Entangled measurements can improve learning from quantum data
Advantage of Entangled Learning Rules in Quantum Measurement Class Learning
Machine Learning
Summary
Learning to predict labels from quantum data usually involves measuring single quantum states separately. The authors show that using special measurements that act on multiple quantum states together—called entangled measurements—can sometimes learn better than these single-state approaches. However, this advantage in how many samples are needed to learn well is limited to a polynomial improvement. This means entangled measurements help, but only up to a certain point in prediction tasks on quantum data.
What this means in practice
- •For quantum machine learning engineers: Design measurement-based quantum learning algorithms that achieve better accuracy by using entangled measurements.
- •For quantum algorithm developers: Optimize sample efficiency for classification tasks by incorporating multi-copy entangled measurements in quantum data processing.
A theory result. No direct application yet.
Authors
Arka Prabha Das, Abram Magner
Abstract
Learning with data in the form of quantum states is of current interest and has led to a variety of problems that boil down to interaction with the available data via quantum measurement and classical post-processing of observed classical outcomes. In quantum measurement PAC learning, one is given a sequence of unknown, prepared quantum states and classical labels, along with a hypothesis class of candidate measurements. The task is to select a measurement from the hypothesis class that minimizes a fixed notion of error in prediction of the classical labels via measurement of a new state by the selected hypothesis. In this work, we consider the advantage of interacting with the given data in the measurement learning framework using learning rules given by measurements that cannot be implemented using local operations and classical communication (LOCC), as opposed to single-copy learning rules. We provide a construction showing that there exist learning scenarios wherein single-copy learning rules are asymptotically suboptimal compared to optimal ones. We then show that learning rules based on entangled measurements enjoy at most a polynomial sample complexity advantage over single-copy learning rules in the PAC learning setting (under a natural joint measurability covering assumption).