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The performance of quantum error correction can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error rates from the syndrome…
We study encodings that give the best known thresholds for the non-zero capacity of quantum channels, i.e., the upper bound for correctable noise, using an entropic approach to calculation of the threshold values. Our results show that…
The error threshold of a one-parameter family of quantum channels is defined as the largest noise level such that the quantum capacity of the channel remains positive. This in turn guarantees the existence of a quantum error correction code…
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic…
The characterization of quantum devices is crucial for their practical implementation but can be costly in experimental effort and classical postprocessing. Therefore, it is desirable to measure only the information that is relevant for…
This paper focuses on error thresholds for Pauli channels. We numerically compute lower bounds for the thresholds using the analytic framework of coset weight enumerators pioneered by DiVincenzo, Shor and Smolin in 1998. In particular, we…
In this work we improve the quantum communication rates of various quantum channels of interest using permutation-invariant quantum codes. We focus in particular on parametrized families of quantum channels and aim to improve bounds on…
Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit,…
We develop a most likely error Pauli error decoding algorithm for stabiliser codes based on general purpose integer optimisation. Using this decoder we analyse the performance of holographic codes against Pauli errors and find numerical…
The Pauli stabilizer formalism is perhaps the most thoroughly studied means of procuring quantum error-correcting codes, whereby the code is obtained through commutative Pauli operators and ``stabilized'' by them. In this work we will show…
A striking feature of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. Such degenerate codes have long been known, but have remained poorly understood. We provide a…
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 instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of…
Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, R is…
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…
We extend a low-rate improvement of the random coding bound on the reliability of a classical discrete memoryless channel to its quantum counterpart. The key observation that we make is that the problem of bounding below the error exponent…
We introduce graph state basis diagonalization to calculate the coherent information of a quantum code passing through a Pauli channel. The scheme is 5000 times faster than the best known one for some concatenated repetition codes,…
Quantum communication and computation heavily rely on entanglement distillation protocols. There is a plethora of distillation protocols for Pauli channels and also for some non-Pauli channels. However, an effort to relate the effectiveness…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…