Minimizing classical resources in variational measurement-based quantum computation for generative modeling

TL;DR

This paper introduces a minimal extension to variational measurement-based quantum computation that enhances generative modeling capabilities while using fewer resources, simplifying optimization.

Contribution

A restricted VMBQC model with only one additional parameter is proposed, enabling it to generate distributions beyond the reach of the unitary model.

Findings

The minimal extension allows generating more complex probability distributions.

Numerical and algebraic evidence shows the model's enhanced expressiveness.

The approach reduces resource requirements compared to traditional VMBQC models.

Abstract

Measurement-based quantum computation (MBQC) is a framework for quantum information processing in which a computational task is carried out through one-qubit measurements on a highly entangled resource state. Due to the indeterminacy of the outcomes of a quantum measurement, the random outcomes of these operations, if not corrected, yield a variational quantum channel family. Traditionally, this randomness is corrected through classical processing in order to ensure deterministic unitary computations. Recently, variational measurement-based quantum computation (VMBQC) has been introduced to exploit this measurement-induced randomness to gain an advantage in generative modeling. A limitation of this approach is that the corresponding channel model has twice as many parameters compared to the unitary model, scaling as $N \times D$, where $N$ is the number of logical qubits (width) and $D$ is the depth of the VMBQC model. This can often make optimization more difficult and may lead to poorly trainable models. In this paper, we present a restricted VMBQC model that extends the unitary setting to a channel-based one using only a single additional trainable parameter. We show, both numerically and algebraically, that this minimal extension is sufficient to generate probability distributions that cannot be learned by the corresponding unitary model.