Related papers: Quantum error correction beyond qubits
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
We present a theoretical framework for state-adaptive quantum error correction that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we…
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.…
The breakthrough of quantum error correction brought with it the picture of quantum information as a sort of combination of two complementary types of classical information, "amplitude" and "phase". Here I show how this intuition can be…
Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
We analyse a generalised quantum error correction code against photon loss where a logical qubit is encoded into a subspace of a single oscillator mode that is spanned by distinct multi-component cat states (coherent-state superpositions).…
In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error…
Keeping single-qubit quantum coherence above some threshold value not far below unity is a prerequisite for fault-tolerant quantum error correction (QEC). We study the initial dephasing of solid-state qubits in the independent-boson model,…
Blind Quantum Computation (BQC) is a delegation computing protocol that allows a client to utilize a remote quantum server to implement desired quantum computations while keeping her inputs, outputs, and algorithms private. However, qubit…
We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Scalable quantum computing can only be achieved if qubits are manipulated fault-tolerantly. Topological error correction - a novel method which combines topological quantum computing and quantum error correction - possesses the highest…
Secure quantum networks are a bedrock requirement for developing a future quantum internet. However, quantum channels are susceptible to channel noise that introduce errors in the transmitted data. The traditional approach to providing…
It was shown by Ahn, Wiseman, and Milburn [PRA {\bf 67}, 052310 (2003)] that feedback control could be used as a quantum error correction process for errors induced by weak continuous measurement, given one perfectly measured error channel…
A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing…
Current approaches to fault-tolerant quantum computation will not enable useful quantum computation on near-term devices of 50 to 100 qubits. Leading proposals, such as the color code and surface code schemes, must devote a large fraction…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known that the three codes…