Testing eigenstate thermalization hypothesis on small scale quantum processors

Abstract: The Eigenstate Thermalization Hypothesis (ETH) is a framework for discussing thermal behavior originating from chaotic dynamics in isolated many-body quantum systems. The PXP model, where certain states do not thermalize, has been compared with the Sachdev-Ye Kitaev (SYK) model, which is believed to be fully thermalizing. A gate-based quantum circuit approach is utilized to simulate time evolution and compute the Out-of-Time-Ordered Correlator (OTOC), a measure of the extent of chaos. Considering restrictions on implementing SYK on gate-based hardware, a simplified model called Spin-XY4 (SXY4), which has a thermal behavior similar to SYK, is tested. An alternate method, which optimizes control on an analog quantum device with the GRAPE (GRadient Ascent Pulse Engineering) algorithm, is also utilized to simulate the SYK model.