Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment

TL;DR

This paper demonstrates that tensor networks with belief propagation are infeasible for simulating Google's quantum echoes experiment due to high entanglement and dense connectivity, confirming classical simulation limitations.

Contribution

The study provides theoretical and numerical evidence that TNBP cannot efficiently simulate Google's quantum echoes experiment, reinforcing its quantum advantage.

Findings

TNBP fails to simulate the highly entangled states in the experiment.

The entanglement generated makes the states largely incompressible.

Classical approaches like tensor network evolution will also fail to reproduce the results.

Abstract

In the recent quantum echoes experiment, Google Quantum AI showed that out-of-time-order correlators (OTOCs) for random-circuit time evolution can be measured using a quantum processor more than 10,000x faster than they can be computed to similar accuracy via classical computation. This claim was substantiated by comparison with a variety of state-of-the-art classical simulation methods. One classical simulation method that was not explicitly tested was tensor networks with belief propagation (TNBP). TNBP should be poorly suited to simulating Google's echoes experiment: the states involved are highly entangled, a challenge for tensor network states; and the Willow chip has dense 2D connectivity, a challenge for belief propagation. Here we confirm, via a combination of theoretical scaling arguments and explicit numerical simulation, the intuition that TNBP is unable to simulate the quantum echoes experiment. We show that the OTOC circuits generate enough entanglement that they are largely incompressible, implying that other approaches in which OTOCs are computed by evolving a tensor network state in the Schr\"odinger picture will also fail. Our results further reinforce the claim that the quantum echoes experiment cannot be reproduced by classical computation.