Limitations of noisy quantum devices in computing and entangling power

Abstract Finding solid and practical quantum advantages via noisy quantum devices without error correction is a critical but challenging problem. Conversely, comprehending the fundamental limitations of the state-of-the-art is equally crucial. In this work, we consider the class of strictly contractive unital noise and derive its analytical representation by decomposition. Under such noise, we observe the polynomial-time indistinguishability of n -qubit devices from random coins when circuit depths exceed ( (n) ) Ω (log (n) ). Even with classical processing, we demonstrate the absence of computational advantage in polynomial-time algorithms with super-logarithmic noisy circuit depths. These results impact variational quantum algorithms, error mitigation, and quantum simulation with polynomial depth. Furthermore, we consider noisy quantum devices with a restricted gate topology. For one-dimensional noisy qubit circuits, we rule out super-polynomial quantum advantages in all-depth regimes. We also establish upper limits on entanglement generation: O ( (n) ) O (log (n) ) for one-dimensional circuits and O (n (n) ) O (n log (n) ) for two-dimensional circuits. Our findings underscore the computational capacity and entanglement scalability constraints in noisy quantum devices.