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Add the 5 vertex example in the paper (#47)
* save * add examples * update * update README * update notebooks guide * Update notebooks/unweighted.jl Co-authored-by: Shengtao Wang <[email protected]> * Update notebooks/unweighted.jl Co-authored-by: Shengtao Wang <[email protected]> * Update notebooks/unweighted.jl Co-authored-by: Shengtao Wang <[email protected]> * Update notebooks/unweighted.jl Co-authored-by: Shengtao Wang <[email protected]> * Update notebooks/unweighted.jl Co-authored-by: Shengtao Wang <[email protected]> * Update notebooks/unweighted.jl Co-authored-by: Shengtao Wang <[email protected]> --------- Co-authored-by: Shengtao Wang <[email protected]>
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‎Project.toml

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name = "UnitDiskMapping"
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uuid = "1b61a8d9-79ed-4491-8266-ef37f39e1727"
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authors = ["QuEra Computing Inc."]
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version = "0.3.1"
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version = "0.3.2"
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[deps]
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Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
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LuxorGraphPlot = "1f49bdf2-22a7-4bc4-978b-948dc219fbbc"
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[compat]
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Graphs = "1.6"
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LuxorGraphPlot = "0.2"
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LuxorGraphPlot = "0.3"
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julia = "1"
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[extras]

‎README.md

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## Examples
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Please check this [notebook](https://queracomputing.github.io/UnitDiskMapping.jl/notebooks/tutorial.html), which contains the following examples:
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Please check the following notebooks:
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1. [Unit Disk Mapping](https://queracomputing.github.io/UnitDiskMapping.jl/notebooks/tutorial.html), which contains the examples in ["Quantum Optimization with Arbitrary Connectivity Using Rydberg Atom Arrays"](https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.4.010316):
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* Reduction from a generic weighted or unweighted maximum independent set (MIS) problem to that on a King's subgraph (KSG).
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* Reduction from a generic or square-lattice QUBO problem to an MIS problem on a unit-disk grid graph.
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* Reduction from an integer factorization problem to an MIS problem on a unit-disk grid graph.
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* Reduction from a generic weighted or unweighted maximum independent set (MIS) problem to that on a diagonal coupled unit-disk grid graph (DUGG).
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* Reduction from a generic or square-lattice QUBO problem to an MIS problem on a unit-disk grid graph.
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* Reduction from an integer factorization problem to an MIS problem on a unit-disk grid graph.
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2. [Unweighted KSG reduction of the independent set problem](https://queracomputing.github.io/UnitDiskMapping.jl/notebooks/unweighted.html), which contains the unweighted reduction from a general graph to a King's subgraph. It covers all example graphs in paper: "Computer-Assisted Gadget Design and Problem Reduction of Unweighted Maximum Independent Set" (To be published).
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![](https://user-images.githubusercontent.com/6257240/198861111-4499c17d-9938-406b-8253-943b01f4633c.png)
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To run the notebook locally, you will need the [Pluto](https://github.com/fonsp/Pluto.jl) and [GenericTensorNetworks](https://github.com/QuEraComputing/GenericTensorNetworks.jl) Julia packages installed. You can run the following after entering the Package mode:
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```
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pkg> add Pluto
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pkg> add GenericTensorNetworks
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To run the notebook locally, you will need to activate and instantiate the local environment that specified in the [`notebooks`](notebooks) directory:
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```bash
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$ cd notebooks
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$ julia --project -e 'using Pkg; Pkg.instantiate()'
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```
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and returning to the Julia REPL (you can do this by hitting Backspace in the Package mode) to run:
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```
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julia> import Pluto; Pluto.run()
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To run the notebook, just type in the same terminal:
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```bash
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julia --project -e "import Pluto; Pluto.run()"
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```
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in the `notebooks` directory of this project. At this point, your browser should automatically launch and display a list of available notebooks you can run. You should just see `tutorial.jl` listed.
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At this point, your browser should automatically launch and display a list of available notebooks you can run. You should just see the notebooks listed.
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## Supporting and Citing

‎examples/petersen.jl

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‎notebooks/tutorial.jl

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### A Pluto.jl notebook ###
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# v0.19.27
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# v0.19.32
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using Markdown
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using InteractiveUtils
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# ╔═╡ 98459516-4833-4e4a-916f-d5ea3e657ceb
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# Visualization setup.
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# To make the plots dark-mode friendly, we use white-background color.
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using UnitDiskMapping.LuxorGraphPlot.Luxor, LuxorGraphPlot; LuxorGraphPlot.DEFAULT_UNIT[] = 25; LuxorGraphPlot.DEFAULT_BACKGROUND_COLOR[]="white";
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using UnitDiskMapping.LuxorGraphPlot.Luxor, LuxorGraphPlot; GraphDisplayConfig.unit[] = 25; GraphDisplayConfig.background_color[]="white";
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# ╔═╡ eac6ceda-f5d4-11ec-23db-b7b4d00eaddf
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md"# Unit Disk Mapping"

