In this case, the team made several key variations. First, it basically implements so-called Clifford gates, which are relatively easy to simulate on classical hardware. But it is sprinkled into a few non-Clifford gates (especially T gates) of a particular type, chosen in part because they are less prone to error. “Z rotations (including T gates) are special in our hardware: they are performed by virtual frame tracking and do not generate additional noise,” the paper noted.
But T gates also help ensure that this is difficult to simulate on a classical computer. “There’s a stronger complexity argument because it’s exponentially harder to sample (T gates) for a classical computer that you can prove on average,” Gambetta told Ars. This will make classical algorithms very difficult to catch.
The work is also linked to a few extra qubits around the periphery of those used for the algorithm, so that fine-grained measurements during operations can detect if errors occur; results were discarded if detected. (Note that this will also eliminate valid results flagged by misreading these extra qubits.)
The result was an algorithm that “combines the extensive output statistics of hard sampling problems with circuit structure that can be used for fault detection and reliability certification.”
The latest of the new findings comes from quantum software developer Algorithmiq, which Google’s “quantum echoes” work. A set of gates first transforms the quantum system, after which the process is reversed. The additional operations performed during the inversion prevent the system from returning to its original state – instead, it creates an imperfect “echo” of the noise forward process. As in one of the previous works, attempts to simulate this in classical hardware require some simplification methods, and then the essence of the problem is different. the unavailability of classical equipment.
