Oracle 蒸馏

中文摘要 AI 辅助

学习和感知是量子技术最有前景的应用之一，通常具有可证明的量子优势。然而，在任何实际实验中，随着问题规模的增大，噪声威胁着这些优势的消失。我们引入了Oracle蒸馏，这是一种将多次对噪声Oracle的查询蒸馏为单个高保真Oracle的过程。这里，Oracle是一个来自已知族中的未知酉算子，它模拟了量子设备学习未知系统时的接口。我们构建了一个显式协议，能够蒸馏任何布尔Oracle，既能在对抗性噪声下（该噪声破坏了输入量子比特的恒定比例）工作，也能在每量子比特恒定速率的独立同分布去极化噪声下工作。该协议的核心是弱查询，即设备故意仅弱查询Oracle，以响应强度换取纠错能力。在所有保持Oracle错误可纠正的蒸馏协议中，我们的协议接近最优，揭示了这两个要求之间的基本张力。该协议的一个重要含义是阈值定理：任何其量子优势在域大小上呈多项式增长的布尔Oracle问题，包括Grover搜索、$k$-forrelation和Simon问题，只要每量子比特的去极化速率低于恒定阈值，就保留量子优势。特别是，Grover搜索的二次量子优势，长期以来被认为在噪声下脆弱，在低错误率下几乎完好保留，即使几乎每次查询都涉及一个或多个量子比特的错误。我们进一步将协议扩展到分数阶和连续时间的布尔Oracle。因此，量子纠错不仅能保护规定的操作，还能保护未知动力学。我们的结果使学习中的一大类量子优势对噪声具有鲁棒性，并为鲁棒计算感知开辟了道路。

英文摘要

Learning and sensing are among the most promising applications of quantum technology, often with provable quantum advantages. In any realistic experiment, however, noise threatens to erase these advantages as the problem size grows. We introduce oracle distillation, a procedure that distills many queries to a noisy oracle into a single high-fidelity oracle. Here the oracle, an unknown unitary from a known family, models the interface through which a quantum device learns about an unknown system. We construct an explicit protocol that distills any Boolean oracle, both under adversarial noise that corrupts a constant fraction of the input qubits and under i.i.d. depolarizing noise at a constant rate on every qubit. At the heart of the protocol is the weak query, in which the device deliberately queries the oracle only weakly, trading response strength for the ability to correct errors. Our protocol is near-optimal among all protocols that distill the oracle while keeping its errors correctable, revealing a fundamental tension between these two requirements. An important implication of the protocol is a threshold theorem: every Boolean oracle problem whose quantum advantage is polynomial in the domain size, including Grover search, $k$-forrelation, and Simon's problem, retains a quantum advantage whenever the per-qubit depolarizing rate is below a constant threshold. In particular, the quadratic quantum advantage of Grover search, long believed fragile under noise, survives nearly intact at low error rates even when almost every query involves errors on one or more qubits. We further extend the protocol to fractional and continuous-time Boolean oracles. Quantum error correction can thus protect not only prescribed operations but also unknown dynamics. Our results make a large family of quantum advantages in learning robust against noise and open a path toward robust computational sensing.

发表机构

• MIT Center for Theoretical Physics - a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院理论物理中心-莱纳韦伯研究所）

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