Faster Quantum Algorithms with "Fractional"-Truncated Series

• URL: http://arxiv.org/abs/2402.05595v2
• Date: Sun, 8 Sep 2024 05:01:48 GMT
• Title: Faster Quantum Algorithms with "Fractional"-Truncated Series
• Authors: Yue Wang, Qi Zhao,
• Abstract summary: We introduce Randomized Truncated Series (RTS), a framework that significantly reduces circuit depth by quadratically improving truncation error and enabling continuous adjustment of the effective truncation order. We generalize the mixing lemma to near-unitary instances to support our error analysis and demonstrate the versatility of RTS through applications in linear combinations of unitaries, quantum signal processing, and quantum differential equations.
• Score: 14.536572102408423
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum algorithms frequently rely on truncated series approximations, which typically require high truncation orders for adequate accuracy, leading to impractical circuit complexity. In response, we introduce Randomized Truncated Series (RTS), a framework that significantly reduces circuit depth by quadratically improving truncation error and enabling continuous adjustment of the effective truncation order. RTS leverages random mixing of series expansions to achieve these enhancements. We generalize the mixing lemma to near-unitary instances to support our error analysis and demonstrate the versatility of RTS through applications in linear combinations of unitaries, quantum signal processing, and quantum differential equations. Our results shed light on the path toward practical quantum advantage.

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