Time series generation for option pricing on quantum computers using
  tensor network
Nozomu Kobayashi Yoshiyuki Suimon Koichi Miyamoto
Finance, especially option pricing, is a promising industrial field that
might benefit from quantum computing. While quantum algorithms for option
pricing have been proposed, it is desired to devise more efficient
implementations of costly operations in the algorithms, one of which is
preparing a quantum state that encodes a probability distribution of the
underlying asset price. In particular, in pricing a path-dependent option, we
need to generate a state encoding a joint distribution of the underlying asset
price at multiple time points, which is more demanding. To address these
issues, we propose a novel approach using Matrix Product State (MPS) as a
generative model for time series generation. To validate our approach, taking
the Heston model as a target, we conduct numerical experiments to generate time
series in the model. Our findings demonstrate the capability of the MPS model
to generate paths in the Heston model, highlighting its potential for
path-dependent option pricing on quantum computers.