Randomization Accelerates Series-Truncated Quantum Algorithms

Quantum algorithms typically demand prohibitively complicated circuits to solve practical problems. Previous studies have shown that classical randomness can accelerate some specific quantum algorithms. In this work, we introduce the Randomized Truncated Series (RTS) which extends this acceleration to all quantum algorithms that rely on truncated series approximations. RTS offers two key advantages: it quadratically suppresses truncation errors and allows for continuous adjustment of the effective truncation order. By leveraging random mixing between two quantum circuits, RTS ensures that their probabilistic combination accurately realizes the desired algorithm, while significantly reducing the average circuit size. We demonstrate the versatility of RTS through concrete applications. Our results shed light on the path toward practical quantum advantage.