Cost function embedding and dataset encoding for machine learning with parameterized quantum circuits

TL;DR

This paper introduces a method to embed cost functions and datasets into quantum circuits for machine learning on NISQ devices, enabling direct quantum manipulation and gradient evaluation of the cost function.

Contribution

It presents a novel routine to encode cost functions and datasets into quantum states, facilitating quantum-native evaluation and optimization in machine learning models.

Findings

Cost function embedding into quantum circuits demonstrated.

Gradient evaluation of embedded cost functions achieved.

Enables quantum-native training of machine learning models.

Abstract

Machine learning is seen as a promising application of quantum computation. For near-term noisy intermediate-scale quantum (NISQ) devices, parametrized quantum circuits (PQCs) have been proposed as machine learning models due to their robustness and ease of implementation. However, the cost function is normally calculated classically from repeated measurement outcomes, such that it is no longer encoded in a quantum state. This prevents the value from being directly manipulated by a quantum computer. To solve this problem, we give a routine to embed the cost function for machine learning into a quantum circuit, which accepts a training dataset encoded in superposition or an easily preparable mixed state. We also demonstrate the ability to evaluate the gradient of the encoded cost function in a quantum state.