Classical Simulation of Quantum Supremacy Circuits

TL;DR

This paper introduces a tensor network-based classical simulation method for quantum circuits used in quantum supremacy experiments, significantly reducing simulation time and challenging the notion of an immediate quantum advantage.

Contribution

It presents a novel classical simulation algorithm that can efficiently simulate quantum supremacy circuits, reducing the estimated required time from thousands of years to less than a month.

Findings

Simulation of quantum supremacy circuits in under 20 days

Reduction of classical simulation time from years to minutes on moderate instances

Demonstrates that quantum supremacy claims may require further hardware advancements

Abstract

It is believed that random quantum circuits are difficult to simulate classically. These have been used to demonstrate quantum supremacy: the execution of a computational task on a quantum computer that is infeasible for any classical computer. The task underlying the assertion of quantum supremacy by Arute et al. (Nature, 574, 505--510 (2019)) was initially estimated to require Summit, the world's most powerful supercomputer today, approximately 10,000 years. The same task was performed on the Sycamore quantum processor in only 200 seconds. In this work, we present a tensor network-based classical simulation algorithm. Using a Summit-comparable cluster, we estimate that our simulator can perform this task in less than 20 days. On moderately-sized instances, we reduce the runtime from years to minutes, running several times faster than Sycamore itself. These estimates are based on explicit simulations of parallel subtasks, and leave no room for hidden costs. The simulator's key ingredient is identifying and optimizing the "stem" of the computation: a sequence of pairwise tensor contractions that dominates the computational cost. This orders-of-magnitude reduction in classical simulation time, together with proposals for further significant improvements, indicates that achieving quantum supremacy may require a period of continuing quantum hardware developments without an unequivocal first demonstration.