Despite the rich literature on quantum algorithms, there is a surprisingly small amount of coverage of their concrete logical design and implementation. Most resource estimation is done at the level of complexity analysis, but actual concrete numbers (of quantum gates, qubits, etc.) can differ by orders of magnitude. The line of work we present here is a formal framework to write, and reason about, quantum algorithms. Specifically, we designed a language, Quipper, with scalability in mind, and we are able to report actual resource counts for seven non-trivial algorithms found in the quantum computer science literature.

}, url = {http://arxiv.org/abs/1412.0625v1}, author = {Jonathan M. Smith and Neil J. Ross and Peter Selinger and Beno{\^\i}t Valiron} } @article {1536, title = {An Introduction to Quantum Programming in Quipper}, journal = {Lecture Notes in Computer Science}, volume = {7948}, year = {2013}, month = {2013/07/05}, pages = {110-124}, abstract = { Quipper is a recently developed programming language for expressing quantum computations. This paper gives a brief tutorial introduction to the language, through a demonstration of how to make use of some of its key features. We illustrate many of Quipper{\textquoteright}s language features by developing a few well known examples of Quantum computation, including quantum teleportation, the quantum Fourier transform, and a quantum circuit for addition. }, isbn = {978-3-642-38986-3}, doi = {10.1007/978-3-642-38986-3_10}, url = {http://arxiv.org/abs/1304.5485v1}, author = {Alexander S. Green and Peter LeFanu Lumsdaine and Neil J. Ross and Peter Selinger and Beno{\^\i}t Valiron} } @article {1535, title = {Quipper: A Scalable Quantum Programming Language}, journal = {ACM SIGPLAN Notices}, volume = {48}, year = {2013}, month = {2013/06/23}, pages = {333-342}, abstract = {The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higher-order quantum programming language. Quipper has been used to program a diverse set of non-trivial quantum algorithms, and can generate quantum gate representations using trillions of gates. It is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware. Quipper has proven effective and easy to use, and opens the door towards using formal methods to analyze quantum algorithms.

}, doi = {10.1145/2499370.2462177}, url = {http://arxiv.org/abs/1304.3390v1}, author = {Alexander S. Green and Peter LeFanu Lumsdaine and Neil J. Ross and Peter Selinger and Beno{\^\i}t Valiron} }