Related papers: Universal Framework for Quantum Error-Correcting C…
The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum…
Duadic group algebra codes are a generalization of quadratic residue codes. This paper settles an open problem raised by Zhu concerning the existence of duadic group algebra codes. These codes can be used to construct degenerate quantum…
In this paper we provide a basic introduction of the core ideas and theories surrounding fault-tolerant quantum computation. These concepts underly the theoretical framework of large-scale quantum computation and communications and are the…
The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at…
We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. The key idea is to define two systems, one modelling…
Quantum gates and measurements on quantum hardware are inevitably subject to hardware imperfections that lead to quantum errors. Mitigating such unavoidable errors is crucial to explore the power of quantum hardware better. In this paper,…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
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…
We describe a method to execute globally controlled quantum information processing which admits a fault tolerant quantum error correction scheme. Our scheme nominally uses three species of addressable two-level systems which are arranged in…
Quantum error correcting codes have been developed to protect a quantum computer from decoherence due to a noisy environment. In this paper, we present two methods for optimizing the physical implementation of such error correction schemes.…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
In this dissertation, I present a general method for studying quantum error correction codes (QECCs). This method not only provides us an intuitive way of understanding QECCs, but also leads to several extensions of standard QECCs,…
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…
Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
Quantum information platforms made great progress in the control of many-body entanglement and the implementation of quantum error correction, but it remains a challenge to realize both in the same setup. Here, we propose a mixture of two…
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…
We describe new implementations of quantum error correction that are continuous in time, and thus described by continuous dynamical maps. We evaluate the performance of such schemes using numerical simulations, and comment on the…
While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary…
The concept of quantum interleaver and a simple method of quantum burst-error correction is proposed. By using the quantum interleaver, any quantum burst-errors that have occurred spread over the interleaved code word, so that we can…