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.

翻译：测量基量子计算（MBQC）是一种量子信息处理框架，其中计算任务通过对高度纠缠资源态进行单量子比特测量来实现。由于量子测量结果的不确定性，这些操作产生的随机结果（若不进行修正）会形成一个变分量子通道族。传统上，这种随机性通过经典处理进行修正，以确保确定性的酉计算。近年来，变分测量基量子计算（VMBQC）被提出，旨在利用这种测量诱导的随机性在生成建模中获得优势。该方法的一个局限性在于，其对应的通道模型参数数量是酉模型的两倍，缩放为 $N \times D$，其中 $N$ 是逻辑量子比特数（宽度），$D$ 是VMBQC模型的深度。这通常会使优化更加困难，并可能导致模型可训练性差。本文提出一种受限的VMBQC模型，该模型通过仅使用一个额外的可训练参数，将酉设定推广至基于通道的设定。我们通过数值和代数方法证明，这一最小扩展足以生成对应酉模型无法学习的概率分布。