Related papers: Learning to Concatenate Quantum Codes
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
It is shown that the noise process in quantum computation can be described by spatially correlated decoherence and dissipation. We demonstrate that the conventional quantum error correcting codes correcting for single-qubit errors are…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…
Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with…
We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds…
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…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Quantum noise fundamentally limits the utility of near-term quantum devices, making error mitigation essential for practical quantum computation. While traditional quantum error correction codes require substantial qubit overhead and…
Studies of quantum error correction (QEC) typically focus on stochastic Pauli errors because the existence of a threshold error rate below which stochastic Pauli errors can be corrected implies that there exists a threshold below which…
Coherent errors, and especially those that occur in correlation among a set of qubits, are detrimental for large-scale quantum computing. Correlations in noise can occur as a result of spatial and temporal configurations of instructions…
Quantum noise is conventionally viewed as a fundamental obstacle in near-term quantum computing, motivating extensive error correction and mitigation strategies. We present numerical evidence that challenges this consensus. Through…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…
Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterise noise. The experiment is…
Fault-tolerant quantum computation demands extremely low logical error rates, yet superconducting qubit arrays are subject to radiation-induced correlated noise arising from cosmic-ray muon-generated quasiparticles. The quasiparticle…
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…
Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be…
Fault-tolerant capacities quantify the ability of a quantum channel to reliably transmit information when every component of the encoding and decoding procedure is noisy. Earlier work analyzed achievable communication rates under such noise…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…