Related papers: Quantum Convolutional Error Correction Codes
We present a method for performing quantum state reconstruction on qubits and qubit registers in the presence of decoherence and inhomogeneous broadening. The method assumes only rudimentary single qubit rotations as well as knowledge of…
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…
It is often assumed that the ancilla qubits required for encoding a qubit in quantum error correction (QEC) have to be in pure states, $|00...0>$ for example. In this letter, we seek an encoding scheme, in which the ancillae may be in a…
Advances in single photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have losses low enough to be correctable using a quantum error correcting code. Such error-corrected…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
We develop a framework for constructing quantum error-correcting codes and logical gates for three types of spaces -- composite permutation-invariant spaces of many qubits or qudits, composite constant-excitation Fock-state spaces of many…
We propose two systematic constructions of deletion-correcting codes for protecting quantum information. The first one works with qudits of any dimension, but only one deletion is corrected and the constructed codes are asymptotically bad.…
Quantum error detection has always been a fundamental challenge in a fault-tolerant quantum computer. Hence, it is of immense importance to detect and deal with arbitrary errors to efficiently perform quantum computation. Several error…
We show how to perform error correction of single qubit dephasing by encoding a single qubit into a minimum of three. This may be performed in a manner closely analogous to classical error correction schemes. Further, the resulting quantum…
Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve performance of next generations of quantum hardware. In order to investigate the importance of the different noise mechanisms affecting…
Traditional quantum error correction involves the redundant encoding of k quantum bits using n quantum bits to allow the detection and correction of any t bit error. The smallest general t=1 code requires n=5 for k=1. However, the dominant…
We describe a fault-tolerant one-way quantum computer on cluster states in three dimensions. The presented scheme uses methods of topological error correction resulting from a link between cluster states and surface codes. The error…
We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and…
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in…
Modular quantum computing architectures require error correction schemes that remain effective in the presense of noisy inter-processor operations. We introduce a distributed quantum error correction framework based on approximate codes to…
A family of high rate quantum error correcting codes adapted to the amplitude damping channel is presented. These codes are nonadditive and exploit self-complementarity structure to correct all first-order errors. Their rates can be higher…
The storage and processing of quantum information are susceptible to external noise, resulting in computational errors that are inherently continuous A powerful method to suppress these effects is to use quantum error correction. Typically,…
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…