Can Chaotic Quantum Circuits Maintain Quantum Supremacy under Noise?

Although the emergence of a fully-functional quantum computer may still be far away from today, in the near future, it is possible to have medium-size, special-purpose, quantum devices that can perform computational tasks not efficiently simulable with any classical computer. This status is known as quantum supremacy (or quantum advantage), where one of the promising approaches is through the sampling of chaotic quantum circuits. Sampling of ideal chaotic quantum circuits has been argued to require an exponential time for classical devices. A major question is whether quantum supremacy can be maintained under noise without error correction, as the implementation of fault-tolerance would cost lots of extra qubits and quantum gates. Here we show that, for a family of chaotic quantum circuits subject to Pauli errors, there exists an non-exponential classical algorithm capable of simulating the noisy chaotic quantum circuits with bounded errors. This result represents a serious challenge to a previous result in the literature suggesting the failure of classical devices in simulating noisy chaotic circuits with about 48 qubits and depth 25. Moreover, even though our model does not cover all types of experimental errors, from a practical point view, our result describes a well-defined setting where quantum supremacy can be tested against the challenges of classical rivals, in the context of chaotic quantum circuits.