Invertible Program Restructurings for Continuing Modular Maintenance

When one chooses a main axis of structural decompostion for a software, such as function- or data-oriented decompositions, the other axes become secondary, which can be harmful when one of these secondary axes becomes of main importance. This is called the tyranny of the dominant decomposition. In the context of modular extension, this problem is known as the Expression Problem and has found many solutions, but few solutions have been proposed in a larger context of modular maintenance. We solve the tyranny of the dominant decomposition in maintenance with invertible program transformations. We illustrate this on the typical Expression Problem example. We also report our experiments with Java and Haskell programs and discuss the open problems with our approach.Comment: 6 pages, Early Research Achievements Track; 16th European Conference on Software Maintenance and Reengineering (CSMR 2012), Szeged : Hungary (2012

The GHZ/W-calculus contains rational arithmetic

Graphical calculi for representing interacting quantum systems serve a number of purposes: compositionally, intuitive graphical reasoning, and a logical underpinning for automation. The power of these calculi stems from the fact that they embody generalized symmetries of the structure of quantum operations, which, for example, stretch well beyond the Choi-Jamiolkowski isomorphism. One such calculus takes the GHZ and W states as its basic generators. Here we show that this language allows one to encode standard rational calculus, with the GHZ state as multiplication, the W state as addition, the Pauli X gate as multiplicative inversion, and the Pauli Z gate as additive inversion.Comment: In Proceedings HPC 2010, arXiv:1103.226

The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)

We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a (2n+1)x(2n+1) binary matrix product and binary quadratic forms. As an application we give two schemes to efficiently decompose Clifford group operations into one and two-qubit operations. We also show how the coefficients of stabilizer states and Clifford group operations in a standard basis expansion can be described by binary quadratic forms. Our results are useful for quantum error correction, entanglement distillation and possibly quantum computing.Comment: 9 page

Automated Code Generation for Lattice Quantum Chromodynamics and beyond

We present here our ongoing work on a Domain Specific Language which aims to simplify Monte-Carlo simulations and measurements in the domain of Lattice Quantum Chromodynamics. The tool-chain, called Qiral, is used to produce high-performance OpenMP C code from LaTeX sources. We discuss conceptual issues and details of implementation and optimization. The comparison of the performance of the generated code to the well-established simulation software is also made

Bicategorical Semantics for Nondeterministic Computation

We outline a bicategorical syntax for the interaction between public and private information in classical information theory. We use this to give high-level graphical definitions of encrypted communication and secret sharing protocols, including a characterization of their security properties. Remarkably, this makes it clear that the protocols have an identical abstract form to the quantum teleportation and dense coding procedures, yielding evidence of a deep connection between classical and quantum information processing. We also formulate public-key cryptography using our scheme. Specific implementations of these protocols as nondeterministic classical procedures are recovered by applying our formalism in a symmetric monoidal bicategory of matrices of relations.Comment: 21 page