Related papers: Nonbinary Codeword Stabilized Quantum Codes
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
We explore what the integrated use of quantum spatial distribution (QSD), or more specifically, superposition of both spin and position states of particles, and gauge symmetry (GS) within stabilizer formalism provides for quantum error…
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…
The trajectories of the pilot-wave formulation of quantum mechanics and hence its empirical predictions may be recovered via the dynamics of a density function on the configuration space of a system, without reference to a physical wave…
The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a…
Graph states are generalized from qubits to collections of $n$ qudits of arbitrary dimension $D$, and simple graphical methods are used to construct both additive and nonadditive quantum error correcting codes. Codes of distance 2…
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…
Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. For quantum codes, a form of puncturing is known, but its description is based on the code space rather than its…
CSS codes are a subfamily of stabilizer codes especially appropriate for fault-tolerant quantum computations. A very simple method is proposed to encode a general qudit when a Calderbank-Shor-Steane quantum code, defined over a q-ary…
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…
Quantum computers are a revolutionary class of computational platforms with applications in combinatorial and global optimization, machine learning, and other domains involving computationally hard problems. While these machines typically…
A quantum codeword is a redundant representation of a logical qubit by means of several physical qubits. It is constructed in such a way that if one of the physical qubits is perturbed, for example if it gets entangled with an unknown…
A divisible binary classical code is one in which every code word has weight divisible by a fixed integer. If the divisor is $2^\nu$ for a positive integer $\nu$, then one can construct a Calderbank-Shor-Steane (CSS) code, where…
A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
Quantum error correction requires the use of error syndromes derived from measurements that may be unreliable. Recently, quantum data-syndrome (QDS) codes have been proposed as a possible approach to protect against both data and syndrome…
We use affine variety codes and their subfield-subcodes for obtaining quantum stabilizer codes via the CSS code construction. With this procedure, we get codes with good parameters and a code whose parameters exceed the CSS quantum…
With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting codes designed to address a single dominant error type.…
Up to now every good quantum error-correcting code discovered has had the structure of an eigenspace of an Abelian group generated by tensor products of Pauli matrices; such codes are known as stabilizer or additive codes. In this letter we…
The stabilizer formalism for quantum error-correcting codes has been, without doubt, the most successful at producing examples of quantum codes with strong error-correcting properties. In this paper, we discuss strong automorphism groups of…