Related papers: A Theorem Prover for Quantum Hoare Logic and Its A…
An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a…
We propose an algebraic formulation for two distinct quantum algorithms: a quantum classification algorithm and a quantum search algorithm with a non-uniform initial distribution, both based on Clifford algebras and spinorial…
We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive…
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…
We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which enables a classical verifier to use a quantum…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
Modern machine learning pipelines are built on numerical algorithms. Reliable numerical methods are thus a prerequisite for trustworthy machine learning and cyber-physical systems. Therefore, we contribute a framework for verified numerical…
We introduce a theorem proving approach to the specification and generation of temporal logical constraints for training neural networks. We formalise a deep embedding of linear temporal logic over finite traces (LTL$_f$) and an associated…
Prolog is a well known declarative programming language based on propositional Horn formulas. It is useful in various areas, including artificial intelligence, automated theorem proving, mathematical logic and so on. An active research area…
We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd (HHL) algorithm for solving a system of linear equations. In our hybrid scheme, a classical information feed-forward is required from the quantum phase estimation…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple…
Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider…
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…
Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…
We formalize the univariate fragment of Ben-Or, Kozen, and Reif's (BKR) decision procedure for first-order real arithmetic in Isabelle/HOL. BKR's algorithm has good potential for parallelism and was designed to be used in practice. Its key…
The partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
Distributed quantum systems and especially the Quantum Internet have the ever-increasing potential to fully demonstrate the power of quantum computation. This is particularly true given that developing a general-purpose quantum computer is…
After learning basic quantum computing concepts, it is desirable to reinforce the learning using an important and relatively complex algorithm through which the students can observe and appreciate how the qubits evolve and interact with…