A game of quantum advantage: linking verification and simulation

TL;DR

This paper introduces a formal framework modeling quantum advantage verification as an interactive game, revealing fundamental limits and effects of noise on classical simulation and verification of quantum devices.

Contribution

It formalizes the verification process as a game, linking distinguishability to simulation complexity, and analyzes noise effects on quantum advantage verification.

Findings

Efficient distinguishability implies efficient simulation for random circuits.

Polynomial-time distinguishability can spoof heavy output generation.

Exponential resources may be necessary for basic verification tasks.

Abstract

We present a formalism that captures the process of proving quantum superiority to skeptics as an interactive game between two agents, supervised by a referee. Bob, is sampling from a classical distribution on a quantum device that is supposed to demonstrate a quantum advantage. The other player, the skeptical Alice, is then allowed to propose mock distributions supposed to reproduce Bob's device's statistics. He then needs to provide witness functions to prove that Alice's proposed mock distributions cannot properly approximate his device. Within this framework, we establish three results. First, for random quantum circuits, Bob being able to efficiently distinguish his distribution from Alice's implies efficient approximate simulation of the distribution. Secondly, finding a polynomial time function to distinguish the output of random circuits from the uniform distribution can also spoof the heavy output generation problem in polynomial time. This pinpoints that exponential resources may be unavoidable for even the most basic verification tasks in the setting of random quantum circuits. Beyond this setting, by employing strong data processing inequalities, our framework allows us to analyse the effect of noise on classical simulability and verification of more general near-term quantum advantage proposals.