Property Testing for Quantum Engineering (ProTeQE)

我们的感官不断地以各种形式向我们灌输关于各种问题的信息。然而，当涉及到决定任何给定的主题时，使用所有这些信息很少是可行的。相反，我们通过对整体中选定的、通常很小的一部分进行深思熟虑来决定。这一不言而喻的认识提出了一些基本问题。例如，给定一个主题，是否有可能通过考虑所有可用信息中的一小部分来做出有意义的决定？即使是这样，这一小部分应该如何选择呢？理论计算机科学试图将这些问题形式化，然后针对特定的数学问题回答它们。这形成了属性测试的主题，该主题涉及到用于近似决策的超快算法的设计。在这种情况下，近似决策是指在具有预定属性的对象和远未具有该属性的对象之间进行选择。应用范围从检查非常大和复杂的软件程序的正确性到基于人体内蛋白质之间相互作用的病理检测。例如，通过检查每一行代码来确定软件的正确性(对于现代汽车来说，这可能超过1亿行)将是昂贵得令人望而却步的、耗时的，而且本身容易出错。超快的性质测试算法只检查这些巨大物体中相对较小和随机的部分。ProTeQE将把性质测试应用于量子工程。量子计算机被认为能够以指数级的速度比经典计算机更有效地解决几个问题。不出所料，这是以指数级的代价出现的。描述一台运行n个量子比特(量子比特)的量子计算机通常需要4^n个数字。一旦这样的系统被设计出来，我们如何决定它是否可以用来建造一台可靠的量子计算机？可靠的量子计算机--从技术上讲被称为容错量子计算机(FTQC)--只有在工程量子系统遵守一组特定的数学特性的情况下才是可能的。ProTeQE的目标是回答这样一个问题：给定一个物体，在这种情况下是一个工程量子系统，它是否具有FTQC所必需的性质，或者远远不具备这些性质？回答这个问题的超快算法将消除量子工程和量子技术发展中的一个严重瓶颈--测试量子设备。目前的测试方案是测量和处理成倍增长的多个数字来做出决定，这种测试方案昂贵得令人望而却步，耗时长，而且本身容易出错。因此，ProTeQE将在工程量子系统的设计和原型制作方面实现更快的周转。这应该会加速可靠的真实世界量子计算机的发展，并促进更广泛的量子工程和技术的更大进步。ProTeQE也应该培养我们基本的好奇心。量子力学是我们目前关于自然的基本理论，它本质上是概率的和非局域性的。当这些概念与属性测试和近似决策的概念相结合时，结果可能会影响我们理解自然规律的基础。特别是，ProTeQE可能最终会阐明一个长期存在的问题：所有的自然基本定律(如量子力学)都是可有效检验的吗？

Our senses incessantly inundate us with information on a multitude of issues in multifarious forms. Yet, when it comes to deciding any given topic, it is seldom feasible to use all of this information. Rather, we decide by deliberating on a selected, typically small, part of the whole.This self-evident realisation raises some fundamental questions. For instance, given a topic, is it even possible to make a meaningful decision by considering a small part of all the available information? Even if it were, how should this small part be selected?Theoretical computer science seeks to formalise these questions, and then answer them for specific mathematical problems. This forms the subject of property testing, which is concerned with the design of ultra-fast algorithms for approximate decision making. In this context, an approximate decision means choosing between objects that have a predetermined property and those that are 'far' from having that property. Applications range from checking the correctness of extremely large and complex software programmes to detecting pathologies based on interactions between proteins in the human body. For instance, deciding the correctness of a software by checking every line of code (which for a modern car can exceed 100 million lines) would be prohibitively expensive, time-consuming, and itself error prone. The ultra-fast property testing algorithms inspect only relatively small and random portions of these huge objects.ProTeQE will apply property testing to quantum engineering.Quantum computers are believed to be capable of solving several problems exponentially more efficiently than classical computers. Unsurprisingly, this comes at an exponential cost. Describing a quantum computer operating of n quantum bits (qubits) typically requires 4^n numbers. Once such a system is engineered, how can we decide if it can be used to build a reliable quantum computer?A reliable quantum computer - technically called a fault-tolerant quantum computer (FTQC) is only possible if the engineered quantum system obeys a specific set of mathematical properties. ProTeQE has the objective of answering the question: Given an object, in this case an engineered quantum system, does it have the properties necessary for FTQC, or is it far from having them?An ultra-fast algorithm to answer this question will remove a severe bottleneck in the development of quantum engineering and quantum technologies - that of testing quantum devices. The present testing regimen of measuring and processing exponentially many numbers to make a decision is prohibitively expensive, time-consuming, and itself error prone. ProTeQE will thus enable a faster turnaround in the designing and prototyping of engineered quantum systems. This should accelerate the development of reliable real-world quantum computers, and facilitate greater advances in quantum engineering and technologies more generally.ProTeQE should also nourish our basic curiosity. Quantum mechanics, which is presently our fundamental theory of Nature, is inherently probabilistic and non-local. When these concepts interface with those of property testing and approximate decision-making, the outcome could impact the foundations of our understanding of the laws of Nature. In particular, ProTeQE may eventually shed light on an abiding question: Are all fundamental laws of Nature (such as quantum mechanics) efficiently testable?