Limitations of Noisy Quantum Devices in Computational and Entangling Power

TL;DR

This paper investigates the fundamental limitations of noisy quantum devices, showing they lack computational and entangling advantages beyond certain depths and topologies, which impacts quantum algorithms and simulations.

Contribution

It analytically characterizes the limitations of noisy quantum devices with specific noise models and topologies, establishing bounds on computational power and entanglement generation.

Findings

Polynomial-time indistinguishability from random coins at certain depths

No super-logarithmic advantage with classical processing in noisy circuits

Upper bounds on entanglement growth in 1D and 2D noisy quantum circuits

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 $\Omega(\log(n))$. 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: $O(\log(n))$ for one-dimensional circuits and $O(\sqrt{n} \log(n))$ for two-dimensional circuits. Our findings underscore the computational capacity and entanglement scalability constraints in noisy quantum devices.