feature: ITensor-based MPS local simulator

[Fe-r-oz]

Resolving Issue #81

Description of changes: Look into ITensor's support for DMRG-based evolution methods to implement tensor network circuit simulation. Users have control over how the simulation is run (e.g. TDVP vs TEBD, maximum bond dimension).

Testing done:
designed a simulate_dmrg wrapper so that we can do something like
result = simulate(simulator, sites, os, method=:DMRG, N=N, sites_type="S=1/2", linkdims=10, nsweeps=2, maxdim=[10, 20], cutoff=1e-8)
I believe this is the right track, but more can be done! I hope it you find it the right track for resoving Issue81

julia> simulator = ITensorSimulator("itensor_backend")

julia> N = 10
10

julia> sites = siteinds("S=1",N);

julia> os = OpSum();

julia> for j=1:N-1
                 os += "Sz",j,"Sz",j+1
                 os += 1/2,"S+",j,"S-",j+1
                 os += 1/2,"S-",j,"S+",j+1
             end

julia> result = simulate(simulator, sites, os, method=:DMRG, N=N, sites_type="S=1/2", linkdims=10, nsweeps=2, maxdim=[10, 20], cutoff=1e-8)
After sweep 1 energy=-12.7987815639034  maxlinkdim=10 maxerr=6.95E-03 time=17.163
After sweep 2 energy=-12.86346578444438  maxlinkdim=20 maxerr=2.74E-06 time=0.043
(-12.86346578444438, MPS
[1] ((dim=3|id=395|"Link,l=1"), (dim=3|id=760|"S=1,Site,n=1"))
[2] ((dim=9|id=210|"Link,l=2"), (dim=3|id=977|"S=1,Site,n=2"), (dim=3|id=395|"Link,l=1"))
[3] ((dim=3|id=476|"S=1,Site,n=3"), (dim=20|id=246|"Link,l=3"), (dim=9|id=210|"Link,l=2"))
[4] ((dim=3|id=22|"S=1,Site,n=4"), (dim=20|id=453|"Link,l=4"), (dim=20|id=246|"Link,l=3"))
[5] ((dim=3|id=292|"S=1,Site,n=5"), (dim=20|id=449|"Link,l=5"), (dim=20|id=453|"Link,l=4"))
[6] ((dim=3|id=22|"S=1,Site,n=6"), (dim=20|id=399|"Link,l=6"), (dim=20|id=449|"Link,l=5"))
[7] ((dim=3|id=377|"S=1,Site,n=7"), (dim=20|id=452|"Link,l=7"), (dim=20|id=399|"Link,l=6"))
[8] ((dim=3|id=130|"S=1,Site,n=8"), (dim=9|id=510|"Link,l=8"), (dim=20|id=452|"Link,l=7"))
[9] ((dim=3|id=392|"S=1,Site,n=9"), (dim=3|id=383|"Link,l=9"), (dim=9|id=510|"Link,l=8"))
[10] ((dim=3|id=904|"S=1,Site,n=10"), (dim=3|id=383|"Link,l=9"))
)

Merge Checklist

Put an x in the boxes that apply. You can also fill these out after creating the PR. If you're unsure about any of them, don't hesitate to ask. We're here to help! This is simply a reminder of what we are going to look for before merging your pull request.

General

• I have read the CONTRIBUTING doc
• I used the commit message format described in CONTRIBUTING
• I have updated any necessary documentation, including READMEs and API docs (if appropriate)

Tests

• I have installed and run git secrets to make sure I did not commit any sensitive information (passwords or credentials)
• I have added tests that prove my fix is effective or that my feature works (if appropriate)
• I have checked that my tests are not configured for a specific region or account (if appropriate)

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.

[Fe-r-oz]

Hi, @kshyatt-aws, I require your input on this. It seems to me that there are two approaches which can be used. By way of PackageExtension, we can make ITensorSimulator a subtype of LocalSimulator (by redefinition) that would allow us to use some of the functionalities like

LocalQuantumTask("dmrg_task", GateModelQuantumTaskResult(energy, psi))

Although GateModelQuantumTaskResult might not be suitable but it conveys the idea that we want to hook the ITensorSimuator to Local Simulator. I used this approach here and locally, and it did work in a sense that by using simulate of ITensorSimulator, it was able to access the methods of LocalSimulator. The other approach is to not make ITensorSimulator a subtype of LocalSimulator.

julia> result = simulate(simulator, sites; method=:DMRG, N=N, sites_type="S=1/2", linkdims=10, nsweeps=2, maxdim=[10, 20], cutoff=1e-8)
After sweep 1 energy=-12.831742146962878  maxlinkdim=10 maxerr=9.24E-03 time=20.468
After sweep 2 energy=-12.886444144050335  maxlinkdim=20 maxerr=6.08E-06 time=0.034
ERROR: MethodError: no method matching Braket.GateModelQuantumTaskResult(::Float64, ::MPS)

Closest candidates are:
  Braket.GateModelQuantumTaskResult(::Any, ::Any, ::Any, ::Any, ::Any, ::Any, ::Any, ::Any, ::Any, ::Any, ::Any, ::Any)
   @ Braket ~/Desktop/New/braket/6/Braket.jl/src/raw_task_result_types.jl:38

We may have to implement methods for LocaQuantumTask that does not require results from the typical Devices. Since LocalSimulator <: Devices, so it seems to me that at the moment, it only takes care of backends that are available on server, not for custom backends like "itensor_backend".

Also, I checked out GPU backends.

using ITensors

i, j, k = Index.((2, 2, 2))
A = random_itensor(i, j)
B = random_itensor(j, k)

# Perform tensor operations on CPU
A * B

###########################################
using CUDA # This will trigger the loading of `NDTensorsCUDAExt` in the background

# Move tensors to NVIDIA GPU
Acu = cu(A)
Bcu = cu(B)

# Perform tensor operations on NVIDIA GPU
Acu * Bcu

###########################################
using Metal # This will trigger the loading of `NDTensorsMetalExt` in the background

# Move tensors to Apple GPU
Amtl = mtl(A)
Bmtl = mtl(B)

# Perform tensor operations on Apple GPU
Amtl * Bmtl

Thanks!

[kshyatt-aws]

I think this needs a lot more development. Ideally the simulator should be able to consume Braket.jl circuits and translate them automatically

[Fe-r-oz]

Thanks for your comments!

[Fe-r-oz]

I don't understand what consume Braket.jl circuit and translate means. Kindly please provide some reference and a bit more context about it.

I checked the documentation but I didn't find anything related it. It might be straightforward but I am missing some points.

[Fe-r-oz]

Hi, I asked main dev from ITensor.jl since PastaQ.jl has implemented wrapper around ITensorMPS.jl: GTorlai/PastaQ.jl#312. This provides me with some pointers!

[Fe-r-oz]

@kshyatt-aws, they extended the deadline to 26th June! I would be delighted to dedicate this week to pursue this PR!

Kindly please provide further details about

Ideally the simulator should be able to consume Braket.jl circuits and translate them automatically"

I am having trouble understanding this part 🙏🏼 . I don't know what consume and translate mean in this context. Please provide further clarification and some starting point for guidance. Thanks! 🙏🏼