A Survey of Quantum Property Testing

The area of property testing tries to design algorithms that can efficiently handle very large amounts of data: given a large object that either has a certain property or is somehow “far” from having that property, a tester should efficiently distinguish between these two cases. In this survey we describe recent results obtained for quantum property testing. This area naturally falls into three parts. First, we may consider quantum testers for properties of classical objects. We survey the main examples known where quantum testers can be much (sometimes exponentially) more efficient than classical testers. Second, we may consider classical testers of quantum objects. This is the situation that arises for instance when one is trying to determine if quantum states or operations do what they are supposed to do, based only on classical input-output behavior. Finally, we may also consider quantum testers for properties of quantum objects, such as states or operations. We survey known bounds on testing various natural properties, such as whether two states are equal, whether a state is separable, whether two operations commute, etc. We also highlight connections to other areas of quantum information theory and mention a number of open questions. Contents

Experimental and theoretical research on program mutation

Issued as Final report, Project no. G-36-636 (continued by G-36-661

A survey of quantum property testing

The area of property testing tries to design algorithms that can efficiently handle very large amounts of data: given a large object that either has a certain property or is somehow "far" from having that property, a tester should efficiently distinguish between these two cases. In this survey we describe recent results obtained for quantum property testing. This area naturally falls into three parts. First, we may consider quantum testers for properties of classical objects. We survey the main examples known where quantum testers can be much (sometimes exponentially) more efficient than classical testers. Second, we may consider classical testers of quantum objects. This is the situation that arises for instance when one is trying to determine if quantum states or operations do what they are supposed to do, based only on classical input-output behavior. Finally, we may also consider quantum testers for properties of quantum objects, such as states or operations. We survey known bounds on te

Programming Languages and Systems

This open access book constitutes the proceedings of the 30th European Symposium on Programming, ESOP 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 24 papers included in this volume were carefully reviewed and selected from 79 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Certified Computation

This paper introduces the notion of certified computation. A certified computation does not only produce a result r, but also a correctness certificate, which is a formal proof that r is correct. This can greatly enhance the credibility of the result: if we trust the axioms and inference rules that are used in the certificate,then we can be assured that r is correct. In effect,we obtain a trust reduction: we no longer have to trust the entire computation; we only have to trust the certificate. Typically, the reasoning used in the certificate is much simpler and easier to trust than the entire computation. Certified computation has two main applications: as a software engineering discipline, it can be used to increase the reliability of our code; and as a framework for cooperative computation, it can be used whenever a code consumer executes an algorithm obtained from an untrusted agent and needs to be convinced that the generated results are correct. We propose DPLs (Denotational Proof Languages)as a uniform platform for certified computation. DPLs enforce a sharp separation between logic and control and over versatile mechanicms for constructing certificates. We use Athena as a concrete DPL to illustrate our ideas, and we present two examples of certified computation, giving full working code in both cases