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Quantum error correction codes based on continuous variables play an important role for the implementation of quantum communication systems. A natural application of such codes occurs within quantum repeater systems which are used to combat…
We investigate the class of CSS-$T$ codes, a family of quantum error-correcting codes that allows for a transversal $T$-gate. We extend the definition of a pair of linear codes $(C_1,C_2)$, $C_i\subseteq\mathbb{F}_q^n$, forming a $q$-ary…
Quantum repeater networks have attracted attention for the implementation of long-distance and large-scale sharing of quantum states. Recently, researchers extended classical network coding, which is a technique for throughput enhancement,…
We investigate CSS and CSS-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a CSS code with good correction…
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes $(C_1, C_2)$ such that $C_1$ contains $C_2$, $C_2$ is even, and…
Quantum repeaters (QRs) provide a way of enabling long distance quantum communication by establishing entangled qubits between remote locations. We investigate a new approach to QRs in which quantum information can be faithfully transmitted…
Continuous-variable (CV) codes and their application in quantum communication have attracted increasing attention. In particular, one typical CV codes, cat-codes, has already been experimentally created using trapped atoms in cavities with…
We give a fault tolerant construction for error correction and computation using two punctured quantum Reed-Muller (PQRM) codes. In particular, we consider the $[[127,1,15]]$ self-dual doubly-even code that has transversal Clifford gates…
We propose an architecture of quantum-error-correction-based quantum repeaters that combines techniques used in discrete- and continuous-variable quantum information. Specifically, we propose to encode the transmitted qubits in a…
One-way quantum repeaters where loss and operational errors are counteracted by quantum error correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
Quantum networks serve as the means to transmit information, encoded in quantum bits or qubits, between quantum processors that are physically separated. Given the instability of qubits, the design of such networks is challenging,…
Transversal gates are logical gate operations on encoded quantum information that are efficient in gate count and depth, and are designed to minimize error propagation. Efficient encoding circuits for quantum codes that admit transversal…
Despite the tremendous progress of quantum cryptography, efficient quantum communication over long distances (>1000km) remains an outstanding challenge due to fiber attenuation and operation errors accumulated over the entire communication…
Calderbank-Shor-Steane (CSS) quantum error-correcting codes are based on pairs of classical codes which are mutually dual containing. Explicit constructions of such codes for large blocklengths and with good error correcting properties are…
Modern platforms for potential qubit candidates, such as trapped ions or neutral atoms, allow long range connectivity between distant physical qubits through shuttling. This opens up an avenue for transversal logical CNOT gates between…
Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with…
Code switching is an established technique that facilitates a universal set of FT quantum gate operations by combining two QEC codes with complementary sets of gates, which each by themselves are easy to implement fault-tolerantly. In this…
We propose a new approach to implement quantum repeaters for long distance quantum communication. Our protocol generates a backbone of encoded Bell pairs and uses the procedure of classical error correction during simultaneous entanglement…
Quantum error-correcting code for higher dimensional systems can, in general, be directly constructed from the codes for qubit systems. What remains unknown is whether there exist efficient code design techniques for higher dimensional…