[Paper Review] Entangled Datasets for Quantum Machine Learning

Louis Schatzki, Andrew Arrasmith+2 more|arXiv (Cornell University)|Sep 8, 2021

Quantum Computing Algorithms and Architecture79 references28 citations

TL;DR

This paper introduces NTangled, a quantum-state dataset with varying multipartite entanglement generated by a quantum neural network, and benchmarks QML models on entanglement-based classification tasks. It also presents scalable, depth-varied entangled-state datasets from hardware-efficient circuits and a method to generate multipartite entangled states.

ABSTRACT

High-quality, large-scale datasets have played a crucial role in the development and success of classical machine learning. Quantum Machine Learning (QML) is a new field that aims to use quantum computers for data analysis, with the hope of obtaining a quantum advantage of some sort. While most proposed QML architectures are benchmarked using classical datasets, there is still doubt whether QML on classical datasets will achieve such an advantage. In this work, we argue that one should instead employ quantum datasets composed of quantum states. For this purpose, we introduce the NTangled dataset composed of quantum states with different amounts and types of multipartite entanglement. We first show how a quantum neural network can be trained to generate the states in the NTangled dataset. Then, we use the NTangled dataset to benchmark QML models for supervised learning classification tasks. We also consider an alternative entanglement-based dataset, which is scalable and is composed of states prepared by quantum circuits with different depths. As a byproduct of our results, we introduce a novel method for generating multipartite entangled states, providing a use-case of quantum neural networks for quantum entanglement theory.

Motivation & Objective

• Argue for using quantum datasets over classical datasets to benchmark QML models and potentially achieve quantum advantage.
• Introduce the NTangled dataset of quantum states with varying multipartite entanglement and show how to generate it with a QNN.
• Benchmark QML models on supervised classification tasks using entanglement as the target label.
• Propose scalable entangled-state datasets produced by hardware-efficient quantum circuits with different depths.
• Provide a practical method for generating multipartite entangled states and connect it to entanglement theory.

Proposed method

• Define a supervised QML framework for classifying quantum states into labels based on entanglement.
• Train a quantum neural network to generate states with a targeted concentratable entanglement (CE) value.
• Use CE and potentially n-tangle measures to train and assess the generated states.
• Explore three generator QNN ansatzes (hardware-efficient, strongly-entangling, convolutional) and their depth.
• Propose loss functions that enforce desired CE and optionally bias state types (e.g., W vs GHZ) via additional terms.
• Demonstrate training and generalization using simulations with TensorFlow Quantum/Cirq and Pennylane.

Experimental results

Research questions

• RQ1 Can quantum datasets enable training and benchmarking of QML models without embedding classical data?
• RQ2 Can a QNN be trained to generate quantum states with prescribed multipartite entanglement measures?
• RQ3 How do different generator QNN ansatzes and depths affect the quality and type of entangled states produced?
• RQ4 Is it possible to classify states by their entanglement level with high accuracy using QML models?
• RQ5 Do entanglement-based datasets provide scalable benchmarks from hardware-efficient circuit depths?

Key findings

• The NTangled dataset can be generated by a QNN trained to produce states with a target CE value.
• Different QNN ansatzes (HWE, SEA, CONV) show varying performance depending on depth and training input (basis vs product states).
• SEA generally outperforms HWE and CONV for high entanglement targets, with high success probabilities across depths.
• Training on computational basis states can yield high generation success even when testing on product states.
• The CE-based continuity bound links trace distance of input states to CE differences, informing generalization.
• Results indicate that entanglement distributions can be shaped via the training loss and input distributions.