Does co-NP have short interactive proofs?
Information Processing Letters
Graph isomorphism is in the low hierarchy
Journal of Computer and System Sciences
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
A Linear-Time Algorithm for Isomorphism of Graphs of Bounded Average Genus
SIAM Journal on Discrete Mathematics
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum mechanical algorithms for the nonabelian hidden subgroup problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum lower bound for the collision problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Adiabatic quantum state generation and statistical zero knowledge
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Graph matching using the interference of continuous-time quantum walks
Pattern Recognition
Graph embedding using a quasi-quantum analogue of the hitting times of continuous time quantum walks
Quantum Information & Computation
On the relation between quantum walks and zeta functions
Quantum Information Processing
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The graph isomorphism problem (GI) plays a central role in the theory of computational complexity and has importance in physics and chemistry as well [1, 2]. No polynomial-time algorithm for solving GI is knowm We investigate classical and quantum physics-based polynomial-time algorithms for solving the graph isomorphism problem in which the graph structure is reflected in the behavior of a dynamical system. We show that a classical dynamical algorithm proposed by Gudkov and Nussinov [25] as well as its simplest quantum generalization fail to distinguish pairs of non-isomorphlc strongly regular graphs. However, by combining the algorithm of Gudkov and Nussinov with a construction proposed by Rudolph [26] in which one examines a graph describing the dynamics of two particles on the original graph, we find an algorithm that successfully distinguishes all pairs of non-isomorphic strongly regular graphs that we tested with up to 29 vertices.