Unconditional quantum advantage with noisy planar architectures

Libor Caha; Robert Koenig; Louis Paletta

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arXiv · 2609.40050

Unconditional quantum advantage with noisy planar architectures

Libor Caha·Robert Koenig·Louis Paletta

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Abstract

We consider quantum devices restricted to local operations in 2D and subject to local stochastic noise below a constant threshold. We show that such circuits are computationally more powerful than AC0-circuits, i.e., noise-free, geometrically-unconstrained constant-depth classical circuits with unbounded fan-in AND, OR and NOT gates. To this end, we exhibit a computational problem with the following properties: (i) Any instance of the problem is correctly solved with high probability by a certain geometrically 2D-local quantum circuit even if the latter is imperfectly implemented, but (ii) any polynomial-size AC0-circuit fails to solve certain instances of the problem with constant probability. To our knowledge, this isthe first complexity-theoretic separation which applies to planar quantum devices, incorporates noise-resilience and is unconditional, i.e., does not rely on complexity-theoretic assumptions. This brings the experimental demonstration of an unconditional quantum advantage closer to experimental realities.

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Libor Caha, Robert Koenig, Louis Paletta. 2026-09-30. Unconditional quantum advantage with noisy planar architectures. https://arxiv.org/abs/2609.40050

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