Related papers: Adaptively correcting quantum errors with entangle…
In the previous research by Grassl, Huber and Winter, they proved a theorem which can make entanglement-assisted quantum error-correcting codes (EAQECC) from general quantum error-correcting codes (QECC). In this paper, we prove that the…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…
The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is defined from the orthogonal group of a simplified stabilizer group. From the Poisson summation formula, this duality leads to the MacWilliams identities and…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In this work, we…
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 correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of…
Connecting multiple smaller qubit modules by generating high-fidelity entangled states is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer is highly dependent on the quality and…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
In this article we study the role that quantum resources play in quantum error correction assisted quantum metrology (QECQM) schemes. We show that there exist classes of such problems where entanglement is not necessary to retrieve noise…
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…
In this paper we introduce a universal operator theoretic framework for quantum fault tolerance. This incorporates a top-down approach that implements a system-level criterion based on specification of the full system dynamics, applied at…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
Quantum entanglement is a unique criterion of the quantum realm and an essential tool to secure quantum communication. Ensuring high-fidelity entanglement has always been a challenging task owing to interaction with the hostile channel…
In this paper I explore the entanglement evolution of qubits that are part of a five qubit quantum error correction code subject to various decohering environments. Specifically, I look for possible parallels between the entanglement…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement…