Artifact for "An Algebraic Language for Specifying Quantum Networks"

The artifact is a Haskell library bellkat plus several examples provided as executables within the same Haskell package. We provide two build options: Nix-based and Stack-based, for each we give a Docker file that can simplify the setup of the development environment. Reproducing the results from the paper can be done in two ways:

• from a respective development environment (Nix- or Stack-based)
• using an executable Docker container providing a Haskell interpreter with bellkat already "in scope" (recommended, see "Preparation" section in "Reproducing the results" below)

Docker note: please, be aware that docker run commands may have to be prefixed with sudo, depending on the docker setup (see details here).

Preparing development environment (recommended to skip)

Please, check Haskell language server documentation for editor support (optional).

Nix

• install Nix package manager
• enable Nix flakes
• to enter environment run nix develop from the artifact's root
• run hpack (no arguments) to generate .cabal file

For convenience, we provide Dockerfile.nixdev with the environment already set up:

docker build --tag bellkat:nixdev --file Dockerfile.nixdev . # build the image
docker run --rm --interactive --tty bellkat:nixdev # to enter the environment

Stack

• install Stack

• install the following extra dependencies:

  • Pango 1.50.6
  • Cairo 1.21.0
  • Zlib 1.3
  • Glib 2.72
  • Ncurses 6.3

  Those can be installed on ubuntu as follows:

  apt-get install libz-dev libtinfo-dev libcairo-dev libpango1.0

For convenience, we provide Dockerfile.stackdev with the environment already set up:

docker build --tag bellkat:stackdev --file Dockerfile.stackdev . # build the image
docker run --rm --interactive --tty bellkat:stackdev # to enter the environment

Building the artifact (recommended to skip)

Nix

cabal build

Stack

stack build

Syntactic differences with the paper:

Bell pairs (e.g., to specify initial states):

• $A \sim B$ is represented by "A" ~ "B"

Basic actions:

• $cr\langle X \rangle$ is represented by create "X"
• $tr\langle X \rightarrow Y \sim Z \rangle$ is represented by trans "X" ("Y", "Z")
• $sw\langle X \sim Y @ Z \rangle$ is represented by swap "Z" ("X", "Y")
• $di\langle X \sim Y\rangle$ is represented by distill ("X", "Y")

Operations:

• sequential composition is represented by <>
• parallel composition $||$ is represented by <||>
• iteration $p^\ast$ is represented by star p

Tests:

• checking absence $[{{X \sim Y}}]$ is represented by test ("X" /~? "Y")
• checking presence ${{X \sim Y}} \blacktriangleright {{X \sim Y}}$ is represented by test ("X" ~~? "Y")

Features:

• Deciding validity of a policy $p$ on inputs from $\mathcal{N}_0$ and set of valid states $\mathcal{N}$ (definition 4.10) is represented by isPolicyValid N0 N p, where N is represented as a predicate $\mathcal{M}(BP) \rightarrow \mathbb{B}$.

• Deciding equivalence of policies $p$ and $q$ on inputs from $\mathcal{N}_0$ (Theorem 4.4) is represented by arePoliciesEquivalent N0 p q.

• Drawing histories of protocols (Figure 3):

  • drawHistoriesSVG p (to create an .svg image)
  • drawHistoriesText p (to output a textual representation)

Reproducing the results

Preparation

• Docker (recommended): change to artifact's root and create the container by running

  docker build --tag bellkat:latest .

  Note all the docker commands below use bind mount to handle input and output files.

• Stack: change to the artifact root

• Nix: change to the artifact root and run nix develop

Example P1 and history in Fig 3 (a)

The protocols are specified in examples/P1.hs, history would be saved in P1.svg.

• Docker (recommended)

  docker run --rm --mount type=bind,source=$(pwd),target=/opt/bellkat -it bellkat:latest\
      examples/P1.hs --width 1000 --output P1.svg
  # or (for textual version)
  docker run --rm --mount type=bind,source=$(pwd),target=/opt/bellkat -it bellkat:latest\
      examples/P1Text.hs

• Stack:

  stack run p1 -- --width 1000 --output P1.svg
  # or (for textual version)
  stack run p1text

• Nix:

  cabal run p1 -- --width 1000 --output P1.svg
  # or (for textual version)
  cabal run p1text

Example P2 and history in Fig 3 (b)

The protocols are specified in examples/P2.hs, history would be saved in P2.svg.

• Docker (recommended)

  docker run --rm --mount type=bind,source=$(pwd),target=/opt/bellkat -it bellkat:latest\
      examples/P2.hs --width 1000 --output P2.svg
  # or (for textual version)
  docker run --rm --mount type=bind,source=$(pwd),target=/opt/bellkat -it bellkat:latest\
      examples/P2Text.hs

• Stack:

  stack run p2 -- --width 1000 --output P2.svg
  # or (for textual version)
  stack run p2text

• Nix:

  cabal run p2 -- --width 1000 --output P2.svg
  # or (for textual version)
  cabal run p2text

Example P3

Perform four checks using examples/P3.hs (uses HSpec library, please check its documentation to understand the uses of describe, it and shouldBe within the example):

• check that the protocol always creates a $A \sim E$ Bell pair
• check that the protocol does not always creates a $A \sim C$ Bell pair
• check that 1 qubit memory at location $A$ are not enough
• check that 3 qubits memory at location $A$ are not enough
• check that 2 qubits at $A$ and 4 qubits at $D$ are enough

The first two are related reachability property (discussed on line 942 of the paper), while the rest are related to memory requirements (discussed on line 943 of the paper):

• Docker (recommended)

  docker run --rm --mount type=bind,source=$(pwd),target=/opt/bellkat -it bellkat:latest\
      examples/P3.hs

• Stack:

  stack run p3

• Nix:

  cabal run p3

Writing and testing your own protocols

Most of the relevant documentation is present in BellKAT.Prelude module. To see it nicely formatted (not for docker), you can build documentation using Haddock:

• Stack: stack haddock
• Nix: cabal haddock

In both cases, the output should display the path to index.html root of the documentation

Setting up and running the examples

If you want to work with your own protocols or modify existing ones you have multiple options:

• modify the existing examples

• create new examples within BellKAT repository

  1. Creating a new file (say MyExample.hs) inside examples/ (e.g., by copying examples/P3.hs)

  2. Tell stack or cabal about the example by adding

     my-example:
       dependencies: 
         - bellkat
       main: examples/MyExample.hs

     to package.yaml

  3. Run your example with stack, using stack run my-example or cabal run my-example

  4. (optional) to enable editor support add

     - path: "examples/MyExample.hs"
       component: "exe:my-example"

     to hie.yaml

  5. Continue editing examples/MyExample.hs as you wish.

• Use BellKAT as a library:

  • Stack: see the template in reuse-templates/stack, then use

    stack build
    stack run

  • Nix: see the template in reuse-templates/nix, then use

    nix develop # to enter the shell
    hpack # to generate .cabal file
    cabal build
    cabal run