The classical shadow formalism and some implications for quantum machine learning

Description

Extracting important information from a quantum system as efficiently and tractably as possible is an important subroutine in most near-term applications of quantum hardware. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties. The required number of measurements is independent of the system size and saturates information-theoretic lower bounds. Subsequently, we combine classical shadows with machine learning (ML). This combination showcases that training data obtained from quantum experiments can be very empowering for classical ML methods. More precisely, we study the complexity of training classical and quantum ML models for predicting outcomes of physical experiments. We prove that, a classical ML model can provide accurate predictions on average by accessing measurement outcomes of quantum experiments a number of times comparable to the optimal quantum ML model. Exponential quantum ML advantages do, however, remain possible if we insist on accurate worst-case prediction. This is joint work with Robert Huang (Caltech) and John Preskill (Caltech and AWS).

Period	28 Apr 2021
Event title	Quantum theory meeting, Amazon Web Services
Event type	Other
Location	United StatesShow on map