13 citations · 31 across the 10 of their papers we have counts for
12 papers
Free Quantum Computing
Jacques Carette, Chris Heunen, Robin Kaarsgaard +2
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is…
One rig to control them all
Chris Heunen, Robin Kaarsgaard, Louis Lemonnier
Controlled commands -- computations whose execution depends on a separate input -- play a central role in reversible Boolean circuits and quantum circuits. However, existing formal…
Universality of a standard two-qubit gate by catalytic embedding
Robin Kaarsgaard
We study the resources required to achieve universal quantum computing via the gate sets that provide the fundamental instructions from which quantum algorithms are built. While si…
Hadamard-Pi: Equational Quantum Programming
Wang Fang, Chris Heunen, Robin Kaarsgaard
Quantum computing offers advantages over classical computation, yet the precise features that set the two apart remain unclear. In the standard quantum circuit model, adding a 1-qu…
Compositional Reversible Computation
Jacques Carette, Chris Heunen, Robin Kaarsgaard +1
Reversible computing is motivated by both pragmatic and foundational considerations arising from a variety of disciplines. We take a particular path through the development of reve…
With a Few Square Roots, Quantum Computing is as Easy as Π
Jacques Carette, Chris Heunen, Robin Kaarsgaard +1
Rig groupoids provide a semantic model of \PiLang, a universal classical reversible programming language over finite types. We prove that extending rig groupoids with just two maps…
The Quantum Effect: A Recipe for QuantumPi
Jacques Carette, Chris Heunen, Robin Kaarsgaard +1
Free categorical constructions characterise quantum computing as the combination of two copies of a reversible classical model, glued by the complementarity equations of classical…
Universal Properties of Partial Quantum Maps
Pablo Andrés-MartíÂ-nez, Chris Heunen, Robin Kaarsgaard
We provide a universal construction of the category of finite-dimensional C*-algebras and completely positive trace-nonincreasing maps from the rig category of finite-dimensional H…
Quantum Information Effects
Chris Heunen, Robin Kaarsgaard
We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is ful…
Graph Traversals as Universal Constructions
Siddharth Bhaskar, Robin Kaarsgaard
We exploit a decomposition of graph traversals to give a novel characterization of depth-first and breadth-first traversals as universal constructions. Specifically, we introduce f…
Bennett and Stinespring, Together at Last
Chris Heunen, Robin Kaarsgaard
We present a universal construction that relates reversible dynamics on open systems to arbitrary dynamics on closed systems: the restriction affine completion of a monoidal restri…
Reversible effects as inverse arrows
Chris Heunen, Robin Kaarsgaard, Martti Karvonen
Reversible computing models settings in which all processes can be reversed. Applications include low-power computing, quantum computing, and robotics. It is unclear how to represe…