Quantum algorithms typically demand prohibitively complex 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 enables all quantum algorithms relying on truncated series approximations to enjoy such acceleration. RTS offers twofold accelerations: it quadratically suppresses truncation errors and allows 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 a path toward practical quantum advantage.

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• Quantum algorithms & computation
• Quantum computation
• Quantum protocols
• Quantum simulation