Additive-error fine-grained quantum supremacy

TL;DR

This paper establishes that certain sub-universal quantum computing models cannot be efficiently simulated by classical computers even with additive errors, strengthening the case for quantum supremacy.

Contribution

It proves the first fine-grained quantum supremacy results for additive-error sampling across multiple quantum models.

Findings

Additive-error quantum supremacy is achievable for IQP, Clifford+$T$, and hybrid models.

Classical simulation of these models with additive errors would violate fine-grained complexity conjectures.

Results extend the understanding of quantum advantage beyond multiplicative-error scenarios.

Abstract

It is known that several sub-universal quantum computing models, such as the IQP model, the Boson sampling model, the one-clean qubit model, and the random circuit model, cannot be classically simulated in polynomial time under certain conjectures in classical complexity theory. Recently, these results have been improved to "fine-grained" versions where even exponential-time classical simulations are excluded assuming certain classical fine-grained complexity conjectures. All these fine-grained results are, however, about the hardness of strong simulations or multiplicative-error sampling. It was open whether any fine-grained quantum supremacy result can be shown for additive-error sampling. In this paper, we show the additive-error fine-grained quantum supremacy. As examples, we consider the IQP model, a mixture of the IQP model and log-depth Boolean circuits, and Clifford+$T$ circuits. Similar results should hold for other sub-universal models.