README.md

TCIITensorConversion

This package provides conversions between TensorTrain objects in TensorCrossInterpolation.jl and MPS/MPO objects in ITensors.jl.

Usage

From TCI2 to TT and ITensors.MPS

We first construct a TCI2 object:

import QuanticsGrids as QG
using QuanticsTCI: quanticscrossinterpolate

B = 2^(-30) # global variable
function f(x)
    return cos(x/B) * cos(x/(4*sqrt(5)*B)) * exp(-x^2) + 2 * exp(-x)
end

R = 40 # number of bits
xmin = 0.0
xmax = 3.0
qgrid = QG.DiscretizedGrid{1}(R, xmin, xmax; includeendpoint=false)
ci, ranks, errors = quanticscrossinterpolate(Float64, f, qgrid; maxbonddim=15)

One can create a tensor train object from the TCI2 object, and then convert it to an ITensor MPS:

import TensorCrossInterpolation as TCI

# Construct a TensorTrain object from the TensorCI2 object
tt = TCI.TensorTrain(ci.tt)

# Convert the TensorTrain object to an ITensor MPS object
using TCIITensorConversion
using ITensors

M = ITensors.MPS(tt)

TT to MPO conversion and back

using ITensors
import TensorCrossInterpolation as TCI
using TCIITensorConversion

tt = TCI.TensorTrain([rand(1, 4, 3, 4), rand(4, 2, 4, 2), rand(2, 5, 1, 7), rand(7, 9, 4, 1)])
mpo = ITensors.MPO(tt)
@assert linkdims(mpo) == [4, 2, 7]
@assert dim.(siteinds(mpo)[1]) == [4, 3]
@assert dim.(siteinds(mpo)[2]) == [2, 4]
@assert dim.(siteinds(mpo)[3]) == [5, 1]
@assert dim.(siteinds(mpo)[4]) == [9, 4]

tt2 = TCI.TensorTrain{Float64, 4}(mpo)
@assert all(tt2[i] == tt[i] for i in 1:length(tt))

sites = reverse.(siteinds(mpo))
ttreverse = TCI.TensorTrain{Float64, 4}(mpo, sites=sites)
@assert all(permutedims(ttreverse[i], [1, 3, 2, 4]) == tt[i] for i in 1:length(tt))