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

arXiv: https://arxiv.org/abs/2604.11578 · HTML: https://mlsanity.com/paper/2604.11578/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Learning in Implicit Generative Models](https://mlsanity.com/paper/1610.03483/) (2016)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Training-efficient density quantum machine learning](https://mlsanity.com/paper/2405.20237/) (2024)
- [Generative quantum advantage for classical and quantum problems](https://mlsanity.com/paper/2509.09033/) (2025)
- [Variational measurement-based quantum computation for generative modeling](https://mlsanity.com/paper/2310.13524/) (2023)
- [Measurement-based quantum computation from Clifford quantum cellular automata](https://mlsanity.com/paper/2312.13185/) (2023)

## Built on by (most cited first, 1 of 1)

- [Representational separation between unitary and channel quantum generative models via shared classical randomness at shallow depth](https://mlsanity.com/paper/2608.05110/) (2026)

## Abstract (arXiv)

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 × 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.