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Quantum higher-order Fourier analysis and the Clifford hierarchy. [PDF]
Proc Natl Acad Sci U S ABu K, Gu W, Jaffe A.
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Quantum-secured routing in drone communication for 6G-enabled smart mobility. [PDF]
Sci RepHafeez S +5 more
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Complexity of quantum tomography from genuine non-Gaussian entanglement. [PDF]
Nat CommunZhao X +4 more
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Homological error correction: Classical and quantum codes [PDF]
Journal of Mathematical Physics, 2007 We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming bound. In the quantum case, we show that for nonorientable surfaces it is impossible to construct homological ...
H Bombin, M A Martín-Delgado
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Perfect Quantum Error Correcting Code
Physical Review Letters, 1996We present a quantum error correction code which protects a qubit of information against general one qubit errors. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We describe a circuit which takes the initial state with four extra qubits in the state $|0〉$
, Laflamme, , Miquel, , Paz, , Zurek
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Permutationally invariant codes for quantum error correction
Linear Algebra and Its Applications, 2004 A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible representations, both those of higher dimension and orthogonal bases for the trivial representation, are available for error ...
Harriet Pollatsek, Mary Beth Ruskai
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Quantum error correction codes.
2022Quantum parallel processing techniques are capable of solving certain complex problems at a substantially lower complexity than their classical counterparts. From the perspective of telecommunications, this quantum-domain parallel processing provides a plausible solution for achieving full-search based multi-stream detection, which is vital for future ...
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Classic and Quantum Error Correcting Codes
2008Algebraic methods play an important role in coding theory. For instance, there are many connections between codes and groups. In this paper we will present two results that show different applications of algebraic methods in coding theory. One of them refers to the classical context and another one to the quantum error correcting theory.
Santos González +2 more
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