Optimal Quantum Sample Complexity of Learning Algorithms
Authors: Srinivasan Arunachalam, Ronald de Wolf
JMLR 2018 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Here we analyze quantum sample complexity, where each example is a coherent quantum state. This model was introduced by Bshouty and Jackson (1999), who showed that quantum examples are more powerful than classical examples in some fixed-distribution settings. However, Atıcı and Servedio (2005), improved by Zhang (2010), showed that in the PAC setting (where the learner has to succeed for every distribution), quantum examples cannot be much more powerful... Our main result is that quantum and classical sample complexity are in fact equal up to constant factors in both the PAC and agnostic models. We give two proof approaches. The first is a fairly simple information-theoretic argument... We then give a second approach that avoids the log-factor loss, based on analyzing the behavior of the Pretty Good Measurement on the quantum state-identification problems that correspond to learning. |
| Researcher Affiliation | Academia | Srinivasan Arunachalam EMAIL QuSoft, CWI, Amsterdam, the Netherlands Ronald de Wolf EMAIL QuSoft, CWI and University of Amsterdam, the Netherlands |
| Pseudocode | No | The paper focuses on theoretical analysis, presenting mathematical proofs and arguments regarding quantum sample complexity. It does not include any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper is theoretical in nature, presenting mathematical proofs and analysis. There is no mention of open-source code being released or links to any code repositories. |
| Open Datasets | No | The paper deals with theoretical concept classes and distributions within quantum learning models. It does not refer to any specific publicly available or open datasets for empirical evaluation. |
| Dataset Splits | No | As the paper is entirely theoretical and does not involve empirical evaluation with specific datasets, there is no information provided regarding training/test/validation dataset splits. |
| Hardware Specification | No | The paper is theoretical, focusing on mathematical proofs and analysis of quantum sample complexity. No experiments are described, and therefore no specific hardware specifications are mentioned. |
| Software Dependencies | No | This paper presents theoretical work on quantum sample complexity. It does not involve any implemented systems or experiments, and thus no specific software dependencies with version numbers are provided. |
| Experiment Setup | No | The paper is theoretical, presenting mathematical analyses and proofs. It does not describe any empirical experiments, and therefore no details on experimental setup, hyperparameters, or system-level training settings are provided. |