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arXiv 1306.2713quant-ph
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任意数量量子比特的量子相位估计

Quantum Phase Estimation with an Arbitrary Number of Qubits

Chen-Fu Chiang

摘要:

由于可扩展性的巨大困难,在量子计算机制的早期阶段,量子计算机在量子比特的数量上受到限制。除了用于存储相应特征向量所需的量子位之外,假设我们还有额外的k个量子位可用。给定这样一个约束k,我们提出了一种方法的相位估计的特征相位的精确n位精度。该方法采用量子傅里叶变换(QFT)的标准递归电路,并采用经典位来实现这一任务。我们的算法具有O(n \log k)的复杂度,而不是O(n^2)在传统的QFT,在旋转门的总调用。我们还设计了一个方案,通过使用k个可用的量子比特通过连续分数的方法或同时丢番图近似实现的因式分解算法。

英文摘要:

Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose we have additional k qubits available. Given such a constraint k, we propose an approach for the phase estimation for an eigenphase of exactly n-bit precision. This approach adopts the standard recursive circuit for quantum Fourier transform (QFT) and adopts classical bits to implement such a task. Our algorithm has the complexity of O(n \log k), instead of O(n^2) in the conventional QFT, in terms of the total invocation of rotation gates. We also design a scheme to implement the factorization algorithm by using k available qubits via either the continued fractions approach or the simultaneous diophantine approximation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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