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Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces. More…
An optical scheme for the reliable transfer of quantum information through a noisy quantum channel is proposed. The scheme is inspired by quantum error-correction protocols, but it avoids the currently infeasible requirement for a…
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.…
We establish a symmetry-operator framework for designing quantum error correcting~(QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes…
The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are…
Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum computation. In the past two decades, various constructions of quantum error-correcting codes (QECCs) have been developed, leading to many good…
Active quantum error correction is a central ingredient to achieve robust quantum processors. In this paper we investigate the potential of quantum machine learning for quantum error correction in a quantum memory. Specifically, we…
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…
Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be…
The dominant noise in an "erasure qubit" is an erasure -- a type of error whose occurrence and location can be detected. Erasure qubits have potential to reduce the overhead associated with fault tolerance. To date, research on erasure…
Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspect of quantum information processing. It was well known from the early developments of this exciting field that the…
Quantum information processing offers dramatic speedups, yet is famously susceptible to decoherence, the process whereby quantum superpositions decay into mutually exclusive classical alternatives, thus robbing quantum computers of their…
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…
Quantum error correction (QEC) is essential for quantum computers to perform useful algorithms, but large-scale fault-tolerant computation remains out of reach due to demanding requirements on operation fidelity and the number of…
Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the…
Traditional quantum error correction involves the redundant encoding of k quantum bits using n quantum bits to allow the detection and correction of any t bit error. The smallest general t=1 code requires n=5 for k=1. However, the dominant…
Quantum error-correcting codes (QECC's) are needed to combat the inherent noise affecting quantum processes. Using ZX calculus, we represent QECC's in a form called a ZX diagram, consisting of a tensor network. In this paper, we present…
Fault-tolerant quantum computing is crucial for realizing large-scale quantum computation, and the interplay between hardware architecture and quantum error-correcting codes is a key consideration. We present a comparative study of two…
We propose a new scheme for quantum error correction using robust continuous variable probe modes, rather than fragile ancilla qubits, to detect errors without destroying data qubits. The use of such probe modes reduces the required number…
Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we…