Babai’s proposed algorithm doesn’t bring graph isomorphism all the way into P, but it comes close. It is quasi-polynomial, he asserts, which means that for a graph with n nodes, the algorithm’s ...

Here we develop a polynomial time algorithm that provably finds the ground state of any 1D quantum system described by a gapped local Hamiltonian with constant ground-state energy.

The result suggests that random circuit sampling won’t yield a quantum advantage by the rigorous standards of computational complexity theory. At the same time, it illustrates the fact that polynomial ...

Graph isomorphism in quasipolynomial time I: The “Local Certificates Algorithm.” Combinatorics and Theoretical Computer Science seminar, Chicago, November 10, 2015.

Computer scientists generally consider an algorithm to be efficient if its running time can be expressed not as a factorial but as a polynomial, such as n 2 or n 3; polynomials grow much more ...