Related papers: Hardness of decoding quantum stabilizer codes
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…
We present a decoding algorithm for quantum convolutional codes that finds the class of degenerate errors with the largest probability conditioned on a given error syndrome. The algorithm runs in time linear with the number of qubits.…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm'…
I. This paper is devoted to the problem of error detection with quantum codes. In the first part we examine possible problem settings for quantum error detection. Our goal is to derive a functional that describes the probability of…
We develop a most likely error Pauli error decoding algorithm for stabiliser codes based on general purpose integer optimisation. Using this decoder we analyse the performance of holographic codes against Pauli errors and find numerical…
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
Decoding sparse quantum codes can be accomplished by syndrome-based decoding using a belief propagation (BP) algorithm.We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard BP…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across…
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…
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…
Utilizing a quantum system for reservoir computing has recently received a lot of attention. Key challenges are related to how on can optimally en- and decode classical information, as well as what constitutes a good reservoir. Our main…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
Maximum-likelihood decoding is one of the central algorithmic problems in coding theory. It has been known for over 25 years that maximum-likelihood decoding of general linear codes is NP-hard. Nevertheless, it was so far unknown whether…
Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…