‎notebooks/unweighted.jl

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### A Pluto.jl notebook ###
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# v0.19.32
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using Markdown
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using InteractiveUtils
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# ╔═╡ f55dbf80-8425-11ee-2e7d-4d1ad4f693af
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# ╠═╡ show_logs = false
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begin
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using Pkg; Pkg.activate(".")
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using Revise
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using PlutoUI
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# left right layout
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function leftright(a, b; width=600)
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HTML("""
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<style>
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table.nohover tr:hover td {
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background-color: white !important;
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}</style>
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<table width=$(width)px class="nohover" style="border:none">
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<tr>
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<td>$(html(a))</td>
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<td>$(html(b))</td>
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</tr></table>
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""")
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end
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# up down layout
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function updown(a, b; width=nothing)
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HTML("""<table class="nohover" style="border:none" $(width === nothing ? "" : "width=$(width)px")>
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<tr>
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<td>$(html(a))</td>
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</tr>
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<tr>
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<td>$(html(b))</td>
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</tr></table>
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""")
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end
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PlutoUI.TableOfContents()
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end
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# ╔═╡ be011e30-74e6-49cd-b45a-288972dc5f18
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using UnitDiskMapping, Graphs # for mapping graphs to a King's subgraph (KSG)
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# ╔═╡ 31250cb9-6f3a-429a-975d-752cb7c07883
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using GenericTensorNetworks # for solving the maximum independent sets
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# ╔═╡ 9017a42c-9791-4933-84a4-9ff509967323
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md"""
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# Unweighted KSG reduction of the independent set problem
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"""
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# ╔═╡ f0e7c030-4e43-4356-a5bb-717a7f382a17
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md"This notebook contains examples from the paper, "Computer-Assisted Gadget Design and Problem Reduction of Unweighted Maximum Independent Set"."
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# ╔═╡ cb4a9655-6df2-46b3-8969-8b6f2db7c59a
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md"""
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## Example 1: The 5-vertex graph
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The five vertex demo graph in the paper.
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"""
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# ╔═╡ 956a5c3a-b8c6-4040-9553-3b4e2337b163
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md"#### Step 1: Prepare a source graph."
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# ╔═╡ d858f57e-1706-4b73-bc23-53f7af073b0c
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# the demo graph in the main text
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function demograph()
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g = SimpleGraph(5)
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for (i, j) in [(1, 2), (2, 4), (3, 4), (1, 3), (4, 5), (1, 5)]
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add_edge!(g, i, j)
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end
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return g
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end
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# ╔═╡ a3a86c62-ee6e-4a3b-99b3-c484de3b5220
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g5 = demograph()
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# ╔═╡ e6170e72-0804-401e-b9e5-65b8ee7d7edb
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show_graph(g5)
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# ╔═╡ 625bdcf4-e37e-4bb8-bd1a-907cdcc5fe24
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md"""
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#### Step 2: Map the source graph to an unweighted King's subgraph (KSG)
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The vertex order is optimized with the Branching path decomposition algorithm
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"""
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# ╔═╡ f9e57a6b-1186-407e-a8b1-cb8f31a17bd2
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g5res = UnitDiskMapping.map_graph(g5; vertex_order=Branching())
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# ╔═╡ e64e7ca4-b297-4c74-8699-bec4b4fbb843
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md"Visualize the mapped KSG graph in terminal"
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# ╔═╡ 0a860597-0610-48f6-b1ee-711939712de4
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print(g5res.grid_graph)
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# ╔═╡ eeae7074-ee21-44fc-9605-3555acb84cee
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md"or in a plotting plane"
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# ╔═╡ 3fa6052b-74c2-453d-a473-68f4b3ca0490
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show_graph(g5res.grid_graph)
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# ╔═╡ 942e8dfb-b89d-4f2d-b1db-f4636d4e5de6
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md"#### Step 3: Solve the MIS size of the mapped graph"
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# ╔═╡ 766018fa-81bd-4c37-996a-0cf77b0909af
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md"The independent set size can be obtained by solving the `SizeMax()` property using the [generic tensor network](https://github.com/QuEraComputing/GenericTensorNetworks.jl) method."
