Related papers: Quantum correction with three codes
We investigate the performance of a three qubit error correcting code in the framework of superconducting qubit implementations. Such a code can recover a quantum state perfectly in the case of dephasing errors but only in situations where…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies…
Classically simulating the dynamics of anyonic excitations in two-dimensional quantum systems is likely intractable in general because such dynamics are sufficient to implement universal quantum computation. However, processes of interest…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant…
In this paper we demonstrate how data encoded in a five-qubit quantum error correction code can be converted, fault-tolerantly, into a seven-qubit Steane code. This is achieved by progressing through a series of codes, each of which…
This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment.…
Quantum states have high affinity for errors and hence error correction is of utmost importance to realise a quantum computer. Laflamme showed that 5 qubits are necessary to correct a single error on a qubit. In a Pauli error model, four…
We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant…
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…
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,…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
The error correcting capabilities of the Calderbank-Shor-Steane [[7,1,3]] quantum code, together with a fault-tolerant syndrome extraction by means of several ancilla states, have been numerically studied. A simple probability expression to…
We consider a two-dimensional quantum memory of qubits on a torus which encode the extended Fibonaccistring-net code, and devise strategies for error correction when those qubits are subjected to depolarizing noise.Building on the concept…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…