Related papers: Linear Quantum Error Correction
Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across…
In general, fault-tolerant quantum error correction (FTQEC) procedures are designed to detect, correct, and be fault-tolerant against errors occurring within the qubit subspace. But in some qubit implementations, additional "leakage" errors…
We propose a new approach to study the evolution of a quantum state that is encoded in a system which is continuously subject to the operations required to implement a quantum error correcting code. In the limit of continuous error…
Quantum error correction (QEC) is often implemented on hardware that experiences biased noise, where dephasing errors occur more frequently than other errors. This has motivated many recent efforts to develop bias-tailored QEC codes, such…
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…
The sensitivity afforded by quantum sensors is limited by decoherence. Quantum error correction (QEC) can enhance sensitivity by suppressing decoherence, but it has a side-effect: it biases a sensor's output in realistic settings. If…
We propose and analyze a new approach based on quantum error correction (QEC) to improve quantum metrology in the presence of noise. We identify the conditions under which QEC allows one to improve the signal-to-noise ratio in…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
We provide a systematic way of constructing entanglement-assisted quantum error-correcting codes via graph states in the scenario of preexisting perfectly protected qubits. It turns out that the preexisting entanglement can help beat the…
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…
A key challenge in fault-tolerant quantum computing is synthesising and optimising circuits in a noisy environment, as traditional techniques often fail to account for the effect of noise on circuits. In this work, we propose and…
Designing efficient fault tolerance schemes is crucial for building useful quantum computers. Most standard schemes assume no knowledge of the underlying device noise and rely on general-purpose quantum error-correcting (QEC) codes capable…
Quantum error mitigation (QEM) has been proposed as an alternative method of quantum error correction to compensate errors in quantum systems without qubit overhead. While Markovian gate errors on digital quantum computers have been mainly…
We describe a method to execute globally controlled quantum information processing which admits a fault tolerant quantum error correction scheme. Our scheme nominally uses three species of addressable two-level systems which are arranged in…
We present a general-purpose quantum error correction primitive based on state purification via the SWAP test, which we refer to as purification quantum error correction (PQEC). This method operates on $N$ noisy copies, requires minimally…
We develop connections between generalised notions of entanglement and quantum computational devices where the measurements available are restricted, either because they are noisy and/or because by design they are only along Pauli…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Correcting errors due to noise in quantum circuits run on current and near-term quantum hardware is essential for any convincing demonstration of quantum advantage. Indeed, in many cases it has been shown that noise renders quantum circuits…
A fault-tolerant approach to reliable quantum memory is essential for scalable quantum computing, as physical qubits are susceptible to noise. Quantum error correction (QEC) must be continuously performed to prolong the memory lifetime. In…