Related papers: Nonadditive quantum error correcting codes adapted…
In this paper we study an error correcting protocol that specifically derives its error correcting properties from elementary units of coherence. The entire protocol from beginning to end is performed using non-coherence increasing…
We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…
The optimal exponential error rate for adaptive discrimination of two channels is discussed. In this problem, adaptive choice of input signal is allowed. This problem is discussed in various settings. It is proved that adaptive choice does…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…
To well understand the behavior of quantum error correction codes (QECC) in noise processes, we need to obtain explicit coding maps for QECC. Due to extraordinary amount of computational labor that they entails, explicit coding maps are a…
Fault tolerant protocol assumes the application of error correction after every quantum gate. However, correcting errors is costly in terms of time and number of qubits. Here we demonstrate that quantum error correction can be applied…
Noise poses a fundamental challenge to quantum information processing, with amplitude-damping (AD) noise being particularly detrimental. Preserving high-fidelity quantum systems therefore relies critically on effective error correction and…
Quantum error correction (QEC) is an essential element of physical quantum information processing systems. Most QEC efforts focus on extending classical error correction schemes to the quantum regime. The input to a noisy system is embedded…
We extend a low-rate improvement of the random coding bound on the reliability of a classical discrete memoryless channel to its quantum counterpart. The key observation that we make is that the problem of bounding below the error exponent…
We demonstrate that the performance of quantum error correction can be improved with noise-aware decoders that are calibrated to the likelihood of physical error configurations in a device. We show that noise-aware decoding increases the…
Current approaches to fault-tolerant quantum computation will not enable useful quantum computation on near-term devices of 50 to 100 qubits. Leading proposals, such as the color code and surface code schemes, must devote a large fraction…
This paper studies the second-order asymptotics of coding rates for the discrete memoryless multiple-access channel with a fixed target error probability. Using constant-composition random coding, coded time-sharing, and a variant of…
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…
We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
The highest information rate at which quantum error-correction schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over…
I report two general methods to construct quantum convolutional codes for $N$-state quantum systems. Using these general methods, I construct a quantum convolutional code of rate 1/4, which can correct one quantum error for every eight…
The Knill-Laflamme (KL) conditions distinguish exact quantum error correction codes, and it has played a critical role in the discovery of state-of-the-art codes. However, the family of exact codes is a very restrictive one and does not…
Fault-tolerant quantum computations require alternating quantum and classical computations, where the classical computations prove vital in detecting and correcting errors in the quantum computation. Recently, interest in using these…