arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2008.06478quant-phcs.ET
收藏

有限空间计算的量子优势

Quantum advantage for computations with limited space

Dmitri Maslov, Jin-Sung Kim, Sergey Bravyi, Theodore J. Yoder, Sarah Sheldon

摘要:

量子计算有望解决经典环境下难以解决的问题。限制所考虑的计算类型通常允许通过量子计算建立可证明的理论优势,然后通过实验证明它。在本文中,我们考虑空间受限的计算,输入是一个只读存储器,只有一个(qu)bit可以计算上,我们表明,$n$ -bit对称布尔函数可以通过使用量子信号处理作为受限空间量子计算使用$O(n^2)$门,但其中一些可能只能评估与概率$1/2 + O(n/\sqrt{2}^n)$由类似定义的经典计算。我们通过实验证明了量子线路对$3$ -、$4$ -、$5$ -和$6$ -位对称布尔函数的计算,利用自定义的两量子位门,算法成功概率超过了经典的最佳可能。这建立并实验验证了另一种量子优势--量子碎片空间比类似的经典空间更有价值--并呼吁深入探索量子线路中的时空权衡。

英文摘要:

Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later demonstrate it experimentally. In this paper, we consider space-restricted computations, where input is a read-only memory and only one (qu)bit can be computed on. We show that $n$-bit symmetric Boolean functions can be implemented exactly through the use of quantum signal processing as restricted space quantum computations using $O(n^2)$ gates, but some of them may only be evaluated with probability $1/2 + O(n/\sqrt{2}^n)$ by analogously defined classical computations. We experimentally demonstrate computations of $3$-, $4$-, $5$-, and $6$-bit symmetric Boolean functions by quantum circuits, leveraging custom two-qubit gates, with algorithmic success probability exceeding the best possible classically. This establishes and experimentally verifies a different kind of quantum advantage -- one where quantum scrap space is more valuable than analogous classical space -- and calls for an in-depth exploration of space-time tradeoffs in quantum circuits.

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。

↑