Quantum Simulation of Galton Machines Using Mid-Circuit Measurement and Reuse.

We propose a novel quantum algorithm for the general approximate simulation of Galton machines with polynomial depth in terms of the number of qubits and with bounded error, obtaining exponential quantum advantage over the corresponding classical algorithm. This work enables the efficient preparation of input distributions, which is particularly important in quantum algorithms for tasks ranging from option pricing to machine learning. To this end, we prove that the proposed procedure may be directly used to efficiently load normal distributions into quantum registers. Moreover, to the best of our knowledge, our work is the first to leverage the power of Mid-Circuit Measurement and Reuse (MCMR) technology in a way that is broadly applicable to a range of state-preparation problems, including those relating to finance. Specifically, our algorithm employs a repeat-until-success scheme, and only requires a constant-bounded number of repetitions in expectation. Furthermore, the algorithm is provably resistant to both phase-flip and bit-flip errors, leading to a first-of-its-kind empirical demonstration on a real quantum computer, the MCMR-enabled Honeywell System Model H0.