Entanglement is Half the Story: Post-Selection vs. Partial Traces
For researchers in quantum machine learning and tensor networks, this provides a practical method to interpolate between classical and quantum models, addressing the resource bottleneck of post-selection.
The paper introduces a hybrid classical-quantum tensor network framework where a hyperparameter controls the transition between classical and quantum regimes via post-selection, enabling trainable allocation of limited quantum resources. This improves quantum machine learning by complementing the bond dimension.
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.