A Quantum Algorithm for st-Transport on Flat Connection Graphs
The paper presents a quantum algorithm for state transport (st-transport) on graphs where edges have quantum operations, provided these operations form a 'flat connection.' The algorithm estimates the squared overlap between two states transported between vertices with bounded error. It achieves optimal time complexity of Oe(n/epsilon) and space complexity of O(log n + log k + log(1/epsilon)) for constant error.