Noise disrupts quantum correlations, effectively shrinking the available quantum circuit volume. We seek to understand if it’s possible to harness the full quantum circuit volume of a processor despite the effect of noise. In other words, we explore if it would be possible to realize an equivalent computation on a quantum processor of a smaller size.
Our research answers this question by revealing regions in the parameter space where the RCS benchmark behaves in a qualitatively different way. These regions (shown in the figure below) are separated by a phase transition. The vertical and horizontal axes correspond to the circuit depth (number of cycles) and error rate per cycle, respectively. In the sufficiently weak noise region (shown in green) quantum correlations extend to the full system, indicating that the quantum computers harness their full computational power. Whereas in the strong noise region (shown in orange) the system may be approximately represented by the product of multiple uncorrelated subsystems, and therefore, a smaller quantum computer could perform an equivalent calculation. In this regime a significant reduction in the cost of classical computation is possible by simulating parts of the system separately.
This is the idea behind spoofing algorithms, which aim to reproduce the RCS benchmark using multiple uncorrelated subsystems instead of the full simulation. Spoofing algorithms crucially rely on the low quantum correlation property of the strong noise regime. Therefore, the existence of the sharp phase transition between the weak and strong noise regions implies that the spoofing algorithms cannot be successful in the weak noise regime.
We employed a three-pronged approach to investigate the phase diagram. First, an analytical model was developed demonstrating the existence of the phase transitions in the large system size limit. Second, extensive numerical simulations were conducted to precisely map out the phase boundaries for our specific quantum hardware. Finally, validation was performed by introducing varying levels of noise into our quantum circuits, observing the transition boundaries experimentally. This multifaceted approach provides compelling evidence for the validity of the phase diagram.
Using numerical simulations we demonstrate that the parameters of our Sycamore processor are well within the low noise regime. In other words, our processor lies firmly in the beyond classical regime, exceeding the capabilities of current supercomputers. This analysis also rules out spoofing algorithms as an efficient method to reproduce our latest RCS benchmark results. The RCS benchmark is a reliable estimator of fidelity in the weak noise regime. The sharp boundary between weak and strong noise regimes provides a clear criterion for ensuring the accuracy of RCS benchmarks.