Related papers: Quantum Error Correction with Uniformly Mixed Stat…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
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…
Quantum bits are more robust to noise when they are encoded non-locally. In such an encoding, errors affecting the underlying physical system can then be detected and corrected before they corrupt the encoded information. In 2001,…
Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction…
Quantum Error Correction (QEC) is one of the fundamental problems in quantum computer systems, which aims to detect and correct errors in the data qubits within quantum computers. Due to the presence of unreliable data qubits in existing…
In the setting of entanglement-assisted quantum error-correcting codes (EAQECCs), the sender and the receiver have access to pre-shared entanglement. Such codes promise better information rates or improved error handling properties.…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
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.…
Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a…
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…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
We propose a quantum error correction without error detection. A quantum state $\rho_0$ combined with an ancilla state $\sigma$ is encoded unitarily and an error operator is applied on the encoded state. The recovery operation then produces…
We calculate the fidelity with which an arbitrary state can be encoded into a [7,1,3] CSS quantum error correction code in a non-equiprobable Pauli operator error environment with the goal of determining whether this encoding can be used…
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 introduce a theory of quantum error correction (QEC) for a subclass of states within a larger Hilbert space. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords.…
Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and controlling a single effective exchange interaction and possibly a global magnetic field. This "encoded universality"…
Quantum computing becomes viable when a quantum state can be preserved from environmentally-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) is capable of identifying…
A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum…
Methods to control errors will be essential for quantum information processing. It is widely believed that fault-tolerant quantum error correction is the leading contender to achieve this goal. Although the theory of fault-tolerant quantum…
An entangled state is said to be $m$-uniform if the reduced density matrix of any $m$ qubits is maximally mixed. This is intimately linked to pure quantum error correction codes (QECCs), which allow not only to correct errors, but also to…