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# ╔═╡ 67fd2dd2-5add-4402-9618-c9b7c7bfe95b
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missize_g5_ksg = solve(IndependentSet(SimpleGraph(g5res.grid_graph)), SizeMax())[]
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# ╔═╡ aaee9dbc-5b9c-41b1-b0d4-35d2cac7c773
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md"The predicted MIS size for the source graph is:"
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# ╔═╡ 114e2c42-aaa3-470b-a267-e5a7c6b08607
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missize_g5_ksg.n - g5res.mis_overhead
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# ╔═╡ e6fa2404-cbe9-4f9b-92a0-0d6fdb649c44
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md"""
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One of the best solutions can be obtained by solving the `SingleConfigMax()` property.
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"""
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# ╔═╡ 0142f661-0855-45b4-852a-78f560e98c67
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mis_g5_ksg = solve(IndependentSet(SimpleGraph(g5res.grid_graph)), SingleConfigMax())[].c.data
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# ╔═╡ fa046f3c-fd7d-4e91-b3f5-fc4591d3cae2
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md"Plot the solution"
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# ╔═╡ 0cbcd2a6-b8ae-47ff-8541-963b9dae700a
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show_config(g5res.grid_graph, mis_g5_ksg)
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# ╔═╡ 4734dc0b-0770-4f84-8046-95a74104936f
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md"#### Step 4: Map the KSG solution back"
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# ╔═╡ 0f27de9f-2e06-4d5e-b96f-b7c7fdadabca
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md"In the following, we will show how to obtain an MIS of the source graph from that of its KSG reduction."
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# ╔═╡ fc968df0-832b-44c9-8335-381405b92199
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mis_g5 = UnitDiskMapping.map_config_back(g5res, collect(mis_g5_ksg))
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# ╔═╡ 29458d07-b2b2-49af-a696-d0cb0ad35481
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md"Show that the overhead in the MIS size is correct"
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# ╔═╡ fa4888b2-fc67-4285-8305-da655c42a898
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md"Verify the result:"
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# ╔═╡ e84102e8-d3f2-4f91-87be-dba8e81462fb
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# the extracted solution is an independent set
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UnitDiskMapping.is_independent_set(g5, mis_g5)
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# ╔═╡ 88ec52b3-73fd-4853-a69b-442f5fd2e8f7
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# and its size is maximized
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count(isone, mis_g5)
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# ╔═╡ 5621bb2a-b1c6-4f0d-921e-980b2ce849d5
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solve(IndependentSet(g5), SizeMax())[].n
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# ╔═╡ 1fe6c679-2962-4c1b-8b12-4ceb77ed9e0f
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md"""
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## Example 2: The Petersen graph
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We just quickly go through a second example, the Petersen graph.
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"""
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# ╔═╡ ea379863-95dd-46dd-a0a3-0a564904476a
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petersen = smallgraph(:petersen)
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# ╔═╡ d405e7ec-50e3-446c-8d19-18f1a66c1e3b
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show_graph(petersen)
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# ╔═╡ 409b03d1-384b-48d3-9010-8079cbf66dbf
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md"We first map it to a grid graph (unweighted)."
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# ╔═╡ a0e7da6b-3b71-43d4-a1da-f1bd953e4b50
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petersen_res = UnitDiskMapping.map_graph(petersen)
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# ╔═╡ 4f1f0ca0-dd2a-4768-9b4e-80813c9bb544
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md"The MIS size of the petersen graph is 4."
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# ╔═╡ bf97a268-cd96-4dbc-83c6-10eb1b03ddcc
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missize_petersen = solve(IndependentSet(petersen), SizeMax())[]
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# ╔═╡ 2589f112-5de5-4c98-bcd1-138b6143cd30
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md" The MIS size of the mapped KSG graph is much larger"
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# ╔═╡ 1b946455-b152-4d6f-9968-7dc6e22d171a
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missize_petersen_ksg = solve(IndependentSet(SimpleGraph(petersen_res.grid_graph)), SizeMax())[]
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# ╔═╡ 4e7f7d9e-fae4-46d2-b95d-110d36b691d9
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md"The difference in the MIS size is:"
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# ╔═╡ d0e49c1f-457d-4b61-ad0e-347afb029114
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petersen_res.mis_overhead
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# ╔═╡ 03d8adb3-0bf4-44e6-9b0a-fffc90410cfc
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md"Find an MIS of the mapped KSG and map it back an MIS on the source graph."
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# ╔═╡ 0d08cb1a-f7f3-4d63-bd70-78103db086b3
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mis_petersen_ksg = solve(IndependentSet(SimpleGraph(petersen_res.grid_graph)), SingleConfigMax())[].c.data
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# ╔═╡ c27d8aed-c81f-4eb7-85bf-a4ed88c2537f
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mis_petersen = UnitDiskMapping.map_config_back(petersen_res, collect(mis_petersen_ksg))
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# ╔═╡ 20f81eef-12d3-4f2a-9b91-ccf2705685ad
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md"""The obtained solution is an independent set and its size is maximized."""
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# ╔═╡ 0297893c-c978-4818-aae8-26e60d8c9e9e
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UnitDiskMapping.is_independent_set(petersen, mis_petersen)
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# ╔═╡ 5ffe0e4f-bd2c-4d3e-98ca-61673a7e5230
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count(isone, mis_petersen)
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# ╔═╡ 8c1d46e8-dc36-41bd-9d9b-5a72c380ef26
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md"The number printed should be consistent with the MIS size of the petersen graph."
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# ╔═╡ Cell order:
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