Kostyantyn Kechedzhi [Google]

Title: Towards practical quantum simulation with quantum echo

Abstract: Simulating quantum phenomena in nature is the most promising early application for quantum computers because they can efficiently process highly entangled wave functions that otherwise require exponentially large classical memory and/or processing times. However, in a typical many-body evolution, the growth of entanglement is associated with thermalization, which quickly erases fine-grained details of the evolution. At the same time, remaining macroscopic features can often be described by an effective (approximate) classical theory. A natural question arises: Is there information about such a many-body quantum system that a quantum computer can learn, but a classical computer cannot? In this talk, we describe a quantum echoes algorithm that allows us to observe inherently quantum characteristics of a many-body system. This algorithm measures even moments of the correlation operator, which correspond to the out-of-time order correlator (the second moment) and its higher-order generalizations. Specifically, we present measurements of the 4th moment of the correlation operator using a Willow superconducting processor for circuits large enough that the equivalent computation on a classical supercomputer (Frontier) requires orders of magnitude longer runtime using the best-known classical algorithms. Crucially, such measurements can be efficiently verified by another quantum processor. Verifiability is a necessary attribute of practical quantum simulation, where a typical task is to estimate the expectation value of a physical observable with a given precision. Our results pave the way for such practical applications of quantum processors, particularly for simulating nuclear magnetic resonance spectroscopy.