Variational measurement-based quantum computation for generative
  modeling
Arunava Majumder Marius Krumm Tina Radkohl Hendrik Poulsen Nautrup Sofiene Jerbi Hans J. Briegel
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.