Related papers: On the Fourier Transform Approach to Quantum Error…
An error avoiding quantum code is presented which is capable of stabilizing Grover's quantum search algorithm against a particular class of coherent errors. This error avoiding code consists of states only which are factorizable in the…
One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it…
Subsystem codes are the most versatile class of quantum error-correcting codes known to date that combine the best features of all known passive and active error-control schemes. The subsystem code is a subspace of the quantum state space…
By defining projective error models we study the mathematical structure of Clifford codes and stabilizer codes using tools from projective representation theory. Furthermore, we introduce a new class of codes which we have called weak…
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…
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…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…
For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation…
In adversarial settings, where attackers can deliberately and strategically corrupt quantum data, standard quantum error correction reaches its limits. It can only correct up to half the code distance and must output a unique answer.…
We introduce a model-checking tool intended specially for the analysis of quantum information protocols. The tool incorporates an efficient representation of a certain class of quantum circuits, namely those expressible in the so-called…
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to…
We show that quantum feedback control can be used as a quantum error correction process for errors induced by weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…
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…
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…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Quantum Fourier analysis is an important topic in mathematical physics. We introduce a systematic protocol for testing and measuring ``magic'' in quantum states and gates, using a quantum Fourier approach. Magic, as a quantum resource, is…