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We study the properties of error correcting codes for noise models in the presence of asymmetries and/or correlations by means of the entanglement fidelity and the code entropy. First, we consider a dephasing Markovian memory channel and…
We study the performance of simple error correcting and error avoiding quantum codes together with their concatenation for correlated noise models. Specifically, we consider two error models: i) a bit-flip (phase-flip) noisy Markovian…
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…
Fault-tolerant quantum computation techniques rely on weakly correlated noise. Here I show that it is enough to assume weak spatial correlations: time correlations can take any form. In particular, single-shot error correction techniques…
Most of the research done on quantum error correction studies an error model in which each qubit is affected by noise, independently of the other qubits. In this paper we study a different noise model -- one in which the noise may be…
We investigate an efficient quantum error correction of a fully correlated noise. Suppose the noise is characterized by a quantum channel whose error operators take fully correlated forms given by $\sigma_x^{\otimes n}$, $\sigma_y^{\otimes…
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…
Surface codes are promising for practical quantum error correction due to their high threshold and experimental feasibility. However, their performance under realistic noise conditions, particularly those involving correlated errors,…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
A scheme to evaluate computation fidelities within the one-way model is developed and explored to understand the role of correlations in the quality of noisy quantum computations. The formalism is promptly applied to many computation…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…
We investigate effective noise channels for encoded quantum systems with and without active error correction. Noise acting on physical qubits forming a logical qubit is thereby described as a logical noise channel acting on the logical…
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…
In order to realize fault-tolerant quantum computation, tight evaluation of error threshold under practical noise models is essential. While non-Clifford noise is ubiquitous in experiments, the error threshold under non-Clifford noise…
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…
In quantum error correction, it is an important assumption that errors on different qubits are independent. In our previous work [Phys. Rev. A {\bf 92}, 052320 (2015)], the generality of the concatenated five-qubit code has been investgated…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
Superdense Coding is a cornerstone in secure quantum communication, exploiting pre-shared entanglement to encode two classical bits within a single qubit. However, noise and decoherence deteriorate entanglement quality, restricting both…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…