Quantum outperforms classical Quantum computers are expected to be better at solving certain computational problems than classical computers. This expectation is based on (well-founded) conjectures in computational complexity theory, but rigorous comparisons between the capabilities of quantum and classical algorithms are difficult to perform. Bravyi et al. proved theoretically that whereas the number of “steps” needed by parallel quantum circuits to solve certain linear algebra problems was independent of the problem size, this number grew logarithmically with size for analogous classical circuits (see the Perspective by Montanaro). This so-called quantum advantage stems from the quantum correlations present in quantum circuits that cannot be reproduced in analogous classical circuits. Science, this issue p. 308; see also p. 289 Parallel quantum circuits outperform classical counterparts at solving certain linear algebra problems. Quantum effects can enhance information-processing capabilities and speed up the solution of certain computational problems. Whether a quantum advantage can be rigorously proven in some setting or demonstrated experimentally using near-term devices is the subject of active debate. We show that parallel quantum algorithms running in a constant time period are strictly more powerful than their classical counterparts; they are provably better at solving certain linear algebra problems associated with binary quadratic forms. Our work gives an unconditional proof of a computational quantum advantage and simultaneously pinpoints its origin: It is a consequence of quantum nonlocality. The proposed quantum algorithm is a suitable candidate for near-future experimental realizations, as it requires only constant-depth quantum circuits with nearest-neighbor gates on a two-dimensional grid of qubits (quantum bits).

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浅电路的量子优势

量子优于经典 量子计算机有望比经典计算机更擅长解决某些计算问题。这种期望基于计算复杂性理论中的（有充分根据的）猜想，但很难在量子算法和经典算法的能力之间进行严格的比较。布拉维等人。理论上证明，虽然并行量子电路解决某些线性代数问题所需的“步骤”数量与问题的大小无关，但这个数字随着类似经典电路的大小呈对数增长（参见蒙塔纳罗的观点）。这种所谓的量子优势源于量子电路中存在的量子相关性，而这种相关性无法在类似的经典电路中重现。科学，这个问题 p。308; 另见第。289 并行量子电路在解决某些线性代数问题方面优于经典对应电路。量子效应可以增强信息处理能力并加速某些计算问题的解决。量子优势是否可以在某些环境中得到严格证明，或者是否可以使用近期设备进行实验证明，这是一个激烈争论的主题。我们表明，在恒定时间段内运行的并行量子算法比经典算法更强大；事实证明，它们更擅长解决与二元二次形式相关的某些线性代数问题。我们的工作提供了计算量子优势的无条件证明，同时指出了它的起源：它是量子非局域性的结果。