41 research outputs found
Foundations of quantum programming
Progress in the techniques of quantum devices has made people widely believe that large-scale and functional quantum computers will be eventually built. By then, super-powered quantum computer will solve many problems affecting economic and social life that cannot be addressed by classical computing. However, our experiences with classical computing suggest that once quantum computers become available in the future, quantum software will play a key role in exploiting their power, and quantum software market will even be much larger than quantum hardware market. Unfortunately, today's software development techniques are not suited to quantum computers due to the essential differences between the nature of the classical world and that of the quantum world. To lay a solid foundation for tomorrow's quantum software industry, it is critically essential to pursue systematic research into quantum programming methodology and techniques. © 2010 Springer-Verlag
The dagger lambda calculus
We present a novel lambda calculus that casts the categorical approach to the
study of quantum protocols into the rich and well established tradition of type
theory. Our construction extends the linear typed lambda calculus with a linear
negation of "trivialised" De Morgan duality. Reduction is realised through
explicit substitution, based on a symmetric notion of binding of global scope,
with rules acting on the entire typing judgement instead of on a specific
subterm. Proofs of subject reduction, confluence, strong normalisation and
consistency are provided, and the language is shown to be an internal language
for dagger compact categories.Comment: In Proceedings QPL 2014, arXiv:1412.810
Quantum entanglement analysis based on abstract interpretation
Entanglement is a non local property of quantum states which has no classical
counterpart and plays a decisive role in quantum information theory. Several
protocols, like the teleportation, are based on quantum entangled states.
Moreover, any quantum algorithm which does not create entanglement can be
efficiently simulated on a classical computer. The exact role of the
entanglement is nevertheless not well understood. Since an exact analysis of
entanglement evolution induces an exponential slowdown, we consider
approximative analysis based on the framework of abstract interpretation. In
this paper, a concrete quantum semantics based on superoperators is associated
with a simple quantum programming language. The representation of entanglement,
i.e. the design of the abstract domain is a key issue. A representation of
entanglement as a partition of the memory is chosen. An abstract semantics is
introduced, and the soundness of the approximation is proven.Comment: 13 page
Proof rules for the correctness of quantum programs
We apply the notion of quantum predicate proposed by D'Hondt and Panangaden to analyze a simple language fragment which may describe the quantum part of a future quantum computer in Knill's architecture. The notion of weakest liberal precondition semantics, introduced by Dijkstra for classical deterministic programs and by McIver and Morgan for probabilistic programs, is generalized to our quantum programs. To help reasoning about the correctness of quantum programs, we extend the proof rules presented by Morgan for classical probabilistic loops to quantum loops. These rules are shown to be complete in the sense that any correct assertion about the quantum loops can be proved using them. Some illustrative examples are also given to demonstrate the practicality of our proof rules. © 2007 Elsevier Ltd. All rights reserved