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 one to directly adjust the degree of randomness to be admitted in the computation. Our algebraic and numerical findings indicate that this additional randomness can lead to significant gains in expressivity and learning performance for certain generative modeling tasks, respectively. 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）为设计量子算法提供了一种根本性独特的范式。实际上，由于量子测量固有的随机性，MBQC中的自然操作并非确定性和幺正的，而是增加了概率性的副产品。然而，迄今为止MBQC的主要算法用途是完全抵消这种概率性，以模拟在电路模型中表达的幺正计算。在这项工作中，我们提出设计能够接纳这种固有随机性的MBQC算法，并将MBQC中的随机副产品视为计算资源。作为一个随机性可能有益的自然应用，我们考虑生成建模——机器学习中一项围绕生成复杂概率分布的任务。针对此任务，我们提出了一种变分MBQC算法，该算法配备了控制参数，允许直接调整计算中允许的随机性程度。我们的代数和数值结果表明，对于某些生成建模任务，这种额外的随机性可以分别带来表达能力和学习性能的显著提升。这些结果凸显了利用MBQC固有随机性的潜在优势，并激励了对基于MBQC算法的进一步研究。