Yue Wang

Quantum algorithms promise transformative speedups, yet their practical impact is often limited by prohibitively deep circuits, with two recurring sources of depth: costly preparation of structured input states and the execution of subroutines based on truncated series approximations. We introduce a unified, resource-efficient paradigm that uses classical randomness as an algorithmic primitive to improve accuracy–depth trade-offs. For realistic states with hierarchical amplitude structure, we propose a randomized state-preparation protocol that probabilistically amplifies small amplitudes using ensembles of low-complexity circuits, reducing the number of amplitudes that must be encoded and achieving up to 99% reductions in CNOT and T-gate counts in simulations on LiH wavefunctions and power-law decay states. Target quantum algorithms, we develop Randomized Truncated Series, a generic acceleration principle for any quantum algorithm built from truncated series, which quadratically suppresses truncation error while enabling continuous tuning of the effective truncation order via random mixing of shallow circuits. Together, these results broaden the regime where end-to-end quantum advantage is feasible on near-term and early fault-tolerant hardware.