Speaker: Vedika Khemani (Stanford University)

Time: 13:00-14:00 p.m., April 28, 2023, GMT+8

Venue: Zoom Meeting ID: 963 5796 8034 Password: 125125

Abstract:

Classical shadows are a powerful method for learning manyproperties of quantum states in a sample-efficient manner, by making use of randomized measurements. I will discuss the sample complexityof learning the expectation value of localIPauli operators via "shallow shadows, a recently-proposed version of classical shadows in which the randomization step is affected by a random unitary circuit of variable depth t. I will show that the sample complexity can be derived from properties of the dynamics induced by the circuit which can becalculated by mapping to simple statistical mechanics models. Specifically, the sample complexity of learning the expectation of localoperators of weight k (i.e., acting nontrivially on k contiguous sites) is determined by the time-evolution of the operator weight starting from afully-packed product initial operator of size k. This entails the competition between two processes: operator spreading (whereby the support of an operator grows over time, increasing its weight) and operator relaxation (whereby the bulk of the operator develops anequilibrium density of identity operators, decreasing its weight). Our results give a bound which, for depth t～log(k) guarantees an exponential gain in sample complexity. This work connects fundamental ideas in quantum many-body dynamics to applications in quantum information science and paves the way to highly-optimized protocols for learning different properties of quantum states.

Source: School of Physics