Related papers: Degenerate Quantum Codes for Pauli Channels
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 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 consider the problem of decoding corrupted error correcting codes with NC$^0[\oplus]$ circuits in the classical and quantum settings. We show that any such classical circuit can correctly recover only a vanishingly small fraction of…
We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single…
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…
In quantum error correction, the description of noise channel cannot be completely accurate, and fluctuation always appears in noise channel. It is found that when fluctuation of physical noise channel is considered, the average effective…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
We determine the optimal rates of universal quantum codes for entanglement transmission and generation under channel uncertainty. In the simplest scenario the sender and receiver are provided merely with the information that the channel…
Encoding schemes and error-correcting codes are widely used in information technology to improve the reliability of data transmission over real-world communication channels. Quantum information protocols can further enhance the performance…
We re-examine a non-Gaussian quantum error correction code designed to protect optical coherent-state qubits against errors due to an amplitude damping channel. We improve on a previous result [Phys. Rev. A 81, 062344 (2010)] by providing a…
Quantum cryptography via key distribution mechanisms that utilize quantum entanglement between sender-receiver pairs will form the basis of future large-scale quantum networks. A key engineering challenge in such networks will be the…
We analyze the practical performance of quantum polar codes, by computing rigorous bounds on block error probability and by numerically simulating them. We evaluate our bounds for quantum erasure channels with coding block lengths between…
We investigate practical finite-blocklength classical-quantum channel coding over the quantum amplitude damping channel (ADC), aiming to transmit classical information reliably through quantum outputs. Our findings indicate that for any…
Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
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…
Coherent noise can be much more damaging than incoherent (probabilistic) noise in the context of quantum error correction. One solution is to use twirling to turn coherent noise into incoherent Pauli channels. In this Article, we show that…
A Quantum Computer is a new type of computer which can solve problems such as factoring and database search very efficiently. The usefulness of a quantum computer is limited by the effect of two different types of errors, decoherence and…
We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…