用一个额外参数让量子生成模型更强大且更易训练。
Minimizing classical resources in variational measurement-based quantum computation for generative modeling
- 仅增加一个可训练参数，将确定性量子电路扩展为随机性通道模型。
- 数值与代数证明：该模型能生成单位制模型无法学习的概率分布。
- 适合想用最少经典资源提升量子生成模型性能的研究者。
基于测量的量子计算（MBQC）通过在高度纠缠的资源态上执行一比特测量来完成计算任务。由于量子测量结果具有不确定性，若不进行校正，会形成一类变分量子通道。传统方法通过经典处理消除随机性以实现确定性酉运算。近期提出的变分测量基量子计算（VMBQC）利用测量带来的随机性，在生成建模中获得优势。但该方法的通道模型参数量是酉模型的两倍，随逻辑量子比特数 $N$ 与深度 $D$ 增长至 $N \times D$，导致优化困难且难训练。本文提出一种受限的VMBQC模型，仅引入一个额外可训练参数，即可将酉设定扩展为通道型模型。我们通过数值实验与代数分析证明，这一最小扩展已足以生成单位制模型无法学习的概率分布。
原文摘要 · Abstract (English)
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.
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