Entanglement is Half the Story: Post-Selection vs. Partial Traces

TL;DR

This paper introduces a hybrid tensor network framework combining classical and quantum models, using post-selection as a key parameter to control quantum constraints and improve quantum machine learning.

Contribution

It derives a unified approach to classical and quantum tensor networks, highlighting post-selection as a crucial factor and proposing a new hyperparameter for transition control.

Findings

Post-selection level influences tensor network capabilities.

The hyperparameter enables controlled transition between classical and quantum models.

Quantum machine learning performance is enhanced by adaptive post-selection allocation.

Abstract

While tensor networks have their traditional application in simulating quantum systems, in the recent decade they have gathered interest as machine learning models. We combine the experience from both fields and derive how quantum constraints placed on a tensor network manifest a change in capabilities. To this end, we employ a method of inference of classical tensor networks on a quantum computer to define a hybrid architecture. This hybrid tensor network is a practical unified framework for it's classical and quantum tensor network edge cases. We identify post-selection as the important property on which this interpolation hinges. The amount of post-selection corresponds to the level to which quantum constraints are enforced on the tensor network. On this basis, we propose a new hyperparameter which controls the transition between the hybrid and the quantum tensor network. In the comparison of classical and quantum tensor networks it complements the bond dimension. Quantum machine learning is improved by using the hyperparameter to allocate the practically limited post-selection to the quantum model in a trainable manner.