ترغب بنشر مسار تعليمي؟ اضغط هنا

Certified Quantum Computation in Isabelle/HOL

73   0   0.0 ( 0 )
 نشر من قبل Anthony Bordg
 تاريخ النشر 2020
والبحث باللغة English




اسأل ChatGPT حول البحث

In this article we present an ongoing effort to formalise quantum algorithms and results in quantum information theory using the proof assistant Isabelle/HOL. Formal methods being critical for the safety and security of algorithms and protocols, we foresee their widespread use for quantum computing in the future. We have developed a large library for quantum computing in Isabelle based on a matrix representation for quantum circuits, successfully formalising the no-cloning theorem, quantum teleportation, Deutschs algorithm, the Deutsch-Jozsa algorithm and the quantum Prisoners Dilemma. We discuss the design choices made and report on an outcome of our work in the field of quantum game theory.



قيم البحث

اقرأ أيضاً

117 - Laura Kovacs , Hanna Lachnitt , 2021
We describe a dataset expressing and proving properties of graph trails, using Isabelle/HOL. We formalize the reasoning about strictly increasing and decreasing trails, using weights over edges, and prove lower bounds over the length of trails in wei ghted graphs. We do so by extending the graph theory library of Isabelle/HOL with an algorithm computing the length of a longest strictly decreasing graph trail starting from a vertex for a given weight distribution, and prove that any decreasing trail is also an increasing one. This preprint has been accepted for publication at CICM 2020.
212 - Filip Maric 2020
The International Mathematical Olympiad (IMO) is perhaps the most celebrated mental competition in the world and as such is among the greatest grand challenges for Artificial Intelligence (AI). The IMO Grand Challenge, recently formulated, requires t o build an AI that can win a gold medal in the competition. We present some initial steps that could help to tackle this goal by creating a public repository of mechanically checked solutions of IMO Problems in the interactive theorem prover Isabelle/HOL. This repository is actively maintained by students of the Faculty of Mathematics, University of Belgrade, Serbia within the course Introduction to Interactive Theorem Proving.
Special Relativity is a cornerstone of modern physical theory. While a standard coordinate model is well-known and widely taught today, several alternative systems of axioms exist. This paper reports on the formalisation of one such system which is c loser in spirit to Hilberts axiomatic approach to Euclidean geometry than to the vector space approach employed by Minkowski. We present a mechanisation in Isabelle/HOL of the system of axioms as well as theorems relating to temporal order. Proofs and excerpts of Isabelle/Isar scripts are discussed, particularly where the formal work required additional steps, alternative approaches, or corrections to Schutz prose.
Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of classical proposit ional logic with only two primitive symbols), the second is the Natural Deduction Assistant (NaDeA), and the third is a one-sided sequent calculus that uses our Sequent Calculus Verifier (SeCaV). We describe each formalization in turn, concentrating on how we used them in our teaching, and commenting on features that are interesting or useful from a logic education perspective. In the conclusion, we reflect on the lessons learned and where they might lead us next.
216 - Russell OConnor 2008
Reasoning about real number expressions in a proof assistant is challenging. Several problems in theorem proving can be solved by using exact real number computation. I have implemented a library for reasoning and computing with complete metric space s in the Coq proof assistant and used this library to build a constructive real number implementation including elementary real number functions and proofs of correctness. Using this library, I have created a tactic that automatically proves strict inequalities over closed elementary real number expressions by computation.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا