Everybody is welcome to contribute to this list, such as to extend/correct/clarify it.
- Entanglement as a way to understand quantum systems
- How useful is entanglement in classifying quantum states?
- Is entanglement more useful than correlation functions in understanding quantum systems?
- Is there a sharper measure than the entanglement entropy to
- characterize the "complexity" of a problem
- characterize the computational cost associated with finding the ground state
- Is there an entanglement measure that would indicate whether a system has a sign-problem in QMC?
(There will be no general answer to this, but has anyone thought about this connection?)
- Can we think of tensor network states as a new representation of quantum mechanics?
- Given the ground state wave-function of a chiral topologically ordered state (such as a Fractional Quantum Hall state), how much information about the phase of matter (such as it's excitations, fusion rules, braiding etc.) can one extract from the entanglement spectrum of this wave-function?
- Is the AdS/CFT - MERA correspondence just analogy? Or speculation? Or is there any quantitative relationship? What does the network mean in terms of AdS?
- Tensor networks states and algorithms
- Which problems have been solved / are within reach to be solved using tensor network algorithms?
- Which open problems are best solved with QMC versus DMRG versus PEPS versus MERA (etc)?
- What interesting problems seem to be "ripe" for our current techniques?
- What interesting problems seem too hard for the current techniques?
- Can we directly represent any arbitrary continuous system with tensor network-like states?
- What are the current capabilities of dynamical methods for (1) spectral functions and related equilibrium quantities;
(2) non-equilibrium systems?
- Is there any relation between the sign problem and difficulty of simulating with a tensor network state?
- Why and how do PEPS/MERA favor ground states with low entanglement? Does that mean that if one state has slightly lower energy than the other one but significantly higher entanglement (but still area law), I would obtain the latter one as my final variationally optimized answer (at least for a range of bond dimensions)?
- What is the exact correspondence between PEPS and slave-particle construction of topologically ordered states? Can one read off the full PSG from a PEPS wave-function?
- What is the connection, if any, between MPS/PEPS and slave-particle (Gutzwiller) constructions of gapless quantum states?
- Is MERA optimal? In other words, can MERA represent any quantum state that can be represented by others with the same network structure and dimension but without isometricity?
- Is tensor optimization for a given network structure a fundamental problem from computational point of view? NP-hard? When is it? Always? Never?