Related papers: Verifying Fault-Tolerance of Quantum Error Correct…
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…
A major obstacle towards realizing a practical quantum computer is the noise that arises due to system-environment interactions. While it is very well known that quantum error correction (QEC) provides a way to protect against errors that…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…
Encoding information redundantly using quantum error-correcting (QEC) codes allows one to overcome the inherent sensitivity to noise in quantum computers to ultimately achieve large-scale quantum computation. The Steane QEC method involves…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
A major milestone of quantum error correction is to achieve the fault-tolerance threshold beyond which quantum computers can be made arbitrarily accurate. This requires extraordinary resources and engineering efforts. We show that even…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
This paper proves the threshold result, which asserts that quantum computation can be made robust against errors and inaccuracies, when the error rate, $\eta$, is smaller than a constant threshold, $\eta_c$. The result holds for a very…
Quantum Error Correction Codes (QECCs) are pivotal in advancing quantum computing by protecting quantum states against the adverse effects of noise and errors. With a variety of QECCs developed, including new developments and modifications…
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
Quantum error correction (QEC) is essential for building scalable quantum computers, but a lack of systematic, end-to-end evaluation methods makes it difficult to assess how different QEC codes perform under realistic conditions. The vast…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
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 computers are highly susceptible to errors due to unintended interactions with their environment. It is crucial to correct these errors without gaining information about the quantum state, which would result in its destruction…
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 computers (QCs) must implement quantum error correcting codes (QECCs) to protect their logical qubits from errors, and modeling the effectiveness of QECCs on QCs is an important problem for evaluating the QC architecture. The…
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…
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…