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arXiv 2602.23664quant-ph
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调和序列态制备

Harmonic sequence state-preparation

MIT Lincoln Laboratory(麻省理工学院林肯实验室)

Benjamin Rempfer, Parker Kuklinski, Justin Elenewski, Kevin Obenland

AI总结:

本文提出了一种高效制备调和序列比例量子态的电路,并探讨了其在块编码矩阵中的应用。

摘要:

我们演示了一个高效的电路,用于制备具有幅度与调和序列成比例的量子态。我们首先通过线性相关的幅度制备一个大量子态,然后应用量子傅里叶变换;这与锯齿波的傅里叶系数遵循调和序列的事实有直接类比。随后,我们考虑了通过块编码具有调和序列沿对角线的矩阵的扩展问题。两种电路的成本都由量子傅里叶变换相关的成本主导。

英文摘要:

We demonstrate an efficient circuit to prepare a quantum state with amplitudes proportional to a harmonic sequence. We do this by first preparing a large quantum state with linearly related amplitudes and then applying a quantum Fourier transform; this has a direct analogy to the fact that the Fourier coefficients of a sawtooth wave follow a harmonic sequence. We then consider an extension of this problem by block-encoding a matrix with a harmonic sequence along its diagonal. The cost of both circuits is dominated by the costs associated with the quantum Fourier transform.

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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