Simulating Quantum Supremacy Using Chaotic Feature Embeddings with Analytic Kernels

Aimé T Shangula

Aimé T Shangula

Aimé Shangula

Aimé T Shangula

Man‐Hong Yung, Xun Gao

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.

Robert Alicki

The recently reported experimental results claiming "quantum supremacy" achieved by Google quantum device are critically discussed. The Google team constructed a quantum chaotic system based on Josephson junction technology which cannot be reliably simulated by the present day supercomputers. However, the similar "supremacy" can be realized for properly designed micro-mechanical devices, like periodically forced Duffing oscillator, using the available technology of quartz clocks. It is also reminded that classical and quantum chaotic systems behave in a similar way. Therefore, in this case, one should speak rather about the "analog supremacy" than "quantum supremacy" what means that even now mechanical analog computers can outperform supercomputers when the computational task can be reduced to sampling of ergodic measures generated by chaotic systems.