早期量子算法在量子通信、量子纠错等领域的应用

Application of Early Quantum Algorithms in Quantum Communication,Error Correction and Other Fields

当今量子算法的一个发展方向是对早期量子算法的再思考。在量子计算领域,每一种早期量子算法都提出了突破性概念。一般认为它们在很大程度上仅属理论范畴,原因它们所求解的问题几乎都没有实用价值。但这些早期量子算法依然重要,因为它们在解决问题的速度上相比经典算法呈指数级别的增长。文中做了两件工作:一方面详细阐述对早期量子算法再思考的最新进展,另一方面则对早期量子算法进行所谓的重新目的化,即重新用于量子密钥分发、纠错等领域。Deutsch-Jozsa算法、Bernstein-Vazirani算法和Simon算法是关注的重点。Deutsch-Jozsa算法用于判定多引数函数(Multi-argument Function)是平衡的还是常数的。最近的研究表明,其应用可以扩展到量子通信和形式语言(Formal Languages)领域。Bernstein-Vazirani算法能够搜索出在函数中编码的字符串,其应用可以扩展至量子密钥分发领域和通信中对信息的纠错处理。Simon算法则用于求解具有特定属性字符串的识别问题,它的现代应用包括量子通信和纠错。

At present,a development direction of quantum algorithm is to rethink the early quantum algorithms.Each of them involves an important,groundbreaking concept in quantum computing.They are generally considered to only belong to the theoretical category due to the fact that the problems they solve are of little practical value.However,they are still important as they can solve a problem exponentially faster than a classical algorithm.Here,this paper elaborates on some recent developments in repurposing the early quantum algorithms for quantum key distribution and other fields.It especially focuses on Deutsch-Jozsa algorithm,Bernstein-Vazirani algorithm and Simon’s algorithm.The Deutsch-Jozsa algorithm is used to determine whether a multi-argument function is balanced or constant.As recent research shows,it can be extended to application in the field of quantum communication and formal languages.The Bernstein-Vazirani algorithm finds a string encoded in a function.Its application can be extended to quantum key distribution and error correction.Simon’s algorithm tackles the problem of identifying a string with a particular property.Its modern applications include quantum communication and error correction.