Complex Quantum Dynamics Versus Classical Simulability of Noisy Random Circuits

Abstract:Claims of quantum advantage rest on the classical hardness of simulating quantum circuits. Magic, operator scrambling, anticoncentration, and non-Gaussianity for fermionic circuits are standard diagnostics of complex quantum dynamics. For pure states, some of these have been rigorously connected to classical simulability. Whether these diagnostics reliably track the limits of efficient classical simulation under noise remains unclear. Here, we show that in noisy Clifford+$T$ and nearest-neighbour matchgate+SWAP circuits, dynamical diagnostics and classical simulability can separate in both directions. In particular, the diagnostics can remain nontrivial after classical simulation becomes efficient, or become trivial before known efficient classical algorithms apply. We trace this mismatch to the different statistical properties they probe: magic and scrambling depend on fourth-order statistics of the Pauli spectrum, whereas the simulation algorithms depend primarily on second-order moments, which local noise suppresses at different rates. Thus, dynamical diagnostics measured on a noisy quantum device do not by themselves constitute evidence for classical hardness.

arXiv:2609.39734 [quant-ph]

(or arXiv:2609.39734v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.39734 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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