An Introduction to Quantum Programming in Quipper

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'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.Comment: 15 pages, RC201

Five Quantum Algorithms Using Quipper

Quipper is a recently released quantum programming language. In this report, we explore Quipper's programming framework by implementing the Deutsch's, Deutsch-Jozsa's, Simon's, Grover's, and Shor's factoring algorithms. It will help new quantum programmers in an instructive manner. We choose Quipper especially for its usability and scalability though it's an ongoing development project. We have also provided introductory concepts of Quipper and prerequisite backgrounds of the algorithms for readers' convenience. We also have written codes for oracles (black boxes or functions) for individual algorithms and tested some of them using the Quipper simulator to prove correctness and introduce the readers with the functionality. As Quipper 0.5 does not include more than \ensuremath{4 \times 4} matrix constructors for Unitary operators, we have also implemented \ensuremath{8 \times 8} and \ensuremath{16 \times 16} matrix constructors.Comment: 27 page

A tutorial introduction to quantum circuit programming in dependently typed Proto-Quipper

We introduce dependently typed Proto-Quipper, or Proto-Quipper-D for short, an experimental quantum circuit programming language with linear dependent types. We give several examples to illustrate how linear dependent types can help in the construction of correct quantum circuits. Specifically, we show how dependent types enable programming families of circuits, and how dependent types solve the problem of type-safe uncomputation of garbage qubits. We also discuss other language features along the way.Comment: Added a section on related work and a paragraph explaining qubit initialization and terminatio

Sized Types for low-level Quantum Metaprogramming

One of the most fundamental aspects of quantum circuit design is the concept of families of circuits parametrized by an instance size. As in classical programming, metaprogramming allows the programmer to write entire families of circuits simultaneously, an ability which is of particular importance in the context of quantum computing as algorithms frequently use arithmetic over non-standard word lengths. In this work, we introduce metaQASM, a typed extension of the openQASM language supporting the metaprogramming of circuit families. Our language and type system, built around a lightweight implementation of sized types, supports subtyping over register sizes and is moreover type-safe. In particular, we prove that our system is strongly normalizing, and as such any well-typed metaQASM program can be statically unrolled into a finite circuit.Comment: Presented at Reversible Computation 2019. Final authenticated publication is available online at https://doi.org/10.1007/978-3-030-21500-2_

Simple digital quantum algorithm for symmetric first order linear hyperbolic systems

This paper is devoted to the derivation of a digital quantum algorithm for the Cauchy problem for symmetric first order linear hyperbolic systems, thanks to the reservoir technique. The reservoir technique is a method designed to avoid artificial diffusion generated by first order finite volume methods approximating hyperbolic systems of conservation laws. For some class of hyperbolic systems, namely those with constant matrices in several dimensions, we show that the combination of i) the reservoir method and ii) the alternate direction iteration operator splitting approximation, allows for the derivation of algorithms only based on simple unitary transformations, thus perfectly suitable for an implementation on a quantum computer. The same approach can also be adapted to scalar one-dimensional systems with non-constant velocity by combining with a non-uniform mesh. The asymptotic computational complexity for the time evolution is determined and it is demonstrated that the quantum algorithm is more efficient than the classical version. However, in the quantum case, the solution is encoded in probability amplitudes of the quantum register. As a consequence, as with other similar quantum algorithms, a post-processing mechanism has to be used to obtain general properties of the solution because a direct reading cannot be performed as efficiently as the time evolution.Comment: 28 pages, 12 figures, major rewriting of the section describing the numerical method, simplified the presentation and notation, reorganized the sections, comments are welcome