22 citations · 69 across the 8 of their papers we have counts for
8 papers
Complexity Bounds on Quantum Search Algorithms in finite-dimensional Networks
Stefan Boettcher, Shanshan Li, Tharso D. Fernandes +1
We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gai…
Analysis of Coined Quantum Walks with Renormalization
Stefan Boettcher, Shanshan Li
We introduce a new framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time q…
Parametric Solution of a Small-Large Black Hole Coexistence Curve
Shanshan Li, Dan-Dan Li, Li-Qin Mi +1
We consider the first-order phase transition of a charged anti-de Sitter black hole, and find that the equation of state with the conditions of the two coexisting phases, leads to…
The Griffiths Phase on Hierarchical Modular Networks with Small-world Edges
Shanshan Li
The Griffiths phase has been proposed to induce a stretched critical regime that facilitates self-organizing of brain networks for optimal function. This phase stems from the intri…
Renormalization of the Unitary Evolution Equation for Coined Quantum Walks
Stefan Boettcher, Shanshan Li, Renato Portugal
We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attentio…
Continuous Time Quantum Walks in finite Dimensions
Shanshan Li, Stefan Boettcher
We consider the quantum search problem with a continuous time quantum walk for networks of finite spectral dimension d_{s} of the network Laplacian. For general networks of fractal…
Evaluation of Spectral Zeta-Functions with the Renormalization Group
Stefan Boettcher, Shanshan Li
We evaluate spectral zeta-functions of certain network Laplacians that can be treated exactly with the renormalization group. As specific examples we consider a class of Hanoi netw…
Real-Space Renormalization Group for Spectral Properties of Hierarchical Networks
Stefan Boettcher, Shanshan Li
We derive the determinant of the Laplacian for the Hanoi networks and use it to determine their number of spanning trees (or graph complexity) asymptotically. While spanning trees…