What gives quantum computers their extra power?

量子计算有望极大地扩展高效可计算的领域，因此可以成为现代社会基于信息的工业的主要推动力。Shor的因子分解算法是展示这种潜力的一个主要例子。目前，人们正在追求各种各样的量子算法，从计算机科学和物理学的各个领域汲取直觉。然而，到目前为止，肖尔和格罗弗发现的重大突破被证明是极其罕见的。因此，为了充分挖掘量子计算的潜力，我们需要更好地了解它的基础。也就是说，我们需要问量子力学的哪些基本性质具有计算价值，以及如何利用这个价值。本建议指出了两种这样的资源，并描述了理解如何最好地应用它们的途径。如果这项研究长期成功，将成为未来高水平量子算法设计的基础。

Quantum computation holds the promise to vastly expand the realm of the efficiently computable, and as such can become a major driving force for the information-based industries of modern society. Shor's factoring algorithm is a prime example to demonstrate this potential. Currently, a wide variety of approaches to quantum algorithms is being pursued, drawing intuition from various areas of computer science and physics. Yet, so far, breakthroughs of the magnitude of Shor's and Grover's discoveries have proven to be extremely rare.Therefore, to tap into the full potential of quantum computation, we need to better understand its foundations. That is, we need to ask which fundamental properties of quantum mechanics have computational value, and how this value can be utilized. This proposal points to two such resources, and describes a path towards understanding how to best apply them. If this research is successful in the long term, it will become a foundation for future high-level quantum algorithm design.