Optimal Usage of Quantum Random Access Memory in Quantum Machine Learning

TL;DR

This paper investigates the fundamental limits of reusing quantum data in quantum machine learning when faced with unreliable oracles, highlighting how qRAM usage can be optimized without increasing complexity despite oracle unreliability.

Contribution

It introduces a tradeoff relation between oracle reliability and data reusability, and shows how to optimize qRAM usage without additional complexity in unreliable oracle scenarios.

Findings

Reusability of quantum data is limited by a fundamental tradeoff.

Correct answers can be obtained without increasing qRAM queries despite unreliability.

Optimal cycling of quantum states maximizes data reusability.

Abstract

By considering an unreliable oracle in a query-based model of quantum learning, we present a tradeoff relation between the oracle's reliability and the reusability of quantum state of the input data. The tradeoff relation manifests as the fundamental upper bound on the reusability. This limitation on the reusability would increase the quantum access to the input data, i.e., the usage of quantum random access memory (qRAM), repeating the preparation of a superposition of `big' input data on the query failure. However, it is found that, a learner can obtain a correct answer even from an unreliable oracle without any additional usage of qRAM---i.e., the complexity of qRAM query does not increase even with an unreliable oracle. This is enabled by repeatedly cycling the quantum state of the input data to the upper bound on the reusability.