局部化函数混合的量子比特编码
Qubit encoding for a mixture of localized functions
AI总结：
针对振幅编码的指数级经典开销问题，提出基于离散 Lorentzian 基的局部化函数线性组合编码，并通过振幅放大与缩减实现确定性高效编码及超导硬件验证。
摘要：
振幅编码是量子计算的关键通用技术之一。尽管已有若干方法被提出，但每种方法通常都需要指数级的经典计算开销，或需要一个未给出显式构造的预言机。鉴于实用量子计算的需求不断增长，我们开发了适度专用的编码技术，用于生成局部化复值函数的任意线性组合。我们证明，以 n_loc 个离散 Lorentzian 函数作为展开基组可实现高效的概率编码；对于配备 log_2 n_loc 个辅助量子比特的 n_q 个数据量子比特，其计算时间为 O(max(n_loc^2 log n_loc, n_loc^2 log n_q, n_q))。此外，将振幅放大与振幅缩减相结合，可在解析上使其成为具有可控误差的确定性过程，计算时间降至 O(max(n_loc^{3/2} log n_loc, n_loc^{3/2} log n_q, n_q))。我们估算了将该方案应用于实空间量子化学所需的资源，并展示了在真实超导量子计算机上的结果，以验证我们技术的有效性。
英文摘要：
One of the crucial generic techniques for quantum computation is amplitude encoding. Although several approaches have been proposed, each of them often requires exponential classical-computational cost or an oracle whose explicit construction is not provided. Given the growing demands for practical quantum computation, we develop moderately specialized encoding techniques that generate an arbitrary linear combination of localized complex functions. We demonstrate that $n_{\mathrm{loc}}$ discrete Lorentzian functions as an expansion basis set lead to eficient probabilistic encoding, whose computational time is $\mathcal{O}( \max ( n_{\mathrm{loc}}^2 \log n_{\mathrm{loc}},n_{\mathrm{loc}}^2 \log n_q, n_q ))$ for $n_q$ data qubits equipped with $\log_2 n_{\mathrm{loc}}$ ancillae. Furthermore, amplitude amplification in combination with amplitude reduction renders it deterministic analytically with controllable errors and the computational time is reduced to $\mathcal{O}( \max ( n_{\mathrm{loc}}^{3/2} \log n_{\mathrm{loc}}, n_{\mathrm{loc}}^{3/2} \log n_q, n_q )).$ We estimate required resources for applying our scheme to quantum chemistry in real space. We also show the results on real superconducting quantum computers to confirm the validity of our techniques.
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。
