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The task of preserving entanglement against noises is of crucial importance for both quantum communication and quantum information transfer. To this aim, quantum error correction (QEC) codes may be employed to compensate, at least…
Quantum error-correcting code (QECC) is the central ingredient in fault-tolerant quantum information processing. An emerging paradigm of dynamical QECC shows that one can robustly encode logical quantum information both temporally and…
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…
The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The…
Many physical systems considered promising qubit candidates are not, in fact, two-level systems. Such systems can leak out of the preferred computational states, leading to errors on any qubits that interact with leaked qubits. Without…
We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
Quantum error correction will be a necessary component towards realizing scalable quantum computers with physical qubits. Theoretically, it is possible to perform arbitrarily long computations if the error rate is below a threshold value.…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and…
A universal set of quantum gates is constructed for the recently developed jump-error correcting quantum codes. These quantum codes are capable of correcting errors arising from the spontaneous decay of distinguishable qubits into…
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…
We first give a construction of binary $t_1$-deletion-$t_2$-insertion-burst correcting codes with redundancy at most $\log(n)+(t_1-t_2-1)\log\log(n)+O(1)$, where $t_1\ge 2t_2$. Then we give an improved construction of binary codes capable…
The study of holographic bulk-boundary dualities has led to the construction of novel quantum error correcting codes. Although these codes have shed new light on conceptual aspects of these dualities, they have widely been believed to lack…
We investigate the use of Quantum Neural Networks for discovering and implementing quantum error-correcting codes. Our research showcases the efficacy of Quantum Neural Networks through the successful implementation of the Bit-Flip quantum…
Multi-valued quantum systems can store more information than binary ones for a given number of quantum states. For reliable operation of multi-valued quantum systems, error correction is mandated. In this paper, we propose a 5-qutrit…
It is important to protect quantum information against decoherence and operational errors, and quantum error-correcting (QEC) codes are the keys to solving this problem. Of course, just the existence of codes is not efficient. It is…
Superconducting qubits, while promising for scalability and long coherence times, contain more than two energy levels, and therefore are susceptible to errors generated by the leakage of population outside of the computational subspace.…
We propose an architecture for a quantum memory distributed over a $2 \times L$ array of modules equipped with a cyclic shift implemented via flying qubits. The logical information is distributed across the first row of $L$ modules and…