TropicalTensors

Solving spinglass ground state with Yao. It contains

• Spinglass solvers for three predefined lattices,including
  • square lattice,
  • cylinder lattice,
  • chimera lattice,
  • second-nearest neighor coupled square lattice.
• GPU backend,
• Forward mode automatic differentiation and reversible programming automatic differention to find the optimal configuration,
• A visualization toolkit.

To Start

Type ] in Julia REPL to enter pkg mode and

pkg> add https://github.com/TensorBFS/TropicalTensors.jl.git#master
pkg> add CuYao

The last line is required only when you use GPU for computing.

Notebooks

Then open the notebook in a Julia REPL with

julia> using TropicalTensors, Pluto

julia> TropicalTensors.notebook("spinglass") # solving square lattice Ising spinglass with the quantum circuit simulator

julia> TropicalTensors.notebook("ising_and_2sat")  # solving Ising spinglass and 2-SAT counting on a 3-regular graph by tensor network contraction

Gists

For someone who are interested in the implementation, we provide a minimum implementation (~50 lines) of tropical circuit based spinglass solver about

1. Finding maximum energy

https://gist.github.com/GiggleLiu/db9efa143aefbbe1d542e7b78d3a65bc

2. Counting degeneracy

https://gist.github.com/wangleiphy/ef1f616f26ab37ef7fd3d329f2a5be0e

Examples

First we define the lattice and coupling.

julia> using TropicalTensors

julia> lt = SquareLattice(10, 8);

julia> Js = rand([-1,1], length(sgbonds(lt)));

julia> hs = zeros(Int, length(sgvertices(lt)));

julia> sg = Spinglass(lt, Js, hs);

Similarly, we can the problem on lattices like

• ChimeraLattice(4, 4)
• Cylinder(10, 8)
• rand_maskedsquare(8, 10, 0.8).

One can visualize the lattice by dumping it to an svg file

julia> using Compose, Viznet

julia> Compose.set_default_graphic_size(12cm, 12cm)

julia> showlattice(lt) |> SVG("_output.svg")
false

You will see the following graph

If it errors, please install required visualization tools with pkg> add Viznet Compose.

Case 1: Computing the maximum energy

julia> solve(sg; usecuda=false)
Layer 1/10
Layer 2/10
Layer 3/10
Layer 4/10
Layer 5/10
Layer 6/10
Layer 7/10
Layer 8/10
Layer 9/10
Layer 10/10
Tropical(106)

Case 2: Computing the energy degeneracy

julia> solve(CountingTropical{Int,Int}, sg; usecuda=false)
Layer 1/10
Layer 2/10
Layer 3/10
Layer 4/10
Layer 5/10
Layer 6/10
Layer 7/10
Layer 8/10
Layer 9/10
Layer 10/10
CountingTropical{Int64,Int64}(106, 1504)

Case 3: Computing the optimal spin configuration with ForwardDiff and CUDA

julia> using ForwardDiff, CUDA

julia> ForwardDiff.gradient(hs) do x
           sg = Spinglass(lt, eltype(x).(Js), x)
           solve(sg; usecuda=true).n
       end
Layer 1/10, stack size: 0 & 0
Layer 2/10, stack size: 0 & 0
Layer 3/10, stack size: 0 & 1
...
  1
 -1
 -1
  1
 -1
  1
 -1
  1
 -1

Case 4: Computing the optimal spin configuration with NiLang

julia> using TropicalTensors.Reversible: opt_config

julia> cfg = opt_config(sg);
Layer 1/10, stack size: 0 & 0
Layer 2/10, stack size: 0 & 0
Layer 3/10, stack size: 0 & 1
Layer 4/10, stack size: 0 & 2
Layer 5/10, stack size: 0 & 3
Layer 6/10, stack size: 0 & 4
Layer 7/10, stack size: 0 & 5
Layer 8/10, stack size: 0 & 6
Layer 9/10, stack size: 0 & 7
Layer 10/10, stack size: 0 & 8
Layer 10/10, stack size: 0 & 8
Layer 9/10, stack size: 0 & 7
Layer 8/10, stack size: 0 & 6
Layer 7/10, stack size: 0 & 5
Layer 6/10, stack size: 0 & 4
Layer 5/10, stack size: 0 & 3
Layer 4/10, stack size: 0 & 2
Layer 3/10, stack size: 0 & 1
Layer 2/10, stack size: 0 & 0
Layer 1/10, stack size: 0 & 0

julia> vizoptconfig(cfg) |> SVG("_optconfig.svg")

You will see the following graph