Related papers: Quantum Data-Syndrome Codes: Subsystem and Impure …
Quantum stabilizer codes often struggle with syndrome errors due to measurement imperfections. Typically, multiple rounds of syndrome extraction are employed to ensure reliable error information. In this paper, we consider phenomenological…
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
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…
Imperfect measurement can degrade a quantum error correction scheme. A solution that restores fault tolerance is to add redundancy to the process of syndrome extraction. In this work, we show how to optimize this process for an arbitrary…
Subsystem codes are a generalization of noiseless subsystems, decoherence free subspaces, and quantum error-correcting codes. We prove a Singleton bound for GF(q)-linear subsystem codes. It follows that no subsystem code over a prime field…
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 computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple…
The standard quantum error correction protocols use projective measurements to extract the error syndromes from the encoded states. We consider the more general scenario of weak measurements, where only partial information about the error…
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…
With quantum devices rapidly approaching qualities and scales needed for fault tolerance, the validity of simplified error models underpinning the study of quantum error correction needs to be experimentally evaluated. In this work, we have…
The performance of quantum error correction can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error rates from the syndrome…
We investigate the stability of logical information in quantum stabilizer codes subject to coherent unitary errors. Beginning with a logical state, we apply a random unitary error channel and subsequently measure stabilizer checks,…
Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is…
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…
Quantum error correction (QEC) entails the encoding of quantum information into a QEC code space, measuring error syndromes to properly locate and identify errors, and, if necessary, applying a proper recovery operation. Here we compare…
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…
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…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Quantum error correcting (QEC) stabilizer codes enable protection of quantum information against errors during storage and processing. Simulation of noisy QEC codes is used to identify the noise parameters necessary for advantageous…
Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in…