12 papers
Single Link Removal Perturbation in Szegedy Quantum Walk: from Graph Completeness Testing to Integrity Monitoring
Sara Giordano, Miguel A. Martin-Delgado
We present a rigorous perturbative analysis of the Szegedy quantum walk search algorithm on the complete graph with marked nodes, when a specific anomaly is present in the graph. T…
Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code
Ji-Ze Xu, Yin Zhong, Miguel A. Martin-Delgado +2
Three-dimensional (3D) topological codes offer the advantage of supporting fault-tolerant implementations of non-Clifford gates, yet their performance against realistic noise remai…
Anomalous Pairing Currents and a Second Topological Edge Channel in Bosonic Lattices
Chitrak Bhadra, Ãngel Rivas, Miguel A. Martin-Delgado
We show that bosonic pairing opens a second chiral current channel on a 2D kagome lattice, absent from any particle-conserving model. From the continuity equation, we derive both a…
Homomorphic Quantum Error Correction
Kornikar Sen, Miguel A. Martin-Delgado
Homomorphic quantum error correction aims to protect quantum data against both unauthorized access and environmental noise during server-based processing. We investigate the algebr…
From Hilbert's Tenth Problem to Quantum Speedup: Explicit Oracles for Bounded Diophantine Systems
Gabriel Escrig, M. A. Martin-Delgado
Solving non-linear Diophantine systems lies at the mathematical core of integer optimization and cryptography. While the general unbounded problem is undecidable, even over bounded…
Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions
Giovanni Canossa, Lode Pollet, Miguel A. Martin-Delgado +2
Fracton codes have been intensively studied as novel topological states of matter, yet their fault-tolerant properties remain largely unexplored. Here, we investigate the optimal t…