An unconditional distribution learning advantage with shallow quantum circuits
This addresses the challenge of demonstrating practical quantum advantages for near-term applications, though it is incremental as it builds on prior sampling results.
The paper proves an unconditional quantum advantage for shallow quantum circuits in the PAC distribution learning framework, showing that constant-depth quantum circuits (QNC^0) outperform constant-depth classical circuits (NC^0) on a specific generative distribution learning problem.
One of the core challenges of research in quantum computing is concerned with the question whether quantum advantages can be found for near-term quantum circuits that have implications for practical applications. Motivated by this mindset, in this work, we prove an unconditional quantum advantage in the probably approximately correct (PAC) distribution learning framework with shallow quantum circuit hypotheses. We identify a meaningful generative distribution learning problem where constant-depth quantum circuits using one and two qubit gates (QNC^0) are superior compared to constant-depth bounded fan-in classical circuits (NC^0) as a choice for hypothesis classes. We hence prove a PAC distribution learning separation for shallow quantum circuits over shallow classical circuits. We do so by building on recent results by Bene Watts and Parham on unconditional quantum advantages for sampling tasks with shallow circuits, which we technically uplift to a hyperplane learning problem, identifying non-local correlations as the origin of the quantum advantage.