Simulating and Sampling from Quantum Circuits with 2D Tensor Networks

Classical simulations of quantum circuits play a vital role in the development of quantum computers and for taking the temperature of the field. In this work, we classically simulate various physically-motivated circuits using flexible 2D tensor network ansätze for the many-body wavefunction which match the geometry of the underlying quantum processor. We then employ a generalized version of the boundary Matrix Product State contraction algorithm to controllably generate samples from the resultant tensor network states. Our approach allows us to systematically converge both the quality of the simulated state and the samples drawn from it to the true distribution defined by the circuit, with GPU hardware providing us with significant speedups over CPU hardware. With these methods, we simulate the largest local unitary Jastrow ansatz circuit taken from recent IBM experiments to numerical precision. We also study a domain-wall quench in a two-dimensional discrete-time Heisenberg model on IBM's and Google's latest quantum processor geometries. There we observe a rapid buildup of complex loop correlations on the Google Willow geometry, while loop correlations build up extremely slowly on heavy-hex processors. This implies that scalable belief propagation approaches can be used to estimate local properties of such systems, even at large circuit depths. Our results underscore the crucial role geometry plays in the classical simulability of near-term quantum processors via modern tensor networks.