Photonic quantum algorithm for Monte Carlo integration

Understand

We present a continuous-variable photonic quantum algorithm for the Monte Carlo evaluation of multi-dimensional integrals.

• Our algorithm encodes n-dimensional integration into n+3 modes and can provide a quadratic speedup in runtime compared to the classical Monte Carlo approach.
• The speedup is achieved by developing a continuous-variable adaptation of amplitude estimation.
• We provide an error analysis for each element of the algorithm and account for the effects of finite squeezing.