Connes Distance in Discrete-Time Quantum Walks

arXiv:2609.31488 · quant-ph · Submitted 2026-09-25 · Read on arXiv

quant-ph

Submitted: 2026-09-25

Updated: 2026-09-25

Terminology

• Hilbert Space — 6× in this paper · explained in 2 episodes
• Objective Function — 4× in this paper · explained in 2 episodes
• Spectral Geometry — 4× in this paper · explained in 2 episodes
• Optimal Transport — 2× in this paper · explained in 5 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Consistency — 1× in this paper · explained in 3 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Universality Class — 1× in this paper · explained in 2 episodes
• Wasserstein Distance — 1× in this paper · explained in 4 episodes

Sources

• A quantum walk with both a continuous-time and a continuous-spacetime limit
• An Introduction to Noncommutative Geometry
• Noncommutative geometry of the Moyal plane: translation isometries, Connes' distance on coherent states, Pythagoras equality
• Connes' distance function on one-dimensional lattices
• Estimating noncommutative distances on graphs
• A New Type of Limit Theorems for the One-Dimensional Quantum Random Walk
• A View on Optimal Transport from Noncommutative Geometry
• Discrete-time quantum walks and gauge theories
• The Dirac equation as a quantum walk: higher dimensions, observational convergence

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity