Related papers: Error-Correcting Codes in TQFT on Multispheres
We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism and classical error correction, and…
The concept of multiple particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer.…
We introduce the notion of trace-norm isometric encoding and explore its implications for passive and active methods to protect quantum information against errors. Beside providing an operational foundations to the "subsystems principle"…
Environmental effects on the transmission of a state result, in general, in a change in the information carried by it. To mitigate this, many techniques such as quantum error--correcting codes, decoherence--free--subspaces [Rev Mod Phys,…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
Quantum error-correcting codes (QECCs) and decoherence-free subspace (DFS) codes provide active and passive means, respectively, to address certain types of errors that arise during quantum computation. The latter technique is suitable to…
Quantum error correction in general is experimentally challenging as it requires significant expansion of the size of quantum circuits and accurate performance of quantum gates to fulfill the error threshold requirement. Here we propose a…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…
The task of preserving entanglement against noises is of crucial importance for both quantum communication and quantum information transfer. To this aim, quantum error correction (QEC) codes may be employed to compensate, at least…
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…
We study quantized non-local order parameters, constructed by using partial time-reversal and partial reflection, for fermionic topological phases of matter in one spatial dimension protected by an orientation reversing symmetry, using…
Locating the boundaries of consecutive blocks of quantum information is a fundamental building block for advanced quantum computation and quantum communication systems. We develop a coding theoretic method for properly locating boundaries…
We show how to convert an arbitrary stabilizer code into a bipartite quantum code. A bipartite quantum code is one that involves two senders and one receiver. The two senders exploit both nonlocal and local quantum resources to encode…
Topological error correction provides an effective method to correct errors in quantum computation. It allows quantum computation to be implemented with higher error threshold and high tolerating loss rates. We present a topological a error…
We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing…
In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…