Mainz 2026 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 67: Poster – Quantum Information
Q 67.28: Poster
Thursday, March 5, 2026, 17:00–19:00, Philo 2. OG
Quantum searches as quantum walks on a graph with variable connectivity — •Giovanni Ragazzi1, Emma King2, Paolo Bordone1, Giovanna Morigi2,3, Matteo Paris4, and Andrea Solfanelli5 — 1Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, I-41125 Modena, Italy — 2Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany — 3Center for Quantum Technologies (QuTe), Saarland University, Campus, 66123 Saarbruecken, Germany — 4Dipartimento di Fisica Aldo Pontremoli, Università di Milano, I-20133 Milano, Italy — 5Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
A quantum walk on a lattice is a paradigm of a quantum search in a database. For quantum walks on a continuous time, the walker diffuses across the lattice and the search ends when it localizes at the target site. The search time T can exhibit Grover’s optimal scaling with the lattice size N, namely, T∼√N, on an all-connected, complete lattice. For finite-range tunneling between sites, instead, Grover’s optimal scaling is warranted when the lattice is a hypercube of d>4 dimensions. In a recent work, it was shown that Grover’s optimum can be reached in lower dimensions on lattices of long-range interacting particles, when the interaction strength scales algebraically with the distance r as 1/rα and 0<α<3d/2. In this contribution, we extend the formalism to determine the computational time complexities of quantum walks on graph with different geometries, considering in particular sparse graphs and chiral effects.
Keywords: Continuous-time quantum walk; Quantum search; Graph theory