Efficient Preparation of Quantum States via Randomized Truncation

While the preparation of a general quantum state is challenging, realistic problem instances, such as those encountered in quantum chemistry and quantum machine learning-typically exhibit hierarchical amplitude structures, consisting of a small number of large components alongside a vast number of small but non-negligible ones. Standard approaches deterministically truncate the small amplitude would incur an approximation error that scales linearly with the discarded amplitude mass, enforcing a rigid trade-off between precision and circuit depth. Here, we circumvent the challenge by introducing a randomized state-preparation protocol with probabilistic amplification of small amplitudes using ensembles of low-complexity circuits. Analytically, we prove that this approach significantly reduces the number of encoded amplitudes, halving the requirement for exponentially decaying states and offering asymptotically larger gains for heavy-tailed power-law decays. Numerical simulations on LiH molecular wavefunctions and deep-learning-derived states demonstrate reductions of up to 99 percent in CNOT and T-gate counts compared with deterministic methods. These results establish a resource-efficient paradigm for initializing complex states, relaxing gate-synthesis precision requirements for both near-term and fault-tolerant hardware, and improving the end-to-end feasibility of quantum computing.