Matrix product state representation

[i2000s]

It would be good to have the MPS fully covered in our code library. Currently, MPS has become an important representation to efficiently represent many-body states and tensor networks. Since my research marginally reaches some one-dimensional spin chain cases and there have been massive progress and on-going discussions on high dimensional many-body systems, I will only be able to provide some limited and biased references and software packages here and let the community contribute more valuable resources. I have got very helpful suggestions from Dr. Lincoln Carr of the Colorado School of Mines and Gopikrishnan Muraleedharan at CQuIC. Feel free to start thinking of implementing those ideas and suggest more references. We will commit this to the Roadmap document for future developers once this thread of discussion has a good shape.

_Limited References_:
[1] G. Vidal, "Efficient classical simulation of slightly entangled quantum computations," Phys. Rev. Lett. 91, 147902 (2003). arXiv version
[2] G. Vidal, "Efficient simulation of one-dimensional quantum many-body systems," Phys. Rev. Lett. 93, 040502 (2004). arXiv version
[3] G. Vidal, "Classical simulation of infinite-size quantum lattice systems in one spatial dimension", Phys. Rev. Lett. 98, 070201 (2007). arXiv version
[4] Ryan V. Mishmash, Quantum many-body dynamics of ultracold Bosons in one-dimensional optical lattices: theoretical aspects, simulation methods and soliton formation and stability, PhD thesis, Colorado
School of Mines. See also M.L Wall and L. D. Carr, New J. Phys. 14, 125015 (2012) (arXiv version here).

Refs. [1-3] mainly focus on 1D spin chain cases and an algorithm to calculate the coefficients of the MPS from symmetric spin chains. Ref. [4] is Ryan's thesis advised by Lincoln Carr. It has theory and algorithms to simulate some phase transition problems with some Matlab and Fortran codes. The open MPS and TEBD packages are developed by that group with their related publications.

_Limited Open-source Packages_
[1] Open Source Matrix Product State (MPS) Simulations -- Numerical routines for variational matrix product state simulations. In Fortran and Python.
[2] Time-Evolving Block Decimation (TEBD) Simulations (Deprecated) -- TEBD simulates the dynamics of entangled quantum many-body systems. In Fortran.

Comments are welcome, indeed invited, along the line.

Thanks,
Qi

[Jutho]

I could certainly provide more background on MPS, which is my day to day research. I do have a julia implementation of MPS simulations (both for ground state optimization and for time evolution) lying around, but I would really need to update it to make it work in julia v0.4 / v0.5 and to disentangle it from the whole code structure that I wast trying to build around it. I hope to find some time at some point to build a good julia MPS implementation in the future, but it certainly won't be before summer.

[i2000s]

@Jutho Thanks for this offer :) I think it is also a good time to integrate your TensorOperations.jl project into the org's ecosystem as well. Our new friend @ntezak is indeed very interested in this effort. @amitjamadagni and others could also be helpful to work on this while the base project is going a little bit deeper.