Nonlocality in instantaneous quantum circuits

TL;DR

This paper investigates the nonlocality of IQP circuits, demonstrating that their nonlocal correlations require post-selection to be observed and linking this to their computational advantages.

Contribution

It proves that nonlocality in IQP circuits can only be shown with post-selection, highlighting the importance of this technique for quantum computational advantage.

Findings

Nonlocality in IQP circuits is linked to Bell tests.

Post-selection is necessary to demonstrate nonlocality.

IQP circuits with hard-to-sample distributions benefit from post-selection.

Abstract

We show that families of Instantaneous Quantum Polynomial (IQP) circuits corresponding to nontrivial Bell tests exhibit nonlocality. However, we also prove that this nonlocality can only be demonstrated using post-selection or nonlinear processing of the measurement outcomes. Therefore if the output of a computation is encoded in the parity of the measurement outcomes, then families of IQP circuits whose full output distributions are hard to sample still only provide a computational advantage relative to locally causal theories under post-selection. Consequently, post-selection is a crucial technique for obtaining a computational advantage for IQP circuits (with respect to decision problems) and for demonstrating nonlocality within IQP circuits, suggesting a strong link between these phenomena.