Entanglement entropy scaling of noisy random quantum circuits in two dimensions

TL;DR

This paper investigates how noise affects the entanglement entropy scaling in 2D random quantum circuits, revealing that noise induces an area law scaling and that volume law scaling requires decreasing noise with system size.

Contribution

It provides a detailed numerical and theoretical analysis of entanglement entropy scaling in noisy 2D quantum circuits, highlighting the impact of noise on quantum advantage.

Findings

Operator entanglement entropy follows area law under constant noise.

Entanglement entropy scales as a power law with noise rate.

Volume law scaling occurs only if noise decreases with system size.

Abstract

Whether noisy quantum devices without error correction can provide quantum advantage over classical computers is a critical issue of current quantum computation. In this work, the random quantum circuits, which are used as the paradigm model to demonstrate quantum advantage, are simulated with depolarizing noise on experiment relevant two-dimensional architecture. With comprehensive numerical simulation and theoretical analysis, we find that the maximum achievable operator entanglement entropy, which indicates maximal simulation cost, has area law scaling with the system size for constant noise rate. On the other hand, we also find that the maximum achievable operator entanglement entropy has power law scaling with the noise rate for fixed system size, and the volume law scaling can be obtained only if the noise rate decreases when system size increase.