Limitations of measure-first protocols in quantum machine learning

• URL: http://arxiv.org/abs/2311.12618v1
• Date: Tue, 21 Nov 2023 14:03:29 GMT
• Title: Limitations of measure-first protocols in quantum machine learning
• Authors: Casper Gyurik, Riccardo Molteni, Vedran Dunjko
• Abstract summary: We study a natural supervised learning setting where quantum states constitute data points, and the labels stem from an unknown measurement. We show that there exist problems that can be efficiently learned by fully-quantum protocols but which require exponential resources for measure-first protocols. Our result underscores the role of quantum data processing in machine learning and highlights scenarios where quantum advantages appear.
• Score: 2.209921757303168
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In recent works, much progress has been made with regards to so-called randomized measurement strategies, which include the famous methods of classical shadows and shadow tomography. In such strategies, unknown quantum states are first measured (or ``learned''), to obtain classical data that can be used to later infer (or ``predict'') some desired properties of the quantum states. Even if the used measurement procedure is fixed, surprisingly, estimations of an exponential number of vastly different quantities can be obtained from a polynomial amount of measurement data. This raises the question of just how powerful ``measure-first'' strategies are, and in particular, if all quantum machine learning problems can be solved with a measure-first, analyze-later scheme. This paper explores the potential and limitations of these measure-first protocols in learning from quantum data. We study a natural supervised learning setting where quantum states constitute data points, and the labels stem from an unknown measurement. We examine two types of machine learning protocols: ``measure-first'' protocols, where all the quantum data is first measured using a fixed measurement strategy, and ``fully-quantum'' protocols where the measurements are adapted during the training process. Our main result is a proof of separation. We prove that there exist learning problems that can be efficiently learned by fully-quantum protocols but which require exponential resources for measure-first protocols. Moreover, we show that this separation persists even for quantum data that can be prepared by a polynomial-time quantum process, such as a polynomially-sized quantum circuit. Our proofs combine methods from one-way communication complexity and pseudorandom quantum states. Our result underscores the role of quantum data processing in machine learning and highlights scenarios where quantum advantages appear.

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