Related papers: Is A Quantum Stabilizer Code Degenerate or Nondege…
Quantum error correction is essential for realizing scalable quantum computation. Among various approaches, low-density parity-check codes over higher-order Galois fields have shown promising performance due to their structured sparsity and…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…
In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based…
A central requirement for any quantum error correction scheme is the ability to perform quantum non-demolition measurements of an error syndrome, corresponding to a special symmetry property of the encoding scheme. It is in particular…
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in…
Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…
We introduce a family of 2D topological subsystem quantum error-correcting codes. The gauge group is generated by 2-local Pauli operators, so that 2-local measurements are enough to recover the error syndrome. We study the computational…
Analysis of quantum error correcting codes is typically done using a stochastic, Pauli channel error model for describing the noise on physical qubits. However, it was recently found that coherent errors (systematic rotations) on physical…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…
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…
Error correction is of utmost necessity for large-scale quantum computing. Quantum error correcting codes can be degenerate, if more than one type of error can map the input state to the same error state. In this paper, we propose a 6-qubit…
In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
Codeword stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and non-additive quantum codes. Standard codeword stabilized quantum codes encode quantum information into…
The quantum Hamming bound was originally put forward as an upper bound on the parameters of nondegenerate quantum codes, but over the past few decades much work has been done to show that many degenerate quantum codes must also obey this…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
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…