Measurement-based quantum computation (MBQC) offers a fundamentally unique paradigm to design quantum algorithms. Indeed, due to the inherent randomness of quantum measurements, the natural operations in MBQC are not deterministic and unitary, but are rather augmented with probabilistic byproducts. Yet, the main algorithmic use of MBQC so far has been to completely counteract this probabilistic nature in order to simulate unitary computations expressed in the circuit model. In this work, we propose designing MBQC algorithms that embrace this inherent randomness and treat the random byproducts in MBQC as a resource for computation. As a natural application where randomness can be beneficial, we consider generative modeling, a task in machine learning centered around generating complex probability distributions. To address this task, we propose a variational MBQC algorithm equipped with control parameters that allow to directly adjust the degree of randomness to be admitted in the computation. Our numerical findings indicate that this additional randomness can lead to significant gains in learning performance in certain generative modeling tasks. These results highlight the potential advantages in exploiting the inherent randomness of MBQC and motivate further research into MBQC-based algorithms.

翻译：基于测量的量子计算（MBQC）提供了一种根本性独特的量子算法设计范式。事实上，由于量子测量的固有随机性，MBQC中的自然操作并非确定性和酉的，而是伴随着概率性副产物而增强的。然而，迄今为止MBQC的主要算法应用在于完全抵消这种概率性质，以模拟在电路模型中表达的酉计算。在本文中，我们提出设计拥抱这种固有随机性的MBQC算法，并将MBQC中的随机副产物视为计算资源。作为随机性可能有益的天然应用，我们考虑生成建模——机器学习中围绕生成复杂概率分布的中心任务。为解决该任务，我们提出一种配备控制参数的变分MBQC算法，该参数允许直接调节计算中允许的随机程度。我们的数值结果表明，在某些生成建模任务中，这种额外随机性可带来学习性能的显著提升。这些结果突显了利用MBQC固有随机性的潜在优势，并激励了基于MBQC的进一步算法研究。