…
Clifford theory of possibly infinite dimensional modules is studied