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COFI-DQI: Curve-based Optimal Function Intersection via Decoded Quantum Interferometry
Gretchen L. Matthews, Julia Shapiro
In 2025, Jordan et al. introduced Decoded Quantum Interferometry (DQI), a quantum algorithm for combinatorial optimization based on decoding. They considered Reed-Solomon decoding…
Entanglement-assisted quantum locally recoverable codes: bounds and constructions with availability
Rutuja Kshirsagar, Gretchen L. Matthews, Julia Shapiro
In this work, we define entanglement-assisted quantum locally recoverable codes with availability, in which any set of up to erased qudits can be recovered from any one of $t…
Combinatorial Analysis of Dyadic and Quasi-Dyadic Codes
Anthony Gómez-Fonseca, Gretchen L. Matthews, Kirsten D. Morris +1
Quantum low-density parity-check (QLDPC) codes offer a promising route to scalable fault-tolerant quantum computation, but their performance under iterative decoding is strongly in…
List-Decodable Folded Quantum Hermitian Codes
Julia Shapiro, Gretchen L. Matthews
Folded Reed-Solomon codes, introduced by Guruswami and Rudra in 2007, have been shown to achieve the information-theoretically best possible trade-off between the rate of a code an…
Permutation decoding of algebraic geometry codes from Hermitian and norm-trace curves
Monica Lichtenwalner, Hiram H. López, Gretchen L. Matthews +1
Permutation decoding is a process that utilizes the permutation automorphism group of a linear code to correct errors in received words. Given a received word, a set of automorphis…