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This Perspective focuses on the several overlaps between quantum algorithms
and Monte Carlo methods in the domains of physics and chemistry. We will
analyze the challenges and possibilities of integrating established quantum
Monte Carlo solutions in quantum algorithms. These include refined energy
estimators, parameter optimization, real and imaginary-time dynamics, and
variational circuits. Conversely, we will review new ideas in utilizing quantum
hardware to accelerate the sampling in statistical classical models, with
applications in physics, chemistry, optimization, and machine learning. This
review aims to be accessible to both communities and intends to foster further
algorithmic developments at the intersection of quantum computing and Monte
Carlo methods. Most of the works discussed in this Perspective have emerged
within the last two years, indicating a rapidly growing interest in this
promising area of research.
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