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Having protected quantum information is essential to perform quantum computations. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
We study the performance of common quantum stabilizer codes in the presence of asymmetric and correlated errors. Specifically, we consider the depolarizing noisy quantum memory channel and perform quantum error correction via the five and…
We model repetitive quantum error correction (QEC) with the single-error-correcting five-qubit code on a network of individually-controlled qubits with always-on Ising couplings, using our previously designed universal set of quantum gates…
Quantum circuits implementing fault-tolerant quantum error correction (QEC) for the three qubit bit-flip code and five-qubit code are studied. To describe the effect of noise, we apply a model based on a generalized effective Hamiltonian…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
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…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…
We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to…
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…
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…
We study stabilizer quantum error correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension. Building upon 1) a general formula relating the error-susceptibility of a…
Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst…
To build a universal quantum computer from fragile physical qubits, effective implementation of quantum error correction (QEC) is an essential requirement and a central challenge. Existing demonstrations of QEC are based on a schedule of…
Decoders of quantum error correction (QEC) experiments make decisions based on detected errors and the expected rates of error events, which together comprise a detector error model. Here we show that the syndrome history of QEC experiments…
We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…
We discuss a method to adapt the codeword stabilized (CWS) quantum code framework to the problem of finding asymmetric quantum codes. We focus on the corresponding Pauli error models for amplitude damping noise and phase damping noise. In…
Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal…
Decoherence errors arising from noisy environments remain a central obstacle to progress in quantum computation and information processing. Quantum error correction (QEC) based on the Gottesman-Kitaev-Preskill (GKP) protocol offers a…