  The efficient preparation of input distributions is an important problem in
obtaining quantum advantage in a wide range of domains. We propose a novel
quantum algorithm for the efficient preparation of arbitrary normal
distributions in quantum registers. To the best of our knowledge, our work is
the first to leverage the power of Mid-Circuit Measurement and Reuse (MCMR), in
a way that is broadly applicable to a range of state-preparation problems.
Specifically, our algorithm employs a repeat-until-success scheme, and only
requires a constant-bounded number of repetitions in expectation. In the
experiments presented, the use of MCMR enables up to a 862.6x reduction in
required qubits. Furthermore, the algorithm is provably resistant to both
phase-flip and bit-flip errors, leading to a first-of-its-kind empirical
demonstration on real quantum hardware, the MCMR-enabled Honeywell System
Models H0 and H1-2.
