Simulating quantum circuits using efficient tensor network contraction algorithms with subexponential upper bound

We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in d ≥ 2 dimensions. By means of the Sphere Separator Theorem, we are able to take advantage of the structure of quantum circuits to speed up contractions to show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be classically simulated in subexponential time in the number of gates. In many practically relevant cases this beats standard simulation schemes. Moreover, our algorithm leads to speedups of several orders of magnitude over naive contraction schemes for two-dimensional quantum circuits on as little as an 8 × 8 lattice. We obtain similarly efficient contraction schemes for Google's Sycamore-type quantum circuits, instantaneous quantum polynomial-time circuits, and non-homogeneous (2+1)-dimensional random quantum circuits.