Related papers: On Transversality Across Two Distinct Quantum Erro…

The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure,…

Asymmetric quantum error-correcting codes (AQCs) may offer some advantage over their symmetric counterparts by providing better error-correction for the more frequent error types. The well-known CSS construction of $q$-ary AQCs is extended…

In order to perform universal fault-tolerant quantum computation, one needs to implement a logical non-Clifford gate. Consequently, it is important to understand codes that implement such gates transversally. In this paper, we adopt an…

In 2018, Renes [IEEE Trans. Inf. Theory, vol. 64, no. 1, pp. 577-592 (2018)] (arXiv:1701.05583) developed a general theory of channel duality for classical-input quantum-output (CQ) channels. That result showed that a number of well-known…

This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…

We present a family of quantum error-correcting codes that support a universal set of transversal logic gates using only local operations on a two-dimensional array of physical qubits. The construction is a subsystem version of color codes…

We analyze and study the effects of locality on the fault-tolerance threshold for quantum computation. We analytically estimate how the threshold will depend on a scale parameter r which estimates the scale-up in the size of the circuit due…

The inherent uncertainty of communication channels implies that any coding scheme has a non-zero probability of failing to correct errors, making retransmission mechanisms essential. To ensure message reliability and integrity, a dual-layer…

Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a…

This article explores the application of coding techniques for fault-tolerant quantum computation and extends their usage to fault-tolerant quantum communication. We review repeater-based quantum networks, emphasizing the roles of coding…

When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very…

In this paper, we focus on the problem of computing the set of diagonal transversal gates fixing a CSS code. We determine the logical actions of the gates as well as the groups of transversal gates that induce non-trivial logical gates 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…

Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…

We transfer the concept of linear feed-back shift registers to quantum circuits. It is shown how to use these quantum linear shift registers for encoding and decoding cyclic quantum error-correcting codes.

Quantum repeaters constitute a promising platform for enabling long distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An…

This dissertation considers new constructions and decoding approaches for error-correcting codes based on non-conventional polynomials, with the objective of providing new coding solutions to the applications mentioned above. With skew…

Quantum error correction (QEC) codes are traditionally defined and searched for without specifying the manner in which its syndrome extraction circuits are executed using elementary gates and measurements. We show how morphing circuits…

Quantum key distribution (QKD) allows two distant parties to share encryption keys with security based on laws of quantum mechanics. In order to share the keys, the quantum bits have to be transmitted from the sender to the receiver over a…

Quantum communication typically involves a linear chain of repeater stations, each capable of reliable local quantum computation and connected to their nearest neighbors by unreliable communication links. The communication rate in existing…