Improve the speed of the Matrix Product States simulator

[aromanro]

There are various ways of doing so... a straightforward one would be to parallelize some of the computations with open mp.
There are also ways of optimizing the execution of some gates.

qiskit aer does it, they have a tensor class oriented towards qubits computations (it holds internally matrices and execution of many operations is optimized), this implementation is more generic and uses Eigen tensors (with suboptimal data copying between matrices and tensors back and forth).

I probably won't go that path, unless really necessary.

[aromanro]

The copying between tensors and matrices could be improved using 'slice' and/or 'chip'.

[aromanro]

For tensor->matrix conversion, here is a way: https://stackoverflow.com/questions/48795789/eigen-unsupported-tensor-to-eigen-matrix

[aromanro]

TensorMap could be used in a less generic way than used in the link above, if needed.

[aromanro]

Another thing that could be used to improve the speed: use multithreading. Eigen tensors have support for 'thread pools', for example one can do a contraction using multiple threads. See Eigen::ThreadPool and Eigen::ThreadPoolDevice for details.